
==== Front
Nat Chem
Nat Chem
Nature Chemistry
1755-4330
1755-4349
Nature Publishing Group UK London

38858517
1549
10.1038/s41557-024-01549-2
Article
Harnessing Maxwell’s demon to establish a macroscale concentration gradient
http://orcid.org/0000-0002-6281-3774
Pruchyathamkorn Jiratheep 1
Nguyen Bao-Nguyen T. 1
Grommet Angela B. 1
http://orcid.org/0009-0008-2570-924X
Novoveska Miroslava 1
http://orcid.org/0000-0002-6917-3685
Ronson Tanya K. 1
http://orcid.org/0000-0002-2422-8478
Thoburn John D. 2
http://orcid.org/0000-0002-4060-5122
Nitschke Jonathan R. jrn34@cam.ac.uk

1
1 https://ror.org/013meh722 grid.5335.0 0000 0001 2188 5934 Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, UK
2 grid.262455.2 0000 0001 2205 6070 Department of Chemistry, Randolph-Macon College, Ashland, VA USA
10 6 2024
10 6 2024
2024
16 9 15581564
30 10 2023
30 4 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by/4.0/ Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Maxwell’s demon describes a thought experiment in which a ‘demon’ regulates the flow of particles between two adjoining spaces, establishing a potential gradient without appearing to do work. This seeming paradox led to the understanding that sorting entails thermodynamic work, a foundational concept of information theory. In the past centuries, many systems analogous to Maxwell’s demon have been introduced in the form of molecular information, molecular pumps and ratchets. Here we report a functional example of a Maxwell’s demon that pumps material over centimetres, whereas previous examples operated on a molecular scale. In our system, this demon drives directional transport of o-fluoroazobenzene between the arms of a U-tube apparatus upon light irradiation, transiting through an aqueous membrane containing a coordination cage. The concentration gradient thus obtained is further harnessed to drive naphthalene transport in the opposite direction.

In the original Maxwell’s demon thought experiment, a potential gradient of particles between two neighbouring compartments is created without the apparent use of work. Now a functional example of this experiment where material is pumped over centimetres has been reported—o-fluoroazobenzene is transported unidirectionally under light stimulation between two arms of a U-tube across an aqueous layer containing coordination cages.

Subject terms

Molecular capsules
Coordination chemistry
issue-copyright-statement© Springer Nature Limited 2024
==== Body
pmcMain

In 1867, James Clerk Maxwell described a thought experiment that probed the limits of the second law of thermodynamics: a ‘demon’ gates the passage of particles between two neighbouring compartments, creating a potential gradient without appearing to do work. In the original thought experiment, two isolated compartments contain gas molecules at equal temperatures (or pressure) and are connected by a molecule-sized gate1–5. An active agent—the demon—selectively opens and closes the gate to partition hot and cold (or high velocity and low velocity) gas molecules into separate compartments. The demon thereby decreases the overall entropy of the system, creating a gradient that represents a source of potential energy. If the gate is frictionless, the demon appears to perform no work during this process—therein lies the paradox. A century later, Szilard developed a variation of Maxwell’s demon whereby a single gas molecule is hypothetically confined within a box and information about the molecule’s location is harnessed to produce work6. This formulation created a connection between Maxwell’s demon and information theory, allowing information to be considered as a physical property. The physicality of storage media thus implies that information must also obey the laws of thermodynamics as it is stored, transmitted and processed7–9. A demon must pay a thermodynamic cost to obtain information about individual molecules, thereby offsetting the reduction in entropy when creating a temperature gradient across the system. Furthermore, a physical demon’s capacity for remembering information about individual molecules must necessarily be finite; in forgetting this information to sort a new collection of molecules, heat must be dissipated.

Experimental analogues of Maxwell’s demon and molecular pumps have been developed10–33. A rotaxane-based molecular information ratchet, realized by David Leigh’s team, was arguably the first physical manifestation of a Maxwell’s demon. In Leigh’s system, a photoresponsive gate is positioned asymmetrically on the axle of a rotaxane, creating two neighbouring ‘compartments’ on either end29. Upon light irradiation, information regarding the proximity of the macrocycle to the gate drives unidirectional movement of the macrocycle across the axle. Whereas Leigh’s demon operates on a molecular scale, Raizen et al. demonstrated a similar principle within a system composed of many atoms, which reside in a potential well created by a magnet34, where a one-way gate composed of two optical beams plays the role of the demon, driving unidirectional movement of particles over an optical barrier and into a higher-energy compartment.

In this Article, we report a sorting system that drives the formation of an o-fluoroazobenzene (FAB) concentration gradient on the macroscale, across centimetres. As in Maxwell’s thought experiment, our system is composed of two neighbouring compartments, consisting of two layers of dodecane solvent in two arms of a U-tube apparatus (Fig. 1). Coordination cage 1 (Fig. 1a) functions as a molecule-sized, demon-attended gate. We also explore the addition of the competing guest naphthalene to push the system further out of equilibrium (Fig. 1b) and the use of our demon as a pump to create a naphthalene concentration gradient (Fig. 1c), as discussed below.Fig. 1 Illustration of experimental setup of the three directional transport systems.

a, The structure of cage 1, showing one of the six ligands that form the edges of the tetrahedron. b, Structures and corresponding symbols for trans-FAB, cis-FAB and naphthalene. Trans-FAB isomerizes to cis-FAB upon irradiation at 530 nm, while the reverse process occurs at 400 nm. c–e, Illustrations of the experimental U-tube configurations discussed later. System 1 relies on differential transport rates between the two FAB isomers to push the system away from equilibrium (c). System 2 couples an additional potential energy gradient, the presence of naphthalene in arm II, to drive the system further away from equilibrium (d). System 3 couples the establishment of a gradient of FAB across the membrane to the counterflow of naphthalene, driving the distribution of naphthalene out of equilibrium (e). Further experimental details can be found in Methods. Blue circles, trans-FAB; green asterisks, cis-FAB; orange squares, naphthalene; green-covered region indicates the tube area exposed to light at 530 nm; purple-covered region indicates the tube area exposed to light at 400 nm.

Results and discussion

Maxwell’s demon creates a concentration gradient

The two compartments within our system are separated by a bulk aqueous membrane containing FeII4L6 coordination cage 1, which transports a molecular cargo, the photoresponsive molecule FAB, between the two arms35. Crucially, cis-FAB has a higher affinity for cage 1 than trans-FAB, as indicated by the displacement of trans-FAB by cis-FAB from the cage cavity (Extended Data Fig. 1). In the system’s initial state, FAB is distributed equally between the dodecane solutions in the two arms. Upon irradiation of arm I at 530 nm, trans-FAB isomerizes to cis-FAB, which is preferentially extracted from arm I by cage 1, transported through the aqueous layer and released into arm II. Subsequent re-isomerization of cis-FAB to trans-FAB—promoted by irradiation of the second compartment at 400 nm—impedes the molecule from returning to arm I. As the FAB molecules are directionally transported between the two arms, the system is driven away from equilibrium.

Our system was prepared by adding an aqueous solution of cage 1 (4 mM, 2.5 ml, 25 mol% relative to the total FAB in both arms) into the bottom of a glass U-tube (internal diameter 1.2 cm), and aliquots of a dodecane solution containing FAB (10 mM, 2 ml, 90% trans) into each arm. To monitor the concentration of FAB isomers in each arm, samples of each dodecane solution (0.3 ml) were withdrawn periodically for 1H nuclear magnetic resonance (NMR) analysis. The aqueous solution of cage 1 was stirred at room temperature for the duration of the experiment, while the dodecane layers were not. Following irradiation of arm I with light at 530 nm, a photostationary state containing 94% of cis-FAB was obtained. Arm II was simultaneously irradiated with 400 nm light, resulting in a photostationary state containing 92% trans-FAB (Supplementary Section 2).

At the start of the experiment, FAB was encapsulated by cage 1, resulting in lower FAB concentration in both arms (Supplementary Section 7). After 10 days of continuous irradiation, a decrease in the total concentration of FAB was observed in arm I, together with an increase in arm II. No further changes in the sum of FAB isomer concentration between arms I (8 mM, 40%) and II (11 mM, 54%) were observed after 20 days, thus establishing a steady-state concentration gradient on the macroscale (Fig. 2). This process was also followed by ultraviolet–visible spectroscopy (UV–vis), confirming conclusions drawn based on NMR data (Supplementary Fig. 15). To confirm the net transport of FAB from arm I to arm II, a control experiment (Supplementary Section 14) was conducted. Two vertical tubes were set up, each analogous to the initial setup of arm I (Tube 1) and arm II (Tube 2), without the presence of the dodecane solution from the other arm. After irradiation, the decrease in the total concentration of FAB in tube 1 (1 mM, Supplementary Fig. 36), solely due to the effect of FAB sequestered within cage 1 in the aqueous layer, was less than that of arm I in system 1 (2 mM). This suggests that the increase in FAB concentration in arm II of the system was the result of the mass transport of FAB from arm I.Fig. 2 Statewise illustration and summary of results from the directional transport of FAB in system 1.

a, U-tube configuration illustrating the distribution of cis-FAB (green asterisks) and trans-FAB (blue dots) between the two arms in system 1. b, Distribution plots of FAB concentration in arms I and II, illustrating the shifts in concentration away from the initial equilibrium state. c, Cartoon representation of the Maxwell’s demon system, showing how the demon gauges which FAB molecules to allow across the gate, resulting in the establishment of a FAB concentration gradient. d, Sum of trans- and cis-FAB concentrations in arm I (grey) and arm II (black) during initial forward transport and its subsequent reversal at day 24, with dots surrounded by error bars representing concentrations measured by 1H NMR, and solid lines showing the predictions of our model (Supplementary Section 10). The distinct stages studied are labelled i–v atop a; these stages are also shown in b and c stacked below the cartoons shown in a and in the time course shown in d. i, the initial equilibrium state of the experiment; ii, shortly after starting forward transport; iii, at the steady state of forward transport (day 24); iv, shortly after reversing the transport direction by changing which arm was illuminated by which wavelength of light and v, at the steady state of reverse transport (day 44). e, Our kinetic model of the system, with rate constants kC and kT for the uptake of cis-FAB and trans-FAB, respectively, by aqueous cage 1 from an organic phase; k−C and k−T, the corresponding release rate constants for cis-FAB and trans-FAB, respectively, from 1; kiCT(I) and kiTC(I) for the isomerization in arm I from cis- to trans-FAB, and trans- to cis-FAB, respectively; and kiCT(II) and kiTC(II) for the isomerization in arm II from cis- to trans-FAB, and trans- to cis-FAB, respectively. Data in d are presented as mean values ± measurement errors, derived from error propagation of the standard deviation and the signal-to-noise ratio (n = 22) of coronene (Supplementary Section 5). aq, aqueous.

In the initial state of the system, each FAB molecule has an equal probability of residing in either dodecane compartment, corresponding to a state with high entropy (Fig. 2a–d, stage i). Light energy provided into the system promotes FAB isomerization from trans to cis in arm I, and cis to trans in arm II, thus driving preferential FAB transport through the gate in one direction (Fig. 2a–d, stage ii). As cis-FAB is transported more rapidly than the trans isomer (Supplementary Fig. 13), the overall FAB concentration decreases in arm I and increases in arm II. After crossing through the gate from arm I to arm II, cis-FAB transforms back into trans-FAB, a process corresponding to the demon ‘forgetting’ the position of the molecule as heat is released back into the system (Fig. 2a–d, stage iii). Light energy thus drives information processing to establish a concentration gradient between the two dodecane compartments, with no violation of the second law of thermodynamics.

Reversal of the stimuli applied to the two arms resulted in a reversal of the direction of FAB transport. After 24 days, arm I was irradiated at 400 nm to promote the relaxation of cis- to trans-FAB, and arm II was irradiated at 530 nm to isomerize trans- to cis-FAB (Fig. 2a–d, stage iv). This reverse transport of FAB was again observed to reach a steady state after 12 days, where the distribution of FAB between arm I (11 mM, 54%) and arm II (8 mM, 40%) mirrored its distribution following forward transport (Fig. 2a–d, stage v).

Kinetic study and modelling

To investigate the kinetics of FAB transport, we developed a kinetic model (Fig. 2e) that considers the uptake and release of cis- and trans-FAB at the interfaces between the dodecane and aqueous layers, alongside the isomerization reactions between the two FAB isomers in each arm (Supplementary Section 10). The experimental data were least-squares fitted to our model (Fig. 2d), as described in Supplementary Section 10. The cis–trans and trans–cis isomerization rate constants in arms I and II (kiCT(I) = 112.7 day−1, kiTC(I) = 1,750 day−1, kiCT(II) = 5,028 day−1 and kiTC(II) = 437.2 day−1 during forward transport) were determined in separate experiments using NMR measurements to track the changes in FAB concentrations under irradiation at both 400 and 530 nm (Supplementary Section 2). The model gave the uptake and release rate constants for cis-FAB of kC = 0.42 mM−1 day−1 and k−C = 1.69 day−1, and for trans-FAB, kT = 0.29 mM−1 day−1 and k−T = 1.23 day−1, respectively.

These rate constants indicate that the rate of cis-FAB uptake by cage 1 is higher than for trans-FAB. The uptake of cis-FAB from arm I is thus faster than that of trans-FAB from arm II at the beginning of the experiment (Extended Data Fig. 2). Cage 1 thus transports cis-FAB from arm I and releases it to arm II. Since the isomerization rate constant of cis- to trans-FAB is also three orders of magnitude greater than the cis-FAB uptake rate constant, cis-FAB relaxes to trans-FAB quickly due to irradiation at 400 nm after it is released into arm II during the forward transport, resulting in the accumulation of trans-FAB in arm II, as observed experimentally.

Furthermore, we hypothesized that the release of a guest bound within 1 would be facilitated by competitive displacement. When cis-FAB is transported from arm I to arm II in isolation, the driving force for cargo egress would thus be smaller than in the presence of trans-FAB in arm II (Supplementary Section 13), where egress of cis-FAB may be facilitated by competitive displacement by trans-FAB, and vice versa. This rationale implies a limit to the degree to which this system may be driven out of equilibrium, as the transport of cis-FAB from arm I to II is partly offset by reverse transport of trans-FAB from arm II to I.

The presence of naphthalene

As in Maxwell’s original thought experiment, our initial system is driven out of equilibrium solely upon inputting light energy. If the egress of cis-FAB into arm II is facilitated by competitive displacement, however, the limits of this experimental setup could be overcome by adding a competing guest to arm II, thereby creating an even larger FAB concentration gradient. We selected naphthalene as this competing guest, which binds more strongly to cage 1 than either trans- or cis-FAB (Extended Data Fig. 1)36.

Using a U-tube apparatus analogous to those described previously, system 2 (Fig. 1d) was set up, in which a solution of trans-FAB (10 mM) in dodecane was loaded into arm I, and naphthalene (11 mM) was loaded together with trans-FAB (10 mM) into arm II. Arms I and II were continuously irradiated with light at 530 nm and 400 nm, respectively. As we hypothesized, the rate of cis-FAB egress into arm II increased in the presence of naphthalene (Supplementary Section 8). Furthermore, the net transport of FAB to arm II was accompanied by a net transport of naphthalene to arm I. The redistribution of both species plateaued after 20 days (Fig. 3a–d). The final overall concentrations of FAB in arms I and II were 7.3 mM (36%) and 13 mM (64%), respectively, and the final concentrations of naphthalene in arms I and II were 5.4 mM (48%) and 4.7 mM (42%), respectively.Fig. 3 Naphthalene and FAB distributions in two arms of the U-tubes in systems 2 and 3.

a,e, Concentration of FAB measured by 1H NMR in arm I (grey dots) and arm II (black dots) in system 2 (a) and system 3 (e) during initial forward transport and its reversal at day 21. b,f, Distribution charts of FAB concentration in arm I (grey bars) and arm II (black bars) in system 2 (b) and system 3 (f) at the end of the forward (day 20) and reverse (day 45) processes, illustrating the shifts in concentration away from the initial equilibria in systems 2 and 3. c,g, Concentration of naphthalene measured by 1H NMR in arm I (light orange dots) and arm II (dark orange dots) in system 2 (c) and system 3 (g) during forward and reverse transport for systems 2 and 3. d,h, Distribution charts of naphthalene concentration in arm I (light orange bars) and arm II (dark orange bars) in system 2 (d) and system 3 (h) at the end of the forward (day 20) and reverse (day 45) process, illustrating the shifts in concentration away from the initial equilibrium in systems 2 and 3. Data are presented as mean values ± measurement errors, derived from error propagation of the standard deviation and the signal-to-noise ratio (n = 22) of coronene (Supplementary Section 5).

Notably, in naphthalene-containing system 2, the difference in the overall concentration of FAB between arms I and II was 6 mM, greater than the difference (3 mM) in system 1, where naphthalene was absent. Furthermore, the sum of the concentrations of FAB in arms I and II is higher in the presence (20 mM) than in the absence (19 mM) of naphthalene (Supplementary Fig. 16), leading us to infer that the introduction of naphthalene in arm II not only drove redistribution of FAB but also reduced the amount of FAB stored within the aqueous membrane. In this system, the driving force supplied by information collected by the demon is supplemented by an additional source of energy: the potential energy associated with applying a concentration gradient of naphthalene across the two arms. The thermodynamic cost associated with pushing the FAB concentration gradient further from equilibrium is thus paid using a corresponding increase in the entropy of the competing cargo, naphthalene.

As with system 1, we sought to reverse the direction of FAB transport by reversing the light stimuli applied to arms I and II, monitoring the process using 1H NMR (Fig. 3a) and UV–vis (Supplementary Fig. 18). The final difference in FAB concentration between arms I and II (1 mM), was less than for the forward process, an effect that we attribute to the varying distribution of naphthalene over the course of the experiment. While the forward process began with naphthalene present solely in arm II, the reverse process began with naphthalene distributed almost equally between the arms (arms I and II contain 5.4 mM and 4.7 mM of naphthalene, respectively). Unlike the forward process, wherein the potential energy associated with the naphthalene concentration gradient drove the system further out of the initial equilibrium, the reverse process lacks that initial source of potential energy and relies primarily on the cis-FAB concentration gradient supplied by the demon.

Using our kinetic model to predict the behaviour of system 2, we initially assumed that naphthalene impacts the system by reducing the number of available cages for FAB transport, reducing the available concentration of cage 1 by a factor of a. Thus, only a·[cage 1]initial of cage 1 was considered to be active, where 0 ≤ a ≤ 1. The resulting model predicted a larger FAB concentration difference between the two arms for lower a at the steady state (Supplementary Section 11), which agrees with our findings for forward transport (Fig. 3a). A reduced rate of FAB transport in the reverse process was observed as more naphthalene was encapsulated in the cage. Experimental configurations with the same total amounts of naphthalene should thus have the same a values, thus leading to the same FAB concentration differences at a steady state. The model was further refined by considering naphthalene transport over time and the competitive displacement mechanism (Supplementary Figs. 29–32), which provides insight into naphthalene transport and the difference in naphthalene concentration at the end of the forward and the reverse transport of system 2 (Fig. 3d).

On the basis of this prediction, we then investigated system 3 (Fig. 1e), where naphthalene was introduced into both arms of the U-tube, at a concentration (6 mM) such that the total amount of naphthalene was equivalent to the amount used in system 2. The FAB concentration was kept at 10 mM in each arm. We then irradiated arm I with light at 530 nm and arm II with light at 400 nm. In agreement with the prediction of our model, the final distribution of FAB in arms I and II of system 3 was further from equivalence than in the absence of naphthalene in system 1, with the forward and reverse processes plateauing at 33% (6.7 mM) and 55% (11 mM) in arm I, and 53% (11 mM) and 40% (8.1 mM) in arm II, respectively (Fig. 3e,f).

Remarkably, we also observed unequal transport behaviour for naphthalene in system 3 (Fig. 1e). The transport of FAB from arm I to II was accompanied by a disproportionally greater net transport of naphthalene from arm II to arm I. A maximum difference was observed in naphthalene concentration of 52% (6.3 mM) in arm I, and 42% (5.0 mM) in arm II (Fig. 3g,h). A similar, but opposite, concentration difference was observed in the reverse transport of system 3, following inversion of the illumination.

Expanding the analogy between our system and Maxwell’s original thought experiment, this experiment offers an example whereby two different species, A and B, are distributed equally throughout two compartments. Despite the demon being blind to the location of species B, the act of collecting information about species A allows B to be driven out of equilibrium. The coincidence of this transient concentration gradient with the induction period of the system suggests that the molecular gate in our system, that is, cage 1, plays an active role in regulating passage of FAB and naphthalene across the aqueous membrane.

As the experiment began, FAB and naphthalene competed to bind within empty cage 1. The different stimuli applied to arms I and II, however, make the competitive processes at each interface also different. At the water–dodecane interfaces in arms I and II, naphthalene primarily competes with cis-FAB and trans-FAB, respectively. Given that trans-FAB is the least competitive binder among these three species, we expected to observe a greater degree of naphthalene ingress at interface II than at interface I. Likewise, we would expect to observe more naphthalene egress at interface I than at interface II, as naphthalene is competitively displaced by cis-FAB (Supplementary Section 11 and Supplementary Figs. 30–33). Taken together, these two effects explain the rapid increase in the concentration of naphthalene in arm I during the induction period.

Conclusions

Our demon can thus be considered as a simple machine, whereby passage through a gate is regulated by changing the state of a molecule21,24,37–48. This type of demon has been described in terms of an energy ratchet49–51 or, in analogy with a system filled with flying umbrellas, divided into two compartments using a barrier containing evenly spaced bars52. Initially, all of the umbrellas are closed, they are narrow enough to pass between the bars, and thus they distribute themselves equally between the compartments. Upon applying a stimulus to one compartment, its umbrellas pop open, become too large to pass between the bars and begin to accumulate in that compartment, thereby establishing a gradient of umbrellas. Instead of umbrellas, one could also imagine two geometrically dissimilar isomers, whereby one isomer could pass through a molecular gate, while the other would be sterically hindered. Our system relies on differences in binding thermodynamics and kinetics experienced by trans-FAB or cis-FAB and cage 1.

Having established a concentration gradient using our demon, we also introduced a strategy to drive the system further from equilibrium by adding a competitive species, naphthalene, initially into one arm only (Fig. 1, System 2). Significantly, by starting with a system containing naphthalene in both arms, we were able to harness the demon to pump naphthalene selectively from one side to the other. Such light-driven selective pumping of chemical species across a membrane may prove useful in the context of chemical separations, the development of new separations methods having been identified as a key challenge to the decarbonization of the world economy43.

Methods

Cage 1 synthesis

Cage 1 was synthesised using the previously reported protocol53. The scheme for the synthesis of the diamino terphenylene subcomponent is provided in the Supplementary Section 1.

FeSO4 • 7 H2O (22.2 mg, 0.0800 mmol, 4 equiv.), the diamino terphenylene subcomponent (52.9 mg, 0.120 mmol, 6 equiv.) and 2-formylpyridine (22.9 µl, 0.240 mmol, 12 equiv.) were placed in a 20 ml vial in a glovebox. A total of 5.0 ml degassed D2O and 5.0 ml dry CH3CN were added, and the mixture was stirred for 12 h at room temperature. The solvent was then removed at low pressure at 25 °C. The concentrated solution was washed with diethyl ether (5 ml × 3) and dried to yield cage 1 (0.0200 mmol, ca. 100%) as a purple solid. D2O was added quickly to prepare 4.0 mM solution of cage 1 for the experiment. 1H NMR (500 MHz, D2O, 298 K): δ = 8.83 (broad s, 12H, H8), 8.42 (unresolved d, 12H, H10), 8.25 (unresolved dd, 12H, H12), 7.58 (unresolved dd, 12H, H11), 7.25 (unresolved d, 12H, H13), 7.06 (unresolved s, 24H, H5), 6.78 (unresolved s, 12H, H2), 5.39 (broad s, 24H, H6), 3.76 (unresolved s, 24H, H14), 3.60 (unresolved s, 12H, H15) and 3.26 (unresolved s, 24H, H16). See Supplementary Fig. 2 for NMR spectrum and proton assignments.

o-TetraFAB synthesis

FAB was synthesised using an optimized version of a reported protocol54.

The 2,6-difluoroaniline (275 μl, 350 mg, 2.73 mmol, 1 equiv.) and lead (IV) acetate (3.05 g, 6.83 mmol, 2.5 equiv.) were dissolved in CHCl3 (25 ml) and refluxed at 100 °C for 1.5 h followed by overnight stirring at room temperature. The reaction mixture was subsequently filtered through celite. The solvent was then evaporated under dynamic vacuum. The crude product was purified through an SiO2 column (dichloromethane: cyclohexane, solvent ratio 1:3) yielding a bright orange solid (64 mg, 20%), which is a mixture of trans- and cis-tetraFAB (ratio 9:1). 1H NMR (400 MHz, CDCl3, 298 K) δH (ppm) trans-FAB was 7.38 (t, 2H, H1−trans) and 7.07 (t, 4H, H2−trans), and cis-FAB was 7.19 (m, 2H, H1−cis) and 6.85 (m, 4H, H2−cis). 13C{1H} NMR (126 MHz, CDCl3, 298 K) δC (ppm) was 156.55 (C4−trans), 154.41 (C3−trans) and 131.29 (C2−trans), 112.56 (C1-cis). 19F{1H} NMR (471 MHz, CDCl3, 298 K) δF (ppm) was −119.64 (Fcis) and −121.48 (Ftrans). For NMR spectra and assignments, see Supplementary Fig. 3.

Light-gated FAB transport experimental setup and measurements

Each experiment was prepared by adding an aqueous solution of cage 1 (4 mM, 2.5 ml and 25 mol% relative to the total FAB in both arms) into the bottom of the U-tube (internal diameter 1.2 cm). Both arm I and arm II contained FAB (trans/cis mixture ratio 9:1) solutions at an equal concentration of 10 mM in dodecane (2 ml). The solutions contained coronene (0.25 mM) as an internal standard. In addition, arm II contained triisopropylbenzene (10 mM) as an indicator. The role of this indicator is to ensure that no physical mixing of the dodecane solutions occurs between arms I and II, and that the transport phenomenon observed in this study is thus the result of transportation through the cage layer. Triisopropylbenzene was chosen as an indicator for two reasons. First, as triisopropylbenzene was not transported by the cage37, this compound would thus remain in arm II and would not interfere with the guest transport process. Second, triisopropylbenzene solution in dodecane shows an absorption peak in the region 200–250 nm, which does not overlap with the absorption region of trans- and cis-FAB. The cage layer was stirred at 250 rpm at room temperature with a cylindrical magnetic stir bar (3 × 6 mm).

Trans-to-cis-FAB isomerization was promoted using light-emitting diode light strips with a wavelength of 530 nm and with luminous flux of 250 lumen m−1 and power of 2.4 W. The reverse reaction, cis to trans, was promoted when irradiated using light-emitting diode light strips at the wavelength of 400 nm and with luminous flux of 200 lumen m−1 and power of 7.2 W. The light strips were wrapped around the U-tube arms.

Light irradiation in both arms was carried out simultaneously. Arm I was irradiated at 530 nm, expecting trans-to-cis isomerization. Arm II was irradiated at 400 nm promoting cis-to-trans relaxation. The two arms were isolated by a black partition and covered to avoid exposure to external sources of light. The system was flushed continuously with nitrogen gas to maintain the experiment at room temperature. Photos of the setup are provided in Supplementary Section 15 and Supplementary Fig. 37.

During the experiments, NMR and UV–vis measurements were taken regularly; 0.3 ml of solution from each of the dodecane phases (arms I and II) was taken for measurements. Each solution was put into an NMR tube, covered in aluminium foil to avoid external light exposure. NMR measurements were then taken before transferring the solutions into cuvettes for UV–vis measurements. The solutions were then put back into the arm of the U-tube from which they had been taken out. Care was taken to avoid external light during all transfers and measurements, by covering the samples with aluminium foil. The process of removing, measuring and returning the solutions to the U-tubes was carried out in less than 30 min in all cases, to minimize thermal isomerization.

Further details on the NMR and UV–vis spectrometers can be found in Supplementary Information. This general procedure was used for all experiments (systems 1–3) in this study.

Online content

Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at 10.1038/s41557-024-01549-2.

Supplementary information

Supplementary Information Supplementary Text 1–15, Supplementary Figs. 1–37 and Tables 1–8.

Supplementary Data 1 Raw data of the NMR and UV measurements for systems 1, 2 and 3.

Extended data

Extended Data Fig. 1 Naphthalene, trans- and cis-FAB hierarchy of encapsulation by 1 in water.

1H NMR (500 MHz, D2O) monitoring of the relative binding strength of trans- and cis-FAB and naphthalene to cage 1 in water. Trans-FAB was first introduced to the cage solution and guest encapsulation was subsequently observed. Upon cis-FAB addition, the trans-FAB ⊂ 1 signals disappeared while the cis-FAB ⊂ 1 signals were observed. Addition of naphthalene displaced the encapsulated cis-FAB from cage 1. (* = CH3CN reference signal).

Extended Data Fig. 2 Model optimization for System 1.

Concentrations of cis-FAB (green) and trans-FAB (blue) in arm I (hollow dots and dashed line) and arm II (solid dots and solid line) during the forward and reverse transport in System 1, showing experimental results measured by 1H NMR (dots), error bars and model predictions (lines) for each arm. In the forward transport, cis-FAB was observed to flow from arm I to arm II where it was isomerized to trans-FAB. Upon switching the light stimuli in the reverse transport, the flow of cis-FAB was reversed (from arm II to arm I) and the subsequent isomerization to trans-FAB was happening in arm I. These processes caused the shift in the total FAB concentrations. The grey dashed line indicates the point which the LED light strips were swapped, switching from forward to reverse transport.

Extended data

is available for this paper at 10.1038/s41557-024-01549-2.

Supplementary information

The online version contains supplementary material available at 10.1038/s41557-024-01549-2.

Acknowledgements

This study was supported by the European Research Council (695009) and the UK Engineering and Physical Sciences Research Council (EP/P027067/1). J.P. acknowledges the Jardine Foundation and Cambridge Trust for PhD funding. B.N.T.N. acknowledges Agency of Science, Technology and Research, National Science Scholarship, Singapore, for PhD funding.

Author contributions

Experiments, collected and processed data were carried out by J.P., B.N.T.N. and T.K.R. Conceptualization and methodology were carried out by A.B.G., B.N.T.N., J.P. and J.R.N. Mathematics and modelling were performed by J.P., M.N. and J.D.T. Funding acquisition was ascertained by J.R.N. Supervision was performed by J.R.N. Writing—original draft was performed by J.P. and B.N.T.N. Writing—review and editing was carried by J.P., B.N.T.N., A.B.G., M.N., J.D.T. and J.R.N.

Peer review

Peer review information

Nature Chemistry thanks the anonymous reviewers for their contribution to the peer review of this work.

Data availability

All data is available in the main text or the supplementary materials.

Code availability

Mathematica code is available in Supplementary Information.

Competing interests

Authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

These authors contributed equally: Jiratheep Pruchyathamkorn, Bao-Nguyen T. Nguyen.
==== Refs
References

1. Lutz E Ciliberto S Information: from Maxwell’s demon to Landauer’s eraser Phys. Today 2015 68 30 35 10.1063/PT.3.2912
Lutz, E. & Ciliberto, S. Information: from Maxwell’s demon to Landauer’s eraser. Phys. Today 68, 30–35 (2015).10.1063/PT.3.2912
2. Koski JV Maisi VF Sagawa T Pekola JP Experimental observation of the role of mutual information in the nonequilibrium dynamics of a Maxwell demon Phys. Rev. Lett. 2014 113 030601 10.1103/PhysRevLett.113.030601 25083623
Koski, J. V., Maisi, V. F., Sagawa, T. & Pekola, J. P. Experimental observation of the role of mutual information in the nonequilibrium dynamics of a Maxwell demon. Phys. Rev. Lett. 113, 030601 (2014).25083623 10.1103/PhysRevLett.113.030601
3. Sánchez R Splettstoesser J Whitney RS Nonequilibrium system as a demon Phys. Rev. Lett. 2019 123 216801 10.1103/PhysRevLett.123.216801 31809128
Sánchez, R., Splettstoesser, J. & Whitney, R. S. Nonequilibrium system as a demon. Phys. Rev. Lett. 123, 216801 (2019).31809128 10.1103/PhysRevLett.123.216801
4. Ribezzi-Crivellari M Ritort F Large work extraction and the Landauer limit in a continuous Maxwell demon. Nat. Physics 2019 15 660 664 10.1038/s41567-019-0481-0
Ribezzi-Crivellari, M. & Ritort, F. Large work extraction and the Landauer limit in a continuous Maxwell demon. Nat. Physics 15, 660–664 (2019).10.1038/s41567-019-0481-0
5. Strasberg P Schaller G Brandes T Esposito M Thermodynamics of a physical model implementing a Maxwell demon Phys. Rev. Lett. 2013 110 040601 10.1103/PhysRevLett.110.040601 25166147
Strasberg, P., Schaller, G., Brandes, T. & Esposito, M. Thermodynamics of a physical model implementing a Maxwell demon. Phys. Rev. Lett. 110, 040601 (2013).25166147 10.1103/PhysRevLett.110.040601
6. Sziland L On the decrease of entropy in a thermodynamic system by the intervention of intelligent beings Behav. Sci. 1964 9 301 310 10.1002/bs.3830090402 5888785
Sziland, L. On the decrease of entropy in a thermodynamic system by the intervention of intelligent beings. Behav. Sci. 9, 301–310 (1964).5888785 10.1002/bs.3830090402
7. Parrondo JMR Horowitz JM Sagawa T Thermodynamics of information Nat. Phys. 2015 11 131 139 10.1038/nphys3230
Parrondo, J. M. R., Horowitz, J. M. & Sagawa, T. Thermodynamics of information. Nat. Phys. 11, 131–139 (2015).10.1038/nphys3230
8. Bo S Del Giudice M Celani A Thermodynamic limits to information harvesting by sensory systems J. Stat. Mech. 2015 2015 P01014 10.1088/1742-5468/2015/01/P01014
Bo, S., Del Giudice, M. & Celani, A. Thermodynamic limits to information harvesting by sensory systems. J. Stat. Mech. 2015, P01014 (2015).10.1088/1742-5468/2015/01/P01014
9. Ford IJ Maxwell’s demon and the management of ignorance in stochastic thermodynamics Contemp. Phys. 2016 57 309 330 10.1080/00107514.2015.1121604
Ford, I. J. Maxwell’s demon and the management of ignorance in stochastic thermodynamics. Contemp. Phys. 57, 309–330 (2016).10.1080/00107514.2015.1121604
10. Cottet N Observing a quantum Maxwell demon at work Proc. Natl Acad. Sci. USA 2017 114 7561 7564 10.1073/pnas.1704827114 28674009
Cottet, N. et al. Observing a quantum Maxwell demon at work. Proc. Natl Acad. Sci. USA 114, 7561–7564 (2017).28674009 10.1073/pnas.1704827114
11. Deffner S Information-driven current in a quantum Maxwell demon Phys. Rev. E 2013 88 062128 10.1103/PhysRevE.88.062128
Deffner, S. Information-driven current in a quantum Maxwell demon. Phys. Rev. E 88, 062128 (2013).10.1103/PhysRevE.88.062128
12. Grzybowski BA Fitzner K Paczesny J Granick S From dynamic self-assembly to networked chemical systems Chem. Soc. Rev. 2017 46 5647 5678 10.1039/C7CS00089H 28703815
Grzybowski, B. A., Fitzner, K., Paczesny, J. & Granick, S. From dynamic self-assembly to networked chemical systems. Chem. Soc. Rev. 46, 5647–5678 (2017).28703815 10.1039/C7CS00089H
13. Angulo-Pachón CA Miravet JF Sucrose-fueled, energy dissipative, transient formation of molecular hydrogels mediated by yeast activity Chem. Commun. 2016 52 5398 5401 10.1039/C6CC01183G
Angulo-Pachón, C. A. & Miravet, J. F. Sucrose-fueled, energy dissipative, transient formation of molecular hydrogels mediated by yeast activity. Chem. Commun. 52, 5398–5401 (2016).10.1039/C6CC01183G
14. Schaller G Cerrillo J Engelhardt G Strasberg P Electronic Maxwell demon in the coherent strong-coupling regime Phys. Rev. B 2018 97 195104 10.1103/PhysRevB.97.195104
Schaller, G., Cerrillo, J., Engelhardt, G. & Strasberg, P. Electronic Maxwell demon in the coherent strong-coupling regime. Phys. Rev. B 97, 195104 (2018).10.1103/PhysRevB.97.195104
15. Debnath S Roy S Ulijn RV Peptide nanofibers with dynamic instability through nonequilibrium biocatalytic assembly J. Am. Chem. Soc. 2013 135 16789 16792 10.1021/ja4086353 24147566
Debnath, S., Roy, S. & Ulijn, R. V. Peptide nanofibers with dynamic instability through nonequilibrium biocatalytic assembly. J. Am. Chem. Soc. 135, 16789–16792 (2013).24147566 10.1021/ja4086353
16. Rikken RSM Shaping polymersomes into predictable morphologies via out-of-equilibrium self-assembly Nat. Commun. 2016 7 12606 10.1038/ncomms12606 27558520
Rikken, R. S. M. et al. Shaping polymersomes into predictable morphologies via out-of-equilibrium self-assembly. Nat. Commun. 7, 12606 (2016).27558520 10.1038/ncomms12606
17. Ibukuro F Kusukawa T Fujita M A thermally switchable molecular lock. Guest–template synthesis of a kinetically stable nanosized cage J. Am. Chem. Soc. 1998 120 8561 8562 10.1021/ja980853f
Ibukuro, F., Kusukawa, T. & Fujita, M. A thermally switchable molecular lock. Guest–template synthesis of a kinetically stable nanosized cage. J. Am. Chem. Soc. 120, 8561–8562 (1998).10.1021/ja980853f
18. Hess H Ross JL Non-equilibrium assembly of microtubules: from molecules to autonomous chemical robots Chem. Soc. Rev. 2017 46 5570 5587 10.1039/C7CS00030H 28329028
Hess, H. & Ross, J. L. Non-equilibrium assembly of microtubules: from molecules to autonomous chemical robots. Chem. Soc. Rev. 46, 5570–5587 (2017).28329028 10.1039/C7CS00030H
19. Aranson IS Collective behavior in out-of-equilibrium colloidal suspensions C.R. Phys. 2013 14 518 527 10.1016/j.crhy.2013.05.002
Aranson, I. S. Collective behavior in out-of-equilibrium colloidal suspensions. C.R. Phys. 14, 518–527 (2013).10.1016/j.crhy.2013.05.002
20. Borsley S Electrostatic forces in field-perturbed equilibria: nanopore analysis of cage complexes Chem 2019 5 1275 1292 10.1016/j.chempr.2019.03.004
Borsley, S. et al. Electrostatic forces in field-perturbed equilibria: nanopore analysis of cage complexes. Chem 5, 1275–1292 (2019).10.1016/j.chempr.2019.03.004
21. Hecht S Kathan M Photoswitchable molecules as key ingredients to drive systems away from the global thermodynamic minimum Chem. Soc. Rev. 2017 46 5536 5550 10.1039/C7CS00112F 28857096
Hecht, S. & Kathan, M. Photoswitchable molecules as key ingredients to drive systems away from the global thermodynamic minimum. Chem. Soc. Rev. 46, 5536–5550 (2017).28857096 10.1039/C7CS00112F
22. Sabatino A Penocchio E Ragazzon G Credi A Frezzato D Individual‐molecule perspective analysis of chemical reaction networks: the case of a light‐driven supramolecular pump Angew. Chem 2019 131 14479 14486 10.1002/ange.201908026
Sabatino, A., Penocchio, E., Ragazzon, G., Credi, A. & Frezzato, D. Individual‐molecule perspective analysis of chemical reaction networks: the case of a light‐driven supramolecular pump. Angew. Chem 131, 14479–14486 (2019).10.1002/ange.201908026
23. Chida K Desai S Nishiguchi K Fujiwara A Power generator driven by Maxwell’s demon Nat. Commun. 2017 8 15301 10.1038/ncomms15301
Chida, K., Desai, S., Nishiguchi, K. & Fujiwara, A. Power generator driven by Maxwell’s demon. Nat. Commun. 8, 15301 (2017).10.1038/ncomms15301
24. Ragazzon G Baroncini M Silvi S Venturi M Credi A Light-powered autonomous and directional molecular motion of a dissipative self-assembling system Nat. Nanotechnol. 2015 10 70 75 10.1038/nnano.2014.260 25420035
Ragazzon, G., Baroncini, M., Silvi, S., Venturi, M. & Credi, A. Light-powered autonomous and directional molecular motion of a dissipative self-assembling system. Nat. Nanotechnol. 10, 70–75 (2015).25420035 10.1038/nnano.2014.260
25. Zanin GL Enhanced photonic Maxwell’s demon with correlated baths Quantum 2022 6 810 10.22331/q-2022-09-20-810
Zanin, G. L. et al. Enhanced photonic Maxwell’s demon with correlated baths. Quantum 6, 810 (2022).10.22331/q-2022-09-20-810
26. Ragazzon G Autonomous non-equilibrium self-assembly and molecular movements powered by electrical energy Angew. Chem. Int. Ed. 2023 62 e202214265 10.1002/anie.202214265
Ragazzon, G. et al. Autonomous non-equilibrium self-assembly and molecular movements powered by electrical energy. Angew. Chem. Int. Ed. 62, e202214265 (2023).10.1002/anie.202214265
27. Freitas N Esposito M Information flows in macroscopic Maxwell’s demons Phys. Rev. E 2023 107 014136 10.1103/PhysRevE.107.014136 36797870
Freitas, N. & Esposito, M. Information flows in macroscopic Maxwell’s demons. Phys. Rev. E 107, 014136 (2023).36797870 10.1103/PhysRevE.107.014136
28. He L Pradana A Cheong JW Chew LY Information processing second law for an information ratchet with finite tape Phys. Rev. E 2022 105 054131 10.1103/PhysRevE.105.054131 35706159
He, L., Pradana, A., Cheong, J. W. & Chew, L. Y. Information processing second law for an information ratchet with finite tape. Phys. Rev. E 105, 054131 (2022).35706159 10.1103/PhysRevE.105.054131
29. Xie X Photocurrent generation based on a light-driven proton pump in an artificial liquid membrane Nat. Chem. 2014 6 202 207 10.1038/nchem.1858 24557134
Xie, X. et al. Photocurrent generation based on a light-driven proton pump in an artificial liquid membrane. Nat. Chem. 6, 202–207 (2014).24557134 10.1038/nchem.1858
30. Steinberg-Yfrach G Conversion of light energy to proton potential in liposomes by artificial photosynthetic reaction centres Nature 1997 385 239 241 10.1038/385239a0
Steinberg-Yfrach, G. et al. Conversion of light energy to proton potential in liposomes by artificial photosynthetic reaction centres. Nature 385, 239–241 (1997).10.1038/385239a0
31. Steinberg-Yfrach G Light-driven production of ATP catalysed by F0F1-ATP synthase in an artificial photosynthetic membrane Nature 1998 392 479 482 10.1038/33116 9548252
Steinberg-Yfrach, G. et al. Light-driven production of ATP catalysed by F0F1-ATP synthase in an artificial photosynthetic membrane. Nature 392, 479–482 (1998).9548252 10.1038/33116
32. Bennett I Active transport of Ca2+ by an artificial photosynthetic membrane Nature 2002 420 398 401 10.1038/nature01209 12459780
Bennett, I. et al. Active transport of Ca2+ by an artificial photosynthetic membrane. Nature 420, 398–401 (2002).12459780 10.1038/nature01209
33. Lagoin M Crauste-Thibierge C Naert A Human-scale Brownian ratchet: a historical thought experiment Phys. Rev. Lett. 2022 129 120606 10.1103/PhysRevLett.129.120606 36179202
Lagoin, M., Crauste-Thibierge, C. & Naert, A. Human-scale Brownian ratchet: a historical thought experiment. Phys. Rev. Lett. 129, 120606 (2022).36179202 10.1103/PhysRevLett.129.120606
34. Serreli V Lee CF Kay ER Leigh DA A molecular information ratchet Nature 2007 445 523 527 10.1038/nature05452 17268466
Serreli, V., Lee, C. F., Kay, E. R. & Leigh, D. A. A molecular information ratchet. Nature 445, 523–527 (2007).17268466 10.1038/nature05452
35. Raizen MG Comprehensive control of atomic motion Science 2009 324 1403 1406 10.1126/science.1171506 19520950
Raizen, M. G. Comprehensive control of atomic motion. Science 324, 1403–1406 (2009).19520950 10.1126/science.1171506
36. Chia PSK Lindoy LF Walker GW Everett GW Supramolecular transport of metal amine complexes through liquid membranes by the ionophore lasalocid Pure Appl. Chem. 1993 65 521 526 10.1351/pac199365030521
Chia, P. S. K., Lindoy, L. F., Walker, G. W. & Everett, G. W. Supramolecular transport of metal amine complexes through liquid membranes by the ionophore lasalocid. Pure Appl. Chem. 65, 521–526 (1993).10.1351/pac199365030521
37. Nguyen BNT Coordination cages selectively transport molecular cargoes across liquid membranes J. Am. Chem. Soc. 2021 143 12175 12180 10.1021/jacs.1c04799 34337947
Nguyen, B. N. T. et al. Coordination cages selectively transport molecular cargoes across liquid membranes. J. Am. Chem. Soc. 143, 12175–12180 (2021).34337947 10.1021/jacs.1c04799
38. Huang H Juan A Katsonis N Huskens J Competitive inclusion of molecular photo-switches in host cavities Tetrahedron 2017 73 4913 4917 10.1016/j.tet.2017.05.026
Huang, H., Juan, A., Katsonis, N. & Huskens, J. Competitive inclusion of molecular photo-switches in host cavities. Tetrahedron 73, 4913–4917 (2017).10.1016/j.tet.2017.05.026
39. Dambenieks AK Vu PHQ Fyles TM Dissipative assembly of a membrane transport system Chem. Sci. 2014 5 3396 3403 10.1039/C4SC01258E
Dambenieks, A. K., Vu, P. H. Q. & Fyles, T. M. Dissipative assembly of a membrane transport system. Chem. Sci. 5, 3396–3403 (2014).10.1039/C4SC01258E
40. Van Esch JH Klajn R Otto S Chemical systems out of equilibrium Chem. Soc. Rev. 2017 46 5474 10.1039/C7CS90088K 28884760
Van Esch, J. H., Klajn, R. & Otto, S. Chemical systems out of equilibrium. Chem. Soc. Rev. 46, 5474 (2017).28884760 10.1039/C7CS90088K
41. Aprahamian I Goldup SM Non-equilibrium steady states in catalysis, molecular motors, and supramolecular materials: why networks and language matter J. Am. Chem. Soc. 2023 145 14169 14183 10.1021/jacs.2c12665 37343130
Aprahamian, I. & Goldup, S. M. Non-equilibrium steady states in catalysis, molecular motors, and supramolecular materials: why networks and language matter. J. Am. Chem. Soc. 145, 14169–14183 (2023).37343130 10.1021/jacs.2c12665
42. Freitas N Esposito M Maxwell demon that can work at macroscopic scales Phys. Rev. Lett. 2022 129 120602 10.1103/PhysRevLett.129.120602 36179174
Freitas, N. & Esposito, M. Maxwell demon that can work at macroscopic scales. Phys. Rev. Lett. 129, 120602 (2022).36179174 10.1103/PhysRevLett.129.120602
43. Astumian RD Kinetic asymmetry allows macromolecular catalysts to drive an information ratchet Nat. Commun. 2019 10 3837 10.1038/s41467-019-11402-7 31444340
Astumian, R. D. Kinetic asymmetry allows macromolecular catalysts to drive an information ratchet. Nat. Commun. 10, 3837 (2019).31444340 10.1038/s41467-019-11402-7
44. Amano S Insights from an information thermodynamics analysis of a synthetic molecular motor Nat. Chem. 2022 14 530 537 10.1038/s41557-022-00899-z 35301472
Amano, S. et al. Insights from an information thermodynamics analysis of a synthetic molecular motor. Nat. Chem. 14, 530–537 (2022).35301472 10.1038/s41557-022-00899-z
45. Arias-Gonzalez JR Fluctuation relations for irreversible emergence of information Sci. Rep. 2022 12 17230 10.1038/s41598-022-21729-9 36241690
Arias-Gonzalez, J. R. Fluctuation relations for irreversible emergence of information. Sci. Rep. 12, 17230 (2022).36241690 10.1038/s41598-022-21729-9
46. Fontana PW Hidden dissipation and irreversibility in Maxwell’s demon Entropy 2022 24 e24010093 10.3390/e24010093
Fontana, P. W. Hidden dissipation and irreversibility in Maxwell’s demon. Entropy 24, e24010093 (2022).10.3390/e24010093
47. Thomas D Pumping between phases with a pulsed-fuel molecular ratchet Nat. Nanotechnol. 2022 17 701 707 10.1038/s41565-022-01097-1 35379944
Thomas, D. et al. Pumping between phases with a pulsed-fuel molecular ratchet. Nat. Nanotechnol. 17, 701–707 (2022).35379944 10.1038/s41565-022-01097-1
48. Bennett, C. H. & Schumacher, B. Maxwell’s demons appear in the lab. Nikkei Sci. 3–5 (2011).
49. Kay ER Leigh DA Zerbetto F Synthetic molecular motors and mechanical machines Angew. Chem. Int. Ed. 2007 46 72 191 10.1002/anie.200504313
Kay, E. R., Leigh, D. A. & Zerbetto, F. Synthetic molecular motors and mechanical machines. Angew. Chem. Int. Ed. 46, 72–191 (2007).10.1002/anie.200504313
50. Lau B Kedem O Schwabacher J Kwasnieski D Weiss EA An introduction to ratchets in chemistry and biology Mater. Horiz. 2017 4 310 318 10.1039/C7MH00062F
Lau, B., Kedem, O., Schwabacher, J., Kwasnieski, D. & Weiss, E. A. An introduction to ratchets in chemistry and biology. Mater. Horiz. 4, 310–318 (2017).10.1039/C7MH00062F
51. Sangchai T Al Shehimy S Penocchio E Ragazzon G Artificial molecular ratchets: tools enabling endergonic processes Angew. Chem. Int. Ed. 2023 62 e202309501 10.1002/anie.202309501
Sangchai, T., Al Shehimy, S., Penocchio, E. & Ragazzon, G. Artificial molecular ratchets: tools enabling endergonic processes. Angew. Chem. Int. Ed. 62, e202309501 (2023).10.1002/anie.202309501
52. Sholl DS Lively RP Seven chemical separations to change the world Nature 2016 532 435 437 10.1038/532435a 27121824
Sholl, D. S. & Lively, R. P. Seven chemical separations to change the world. Nature 532, 435–437 (2016).27121824 10.1038/532435a
53. Bolliger JL Belenguer AM Nitschke JR Enantiopure water-soluble [Fe4L6] cages: host–guest chemistry and catalytic activity Angew. Chem. Int. Ed. 2013 52 7958 7962 10.1002/anie.201302136
Bolliger, J. L., Belenguer, A. M. & Nitschke, J. R. Enantiopure water-soluble [Fe4L6] cages: host–guest chemistry and catalytic activity. Angew. Chem. Int. Ed. 52, 7958–7962 (2013).10.1002/anie.201302136
54. Müller K Photoswitchable nanoporous films by loading azobenzene in metal–organic frameworks of type HKUST-1 Chem. Commun. 2017 53 8070 8073 10.1039/C7CC00961E
Müller, K. et al. Photoswitchable nanoporous films by loading azobenzene in metal–organic frameworks of type HKUST-1. Chem. Commun. 53, 8070–8073 (2017).10.1039/C7CC00961E
