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Bone RA, Sharpe DJ, Wales DJ, Green JR. Stochastic paths controlling speed and dissipation. Phys Rev E 2022; 106:054151. [PMID: 36559408 DOI: 10.1103/physreve.106.054151] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2021] [Accepted: 10/28/2022] [Indexed: 11/24/2022]
Abstract
Natural processes occur in a finite amount of time and dissipate energy, entropy, and matter. Near equilibrium, thermodynamic intuition suggests that fast irreversible processes will dissipate more energy and entropy than slow quasistatic processes connecting the same initial and final states. For small systems, recently discovered thermodynamic speed limits suggest that faster processes will dissipate more than slower processes. Here, we test the hypothesis that this relationship between speed and dissipation holds for stochastic paths far from equilibrium. To analyze stochastic paths on finite timescales, we derive an exact expression for the path probabilities of continuous-time Markov chains from the path summation solution to the master equation. We present a minimal model for a driven system in which relative energies of the initial and target states control the speed, and the nonequilibrium currents of a cycle control the dissipation. Although the hypothesis holds near equilibrium, we find that faster processes can dissipate less under far-from-equilibrium conditions because of strong currents. This model serves as a minimal prototype for designing kinetics to sculpt the nonequilibrium path space so that faster paths produce less dissipation.
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Affiliation(s)
- Rebecca A Bone
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Daniel J Sharpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, Cambridge, United Kingdom
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, Cambridge, United Kingdom
| | - Jason R Green
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA.,Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
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2
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Asnicar D, Penocchio E, Frezzato D. Sample size dependence of tagged molecule dynamics in steady-state networks with bimolecular reactions: Cycle times of a light-driven pump. J Chem Phys 2022; 156:184116. [PMID: 35568563 DOI: 10.1063/5.0089695] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Abstract
Here, steady-state reaction networks are inspected from the viewpoint of individual tagged molecules jumping among their chemical states upon the occurrence of reactive events. Such an agent-based viewpoint is useful for selectively characterizing the behavior of functional molecules, especially in the presence of bimolecular processes. We present the tools for simulating the jump dynamics both in the macroscopic limit and in the small-volume sample where the numbers of reactive molecules are of the order of few units with an inherently stochastic kinetics. The focus is on how an ideal spatial "compartmentalization" may affect the dynamical features of the tagged molecule. Our general approach is applied to a synthetic light-driven supramolecular pump composed of ring-like and axle-like molecules that dynamically assemble and disassemble, originating an average ring-through-axle directed motion under constant irradiation. In such an example, the dynamical feature of interest is the completion time of direct/inverse cycles of tagged rings and axles. We find a surprisingly strong robustness of the average cycle times with respect to the system's size. This is explained in the presence of rate-determining unimolecular processes, which may, therefore, play a crucial role in stabilizing the behavior of small chemical systems against strong fluctuations in the number of molecules.
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Affiliation(s)
- Daniele Asnicar
- Department of Chemical Sciences, University of Padova, via Marzolo 1, I-35131 Padova, Italy
| | - Emanuele Penocchio
- Department of Physics and Materials Science, University of Luxembourg, Avenue de la Faïencerie, Luxembourg City L-1511, G.D. Luxembourg
| | - Diego Frezzato
- Department of Chemical Sciences, University of Padova, via Marzolo 1, I-35131 Padova, Italy
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3
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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 Int Ed Engl 2019. [DOI: 10.1002/ange.201908026] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Andrea Sabatino
- Dipartimento di Scienze Chimiche Università degli Studi di Padova Via Marzolo 1 35131 Padova Italy
| | - Emanuele Penocchio
- Complex Systems and Statistical Mechanics, Physics and Materials Science Unit University of Luxembourg 162 A, avenue de la Faïencerie 1511 Luxembourg Luxembourg
| | - Giulio Ragazzon
- Department of Chemical and Pharmaceutical Sciences Università degli Studi di Trieste via Giorgieri 1 34127 Trieste Italy
| | - Alberto Credi
- Center for Light Activated Nanostructures (CLAN) Dipartimento di Scienze e Tecnologie Agro-alimentari Università di Bologna, and Istituto ISOF Consiglio Nazionale delle Ricerche Via Gobetti 101 40129 Bologna Italy
| | - Diego Frezzato
- Dipartimento di Scienze Chimiche Università degli Studi di Padova Via Marzolo 1 35131 Padova Italy
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4
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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 Int Ed Engl 2019; 58:14341-14348. [PMID: 31379048 PMCID: PMC6899705 DOI: 10.1002/anie.201908026] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2019] [Indexed: 11/10/2022]
Abstract
The first study in which stochastic simulations of a two‐component molecular machine are performed in the mass‐action regime is presented. This system is an autonomous molecular pump consisting of a photoactive axle that creates a directed flow of rings through it by exploiting light energy away from equilibrium. The investigation demonstrates that the pump can operate in two regimes, both experimentally accessible, in which light‐driven steps can be rate‐determining or not. The number of photons exploited by an individual molecular pump, as well as the precision of cycling and the overall efficiency, critically rely on the operating regime of the machine. This approach provides useful information not only to guide the chemical design of a self‐assembling molecular device with desired features, but also to elucidate the effect of the environment on its performance, thus facilitating its experimental investigation.
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Affiliation(s)
- Andrea Sabatino
- Dipartimento di Scienze Chimiche, Università degli Studi di Padova, Via Marzolo 1, 35131, Padova, Italy
| | - Emanuele Penocchio
- Complex Systems and Statistical Mechanics, Physics and Materials Science Unit, University of Luxembourg, 162 A, avenue de la Faïencerie, 1511, Luxembourg, Luxembourg
| | - Giulio Ragazzon
- Department of Chemical and Pharmaceutical Sciences, Università degli Studi di Trieste, via Giorgieri 1, 34127, Trieste, Italy
| | - Alberto Credi
- Center for Light Activated Nanostructures (CLAN), Dipartimento di Scienze e Tecnologie Agro-alimentari, Università di Bologna, and Istituto ISOF, Consiglio Nazionale delle Ricerche, Via Gobetti 101, 40129, Bologna, Italy
| | - Diego Frezzato
- Dipartimento di Scienze Chimiche, Università degli Studi di Padova, Via Marzolo 1, 35131, Padova, Italy
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Sabatino A, Frezzato D. Tagged-moiety viewpoint of chemical reaction networks. J Chem Phys 2019; 150:134104. [DOI: 10.1063/1.5081675] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Andrea Sabatino
- Department of Chemical Sciences, University of Padova, Via Marzolo 1, I-35131 Padova, Italy
| | - Diego Frezzato
- Department of Chemical Sciences, University of Padova, Via Marzolo 1, I-35131 Padova, Italy
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Nicholson SB, Alaghemandi M, Green JR. Effects of temperature and mass conservation on the typical chemical sequences of hydrogen oxidation. J Chem Phys 2018; 148:044102. [PMID: 29390841 DOI: 10.1063/1.5012760] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Macroscopic properties of reacting mixtures are necessary to design synthetic strategies, determine yield, and improve the energy and atom efficiency of many chemical processes. The set of time-ordered sequences of chemical species are one representation of the evolution from reactants to products. However, only a fraction of the possible sequences is typical, having the majority of the joint probability and characterizing the succession of chemical nonequilibrium states. Here, we extend a variational measure of typicality and apply it to atomistic simulations of a model for hydrogen oxidation over a range of temperatures. We demonstrate an information-theoretic methodology to identify typical sequences under the constraints of mass conservation. Including these constraints leads to an improved ability to learn the chemical sequence mechanism from experimentally accessible data. From these typical sequences, we show that two quantities defining the variational typical set of sequences-the joint entropy rate and the topological entropy rate-increase linearly with temperature. These results suggest that, away from explosion limits, data over a narrow range of thermodynamic parameters could be sufficient to extrapolate these typical features of combustion chemistry to other conditions.
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Affiliation(s)
- Schuyler B Nicholson
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Mohammad Alaghemandi
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
| | - Jason R Green
- Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
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