Thermodynamic Uncertainty Relation and Thermodynamic Speed Limit in Deterministic Chemical Reaction Networks.
TL;DR: In this article, the authors generalize the thermodynamic uncertainty relation (TUR) and thermodynamic speed limit (TSL) for deterministic chemical reaction networks (CRNs) and derive the scaled diffusion coefficient derived by considering the connection between macro-and mesoscopic CRNs.
Abstract: We generalize the thermodynamic uncertainty relation (TUR) and thermodynamic speed limit (TSL) for deterministic chemical reaction networks (CRNs). The scaled diffusion coefficient derived by considering the connection between macro- and mesoscopic CRNs plays an essential role in our results. The TUR shows that the product of the entropy production rate and the ratio of the scaled diffusion coefficient to the square of the rate of concentration change is bounded below by two. The TSL states a trade-off relation between speed and thermodynamic quantities, the entropy production, and the time-averaged scaled diffusion coefficient. The results are proved under the general setting of open and nonideal CRNs.
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01 Nov 2021
TL;DR: In this paper, the authors studied the relationship between optimal transport theory and stochastic thermodynamics for the Fokker-Planck equation and derived a lower bound on the partial entropy production as a generalization of information thermodynamics.
Abstract: We study a relationship between optimal transport theory and stochastic thermodynamics for the Fokker-Planck equation. We show that the lower bound on the entropy production is the action measured by the path length of the ${L}^{2}$-Wasserstein distance. Because the ${L}^{2}$-Wasserstein distance is a geometric measure of optimal transport theory, our result implies a geometric interpretation of the entropy production. Based on this interpretation, we obtain a thermodynamic trade-off relation between transition time and the entropy production. This thermodynamic trade-off relation is regarded as a thermodynamic speed limit which gives a tighter bound of the entropy production. We also discuss stochastic thermodynamics for the subsystem and derive a lower bound on the partial entropy production as a generalization of the second law of information thermodynamics. Our formalism also provides a geometric picture of the optimal protocol to minimize the entropy production. We illustrate these results by the optimal stochastic heat engine and show a geometrical bound of the efficiency.
26 citations
TL;DR: In this article , a tight finite-time Landauer's bound was established by establishing a general form of the classical speed limit for quasistatic processes, which captures the divergent behavior associated with the additional cost of a highly irreversible process which scales differently from a nearly irreversible process.
Abstract: Landauer's bound is the minimum thermodynamic cost for erasing one bit of information. As this bound is achievable only for quasistatic processes, finite-time operation incurs additional energetic costs. We find a tight finite-time Landauer's bound by establishing a general form of the classical speed limit. This tight bound well captures the divergent behavior associated with the additional cost of a highly irreversible process, which scales differently from a nearly irreversible process. We also find an optimal dynamics which saturates the equality of the bound. We demonstrate the validity of this bound via discrete one-bit and coarse-grained bit systems. Our work implies that more heat dissipation than expected occurs during high-speed irreversible computation.
9 citations
TL;DR: In this article , the authors derive the Hessian geometric structure of nonequilibrium chemical reaction networks on the flux and force spaces induced by the Legendre duality of convex dissipation functions and characterize their dynamics as a generalized flow.
Abstract: We derive the Hessian geometric structure of nonequilibrium chemical reaction networks on the flux and force spaces induced by the Legendre duality of convex dissipation functions and characterize their dynamics as a generalized flow. With this geometric structure, we can extend theories of nonequilibrium systems with quadratic dissipation functions to more general cases with nonquadratic ones, which are pivotal for studying chemical reaction networks. By applying generalized notions of orthogonality in Hessian geometry to chemical reaction networks, two generalized decompositions of the entropy production rate are obtained, each of which captures gradient-flow and minimum-dissipation aspects in nonequilibrium dynamics.
9 citations
TL;DR: In this article , a thermodynamic framework for discrete optimal transport was developed for continuous-state Langevin dynamics, and the Wasserstein distance was shown to be the minimum product of irreversible entropy production and dynamical state mobility over all admissible Markovian dynamics.
Abstract: Thermodynamics serves as a universal means for studying physical systems from an energy perspective. In recent years, with the establishment of the field of stochastic and quantum thermodynamics, the ideas of thermodynamics have been generalized to small fluctuating systems. Independently developed in mathematics and statistics, the optimal transport theory concerns the means by which one can optimally transport a source distribution to a target distribution, deriving a useful metric between probability distributions, called the Wasserstein distance. Despite their seemingly unrelated nature, an intimate connection between these fields has been unveiled in the context of continuous-state Langevin dynamics, providing several important implications for nonequilibrium systems. In this study, we elucidate an analogous connection for discrete cases by developing a thermodynamic framework for discrete optimal transport. We first introduce a novel quantity called dynamical state mobility, which significantly improves the thermodynamic uncertainty relation and provides insights into the precision of currents in nonequilibrium Markov jump processes. We then derive variational formulas that connect the discrete Wasserstein distances to stochastic and quantum thermodynamics of discrete Markovian dynamics described by master equations. Specifically, we rigorously prove that the Wasserstein distance equals the minimum product of irreversible entropy production and dynamical state mobility over all admissible Markovian dynamics. These formulas not only unify the relationship between thermodynamics and the optimal transport theory for discrete and continuous cases, but also generalize it to the quantum case. In addition, we demonstrate that the obtained variational formulas lead to remarkable applications in stochastic and quantum thermodynamics, such as stringent thermodynamic speed limits and the finite-time Landauer principle. These bounds are tight and can be saturated for arbitrary temperatures, even in the zero-temperature limit. Notably, the finite-time Landauer principle can explain finite dissipation even at extremely low temperatures, which cannot be explained by the conventional Landauer principle.1 MoreReceived 26 July 2022Revised 1 December 2022Accepted 13 December 2022DOI:https://doi.org/10.1103/PhysRevX.13.011013Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEntropy productionNonequilibrium & irreversible thermodynamicsNonequilibrium statistical mechanicsQuantum thermodynamicsStochastic processesStochastic thermodynamicsThermodynamics of computationTechniquesGraph theoryStatistical PhysicsInterdisciplinary PhysicsGeneral Physics
6 citations
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TL;DR: In this paper, the thermodynamic implications of two control mechanisms of open chemical reaction networks were investigated, i.e., the first controls the concentrations of the species that are exchanged with the surroundings, while the other controls the exchange fluxes.
Abstract: We investigate the thermodynamic implications of two control mechanisms of open chemical reaction networks. The first controls the concentrations of the species that are exchanged with the surroundings, while the other controls the exchange fluxes. We show that the two mechanisms can be mapped one into the other and that the thermodynamic theories usually developed in the framework of concentration control can be applied to flux control as well. This implies that the thermodynamic potential and the fundamental forces driving chemical reaction networks out of equilibrium can be identified in the same way for both mechanisms. By analyzing the dynamics and thermodynamics of a simple enzymatic model we also show that, while the two mechanisms are equivalent a steady state, the flux control may lead to fundamentally different regimes where systems achieve stationary growth.
5 citations
References
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TL;DR: Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
Abstract: Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation–dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production. (Some figures may appear in colour only in the online journal) This article was invited by Erwin Frey.
2,834 citations
TL;DR: The article ''On the Equilibrium of Heterogeneous Substances'', which was published in ''Transactions of the Connecticut Academy of Arts and Sciences'', vol. 3 (1874-78), pp. 108-248 and 343-524 as mentioned in this paper
Abstract: Review of the article ''On the Equilibrium of Heterogeneous Substances'', which was published in ''Transactions of the Connecticut Academy of Arts and Sciences'', vol. 3 (1874-78), pp. 108-248 and 343-524.
1,728 citations
TL;DR: In this article, it is shown that the chemical Langevin equation can be derived from the microphysical premise from which the chemical master equation is derived, which leads directly to an approximate time-evolution equation of the Langevin type.
Abstract: The stochastic dynamical behavior of a well-stirred mixture of N molecular species that chemically interact through M reaction channels is accurately described by the chemical master equation. It is shown here that, whenever two explicit dynamical conditions are satisfied, the microphysical premise from which the chemical master equation is derived leads directly to an approximate time-evolution equation of the Langevin type. This chemical Langevin equation is the same as one studied earlier by Kurtz, in contradistinction to some other earlier proposed forms that assume a deterministic macroscopic evolution law. The novel aspect of the present analysis is that it shows that the accuracy of the equation depends on the satisfaction of certain specific conditions that can change from moment to moment, rather than on a static system size parameter. The derivation affords a new perspective on the origin and magnitude of noise in a chemically reacting system. It also clarifies the connection between the stochas...
1,537 citations
TL;DR: It is shown that ATP production with a low rate and high yield can be viewed as a form of cooperative resource use and may evolve in spatially structured environments and argued that the high ATP yield of respiration may have facilitated the evolutionary transition from unicellular to undifferentiated multicellular organisms.
Abstract: Heterotrophic organisms generally face a trade-off between rate and yield of adenosine triphosphate (ATP) production. This trade-off may result in an evolutionary dilemma, because cells with a higher rate but lower yield of ATP production may gain a selective advantage when competing for shared energy resources. Using an analysis of model simulations and biochemical observations, we show that ATP production with a low rate and high yield can be viewed as a form of cooperative resource use and may evolve in spatially structured environments. Furthermore, we argue that the high ATP yield of respiration may have facilitated the evolutionary transition from unicellular to undifferentiated multicellular organisms.
1,206 citations
TL;DR: In this paper, it was shown that the chemical master equation is exact for any gas-phase chemical system that is kept well stirred and thermally equilibrated, and that the exactness of the master equation has no rigorous microphysical basis, and hence no a priori claim to validity.
Abstract: It is widely believed that the chemical master equation has no rigorous microphysical basis, and hence no a priori claim to validity. This view is challenged here through arguments purporting to show that the chemical master equation is exact for any gas-phase chemical system that is kept well stirred and thermally equilibrated.
1,123 citations