Abstract: All current formulations of nonequilibrium thermodynamics of open chemical reaction networks rely on the assumption of non-interacting species. We develop a general theory that accounts for interactions between chemical species within a mean-field approach using activity coefficients. Thermodynamic consistency requires that rate equations do not obey standard mass-action kinetics but account for the interactions with concentration dependent kinetic constants. Many features of the ideal formulations are recovered. Crucially, the thermodynamic potential and the forces driving non-ideal chemical systems out of equilibrium are identified. Our theory is general and holds for any mean-field expression of the interactions leading to lower bounded free energies.

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Topics: Non-equilibrium thermodynamics (60%), Thermodynamic potential (58%), Chemical reaction network theory (52%) ... show more

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7 results found

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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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Topics: Entropy production (54%), Diffusion (business) (51%)

3 Citations

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Abstract: We consider thermodynamically consistent autonomous Markov jump processes displaying a macroscopic limit in which the logarithm of the probability distribution is proportional to a scale-independent rate function (i.e., a large deviations principle is satisfied). In order to provide an explicit expression for the probability distribution valid away from equilibrium, we propose a linear response theory performed at the level of the rate function. We show that the first order non-equilibrium contribution to the steady state rate function, $g(x)$, satisfies $u(x)\cdot
abla g(x) = -\beta \dot W(x)$ where the vector field $u(x)$ defines the macroscopic deterministic dynamics, and the scalar field $\dot W(x)$ equals the rate at which work is performed on the system in a given state $x$. This equation provides a practical way to determine $g(x)$, significantly outperforms standard linear response theory applied at the level of the probability distribution, and approximates the rate function surprisingly well in some far-from-equilibrium conditions. The method applies to a wealth of physical and chemical systems, that we exemplify by two analytically tractable models - an electrical circuit and an autocatalytic chemical reaction network - both undergoing a non-equilibrium transition from a monostable phase to a bistable phase. Our approach can be easily generalized to transient probabilities and non-autonomous dynamics. Moreover, its recursive application generates a virtual flow in the probability space which allows to determine the steady state rate function arbitrarily far from equilibrium.

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Topics: Probability distribution (60%), Rate function (59%), Large deviations theory (56%) ... show more

1 Citations

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Emanuele Penocchio^{1}, Riccardo Rao^{1}, Riccardo Rao^{2}, Massimiliano Esposito^{1}•Institutions (2)

Abstract: Current formulations of nonequilibrium thermodynamics of open chemical reaction networks only consider chemostats as free-energy sources sustaining nonequilibrium behaviors. Here, we extend the theory to include incoherent light as a source of free energy. We do so by relying on a local equilibrium assumption to derive the chemical potential of photons relative to the system they interact with. This allows us to identify the thermodynamic potential and the thermodynamic forces driving light-reacting chemical systems out-of-equilibrium. We use this framework to treat two paradigmatic photochemical mechanisms describing light-induced unimolecular reactions—namely, the adiabatic and diabatic mechanisms—and highlight the different thermodynamics they lead to. Furthermore, using a thermodynamic coarse-graining procedure, we express our findings in terms of commonly measured experimental quantities, such as quantum yields.

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Topics: Non-equilibrium thermodynamics (62%), Thermodynamic potential (59%), Adiabatic process (56%)

1 Citations

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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.

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Topics: Thermodynamic potential (57%)

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Abstract: Dissipative accounts of structure formation show that the self-organisation of complex structures is thermodynamically favoured, whenever these structures dissipate free energy that could not be accessed otherwise. These structures therefore open transition channels for the state of the universe to move from a frustrated, metastable state to another metastable state of higher entropy. However, these accounts apply as well to relatively simple, dissipative systems, such as convection cells, hurricanes, candle flames, lightning strikes, or mechanical cracks, as they do to complex biological systems. Conversely, interesting computational properties—that characterize complex biological systems, such as efficient, predictive representations of environmental dynamics—can be linked to the thermodynamic efficiency of underlying physical processes. However, the potential mechanisms that underwrite the selection of dissipative structures with thermodynamically efficient subprocesses is not completely understood. We address these mechanisms by explaining how bifurcation-based, work-harvesting processes—required to sustain complex dissipative structures—might be driven towards thermodynamic efficiency. We first demonstrate a simple mechanism that leads to self-selection of efficient dissipative structures in a stochastic chemical reaction network, when the dissipated driving chemical potential difference is decreased. We then discuss how such a drive can emerge naturally in a hierarchy of self-similar dissipative structures, each feeding on the dissipative structures of a previous level, when moving away from the initial, driving disequilibrium.

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Topics: Dissipative system (65%)

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34 results found

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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.

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Topics: Entropy production (62%), Fluctuation theorem (61%), Master equation (56%) ... show more

2,273 Citations

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Abstract: The familiar idea of mass action kinetics is extended to embrace situations more general than chemically reacting mixtures in closed vessels. Thus, for example, many reaction regions connected by convective or diffusive mass transport, such as the cellular aggregates of biological tissue, are drawn into a common mathematical scheme. The ideas of chemical thermodynamics, such as the algebraic nature of the equilibrium conditions and the decreasing property of the free energy, are also generalized in a natural way, and it is then possible to identify classes of generalized kinetic expressions which ensure consistency with the extended thermodynamic conditions. The principal result of this work shows that there exists a simply identifiable class of kinetic expressions, including the familiar detailed balanced kinetics as a proper subclass, which ensure consistency with the extended thermodynamic conditions. For kinetics of this class, which we call complex balanced kinetics, exotic behavior such as bistability and oscillation is precluded, so the domain of search for kinetic expressions with this type of behavior, which is of considerable biological interest, is greatly narrowed. It is also shown that the ideas of complex balancing and of detailed balancing are closely related to symmetry under time reversal.

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Topics: Chemical reaction network theory (53%)

1,030 Citations

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Abstract: The reason we never observe violations of the second law of thermodynamics is in part a matter of statistics: When ∼1023 degrees of freedom are involved, the odds are overwhelmingly stacked against the possibility of seeing significant deviations away from the mean behavior. As we turn our attention to smaller systems, however, statistical fluctuations become more prominent. In recent years it has become apparent that the fluctuations of systems far from thermal equilibrium are not mere background noise, but satisfy strong, useful, and unexpected properties. In particular, a proper accounting of fluctuations allows us to rewrite familiar inequalities of macroscopic thermodynamics as equalities. This review describes some of this progress, and argues that it has refined our understanding of irreversibility and the second law.

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Topics: Entropy (arrow of time) (57%), Fluctuation theorem (55%), Second law of thermodynamics (54%) ... show more

821 Citations

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Abstract: A general microscopic and macroscopic theory is developed for systems which are governed by a (linear) master equation. The theory is based on a network representation of the master equation, and the results are obtained mostly by application of some basic theorems of mathematical graph theory. In the microscopic part of the theory, the construction of a steady state solution of the master equation in terms of graph theoretical elements is described (Kirchhoff's theorem), and it is shown that the master equation satisfies a global asymptotic Liapunov stability criterion with respect to this state. The Glansdorff-Prigogine criterion turns out to be the differential version and thus a special case of the global criterion. In the macroscopic part of the theory, a general prescription is given describing macrostates of the systems arbitrarily far from equilibrium in the language of generalized forces and fluxes of nonlinear irreversible thermodynamics. As a particular result, Onsager's reciprocity relations for the phenomenological coefficients are obtained as coinciding with the reciprocity relations of a near-to-equilibrium network.

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Topics: Master equation (62%), Stability criterion (57%), Reciprocity (electromagnetism) (51%) ... show more

819 Citations

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Abstract: We revisit stochastic thermodynamics for a system with discrete energy states in contact with a heat and particle reservoir.

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Topics: Entropy (classical thermodynamics) (75%), Fluctuation theorem (65%)

266 Citations