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Living systems are forced away from thermodynamic equilibrium by exchange of mass and energy with their environment. In order to model a biochemical reaction network in a non-equilibrium state one requires a mathematical formulation to…

Molecular Networks · Quantitative Biology 2012-02-21 Ronan M. T. Fleming , Ines Thiele

Chemical reaction systems operating in nonequilibrium open-system states arise in a great number of contexts, including the study of living organisms, in which chemical reactions, in general, are far from equilibrium. Here we introduce a…

Subcellular Processes · Quantitative Biology 2007-05-23 Daniel A. Beard , Hong Qian

A spatio-temporal evolution of chemicals appearing in a reversible enzyme reaction and modelled by a four component reaction-diffusion system with the reaction terms obtained by the law of mass action is considered. The large time behaviour…

Analysis of PDEs · Mathematics 2016-10-25 Jan Elias

The work done when a system at thermal equilibrium is externally driven by a unitary control parameter leads to irreversible entropy production. The entropy produced can be thought of as a combination of coherence generation and a…

Quantum Physics · Physics 2024-12-30 Krishna Shende , Kavita Dorai , Arvind

There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time-reversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations…

Statistical Mechanics · Physics 2007-05-23 C. Maes , K. Netocny

We generalize nonequilibrium integral equalities to situations involving absolutely irreversible processes for which the forward-path probability vanishes and the entropy production diverges, rendering conventional integral fluctuation…

Statistical Mechanics · Physics 2016-08-11 Yûto Murashita , Ken Funo , Masahito Ueda

In contrast to common opinion, it is shown that equilibrium constants determine the time-dependent behavior of particular ratios of concentrations for any system of reversible first-order reactions. Indeed, some special ratios actually…

Mathematical Physics · Physics 2010-07-28 Gregory S. Yablonsky , Denis Constales , Guy B. Marin

Even though irreversibility is one of the major hallmarks of any real life process, an actual understanding of irreversible processes remains still mostly semiempirical. In this paper we formulate a thermodynamic uncertainty principle for…

Statistical Mechanics · Physics 2021-03-17 Rudolf Hanel , Petr Jizba

A generalization of the Gibbs entropy postulate is proposed based on the BBGKY hierarchy as the nonequilibrium entropy for a system of N interacting particles. This entropy satisfies the basic principles of thermodynamics in the sense that…

Statistical Mechanics · Physics 2007-05-23 A. Perez-Madrid

Onsager's phenomenological equations successfully describe irreversible thermodynamic processes. They assume a symmetric coupling matrix between thermodynamic fluxes and forces. It is easily shown that the antisymmetric part of a coupling…

Chemical Physics · Physics 2020-08-10 Thomas Heimburg

Entropy generation in a chemical reaction is analyzed without using the general formalism of non-equilibrium thermodynamics at a level adequate for advanced undergraduates. In a first approach to the problem, the phenomenological kinetic…

General Physics · Physics 2015-06-11 E. N. Miranda

Methods are presented to evaluate the entropy production rate in stochastic reactive systems. These methods are shown to be consistent with known results from nonequilibrium chemical thermodynamics. Moreover, it is proved that the time…

Chaotic Dynamics · Physics 2025-12-17 Pierre Gaspard

The collapse of man-made and natural structures is a complex phenomenon that has been studied for centuries. We propose a new approach to understanding catastrophic instabilities, based on the idea that they do not occur at the critical…

Pattern Formation and Solitons · Physics 2023-08-29 Klaus Regenauer-Lieb , Manman Hu

The question of the onset of the homochirality on prebiotic Earth still remains a fundamental question in the quest for the origin of life. Recent works in this field introduce the concept of recycling, rather than the traditional open-flow…

Molecular Networks · Quantitative Biology 2011-05-23 Raphael Plasson

In nonequilibrium chemical reaction systems, a fundamental relationship between unbalanced kinetic one-way fluxes and thermodynamic chemical driving forces is believed to exists. However this relation has been rigorously demonstrated only…

Chemical Physics · Physics 2020-07-22 Yongli Peng , Hong Qian , Daniel A. Beard , Hao Ge

An equilibrium reversible cycle with a certain engine to transduce the energy of any chemical reaction into mechanical energy is proposed. The efficiency for chemical energy transduction is also defined so as to be compared with Carnot…

Soft Condensed Matter · Physics 2009-10-30 Tatsuo Shibata , Shin-ichi Sasa

For chemical reaction networks described by a master equation, we define energy and entropy on a stochastic trajectory and develop a consistent nonequilibrium thermodynamic description along a single stochastic trajectory of reaction…

Statistical Mechanics · Physics 2009-11-11 Tim Schmiedl , Udo Seifert

The transition from a non-equilibrium state to an equilibrium state is characterized not only by the disappearance of the entropy production, but mainly by the disappearance of the organized currents, due to the gradients present in a…

Statistical Mechanics · Physics 2013-08-15 E. G. D. Cohen , R. L. Merlino

Mass action type deterministic kinetic models of ion channels are usually constructed in such a way as to obey the principle of detailed balance (or, microscopic reversibility) for two reasons: first, the authors aspire to have models…

Molecular Networks · Quantitative Biology 2011-09-21 I. Nagy , J. Tóth

We study a process of pattern formation for a generic model of species anchored to the nodes of a network where local reactions take place, and that experience non-reciprocal long-range interactions, encoded by the network directed links.…

Pattern Formation and Solitons · Physics 2025-10-22 Timoteo Carletti , Riccardo Muolo