Universal Relation Between Thermodynamic Driving Force and One-Way Fluxes in a Nonequilibrium Chemical Reaction with Complex Mechanism
TL;DR: In this article, the one-way fluxes for a general chemical reaction far from equilibrium, with arbitrary complex mechanisms, multiple intermediates, and internal kinetic cycles, were formulated in terms of its stochastic kinetic representation.
Abstract: 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 in a few cases in which one-way fluxes are well defined. In terms of its stochastic kinetic representation, we formulate the one-way fluxes for a general chemical reaction far from equilibrium, with arbitrary complex mechanisms, multiple intermediates, and internal kinetic cycles. For each kinetic cycle, the logarithm of the ratio of the steady-state forward and backward one-way fluxes is equal to the free energy difference between the reactants and products along the cycle. This fundamental relation is further established for general chemical reaction networks with multiple input and output complexes. Our result not only provides an equivalent definition of free energy difference in nonequilibrium chemical reaction networks, it also unifies the stochastic and macroscopic nonequilibrium chemical thermodynamics in a very broad sense.
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23 Feb 2021
TL;DR: In this paper, a connection between chemical thermodynamics and information geometry is made, and the authors show a link between speed limits and the Cram\'er-Rao inequality and information-geometric trade-off relations in chemical reaction networks.
Abstract: This paper studies a connection between chemical thermodynamics and information geometry. The authors show a link between speed limits and the Cram\'er--Rao inequality, and information-geometric trade-off relations in chemical reaction networks.
28 citations
01 Jan 2004
TL;DR: Theorem 2.2.3 Large deviations and fluctuation Theorem as discussed by the authors, which states that large deviations and large fluctuation is a sign of irreversibility and entropy production.
Abstract: 2.1 Circulation Distribution
2.2 Irreversibility and Entropy Production
2.3 Large Deviations and Fluctuation Theorem
1 citations
01 Jan 2004
TL;DR: In this article, directed circuits, cycle functions, and passage functions are discussed, followed by the derived chain and the circulation distribution of recurrent Markov chains, and large deviations and fluctuation Theorem.
Abstract: 1.1 Directed Circuits, Cycles and Passage Functions
1.2 The Derived Chain
1.3 Circulation Distribution of Recurrent Markov Chains
1.4 Irreversibility and Entropy Production
1.5 Large Deviations and Fluctuation Theorem
1.6 Appendix
1 citations
References
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TL;DR: This primer covers the theoretical basis of the approach, several practical examples and a software toolbox for performing the calculations.
Abstract: Flux balance analysis is a mathematical approach for analyzing the flow of metabolites through a metabolic network. This primer covers the theoretical basis of the approach, several practical examples and a software toolbox for performing the calculations.
3,229 citations
TL;DR: A generalized version of the fluctuation theorem is derived for stochastic, microscopically reversible dynamics and this generalized theorem provides a succinct proof of the nonequilibrium work relation.
Abstract: There are only a very few known relations in statistical dynamics that are valid for systems driven arbitrarily far-from-equilibrium. One of these is the fluctuation theorem, which places conditions on the entropy production probability distribution of nonequilibrium systems. Another recently discovered far from equilibrium expression relates nonequilibrium measurements of the work done on a system to equilibrium free energy differences. In this paper, we derive a generalized version of the fluctuation theorem for stochastic, microscopically reversible dynamics. Invoking this generalized theorem provides a succinct proof of the nonequilibrium work relation.
2,278 citations
TL;DR: This presents the first test of the Ruelle principle on a many particle system far from equilibrium, and a specific prediction, obtained without the need to construct explicitly the SRB itself, is shown to be in agreement with a recent computer experiment on a strongly sheared fluid.
Abstract: Ruelle`s principle for turbulence leading to what is usually called the Sinai-Ruelle-Bowen (SRB) distribution is applied to the statistical mechanics of many particle systems in nonequilibrium stationary states. A specific prediction, obtained without the need to construct explicitly the SRB itself, is shown to be in agreement with a recent computer experiment on a strongly sheared fluid. This presents the first test of the principle on a many particle system far from equilibrium. A possible application to fluid mechanics is also discussed.
1,587 citations
TL;DR: The equation of Michaelis and Menten [1913] has been applied with success by Kuhn [1924] and others to numerous cases of enzyme action and it is desirable to examine its theoretical basis.
Abstract: THE equation of Michaelis and Menten [1913] has been applied with success by Kuhn [1924] and others to numerous cases of enzyme action. It is therefore desirable to examine its theoretical basis. Consider the irreversible reaction A -+ B, unimolecular as regards A, and catalysed by an enzyme. Suppose one molecule of A to combine reversibly with one of enzyme, the compound then changing irreversibly into free enzyme and B, where B may represent several molecules. We may represent this as: A+E = AE B+ E. (a-x) (e-p) p x Now let a be the initial concentration of A, e the total concentration of entyme, x the concentration of B produced after time t, and p the concentration of enzyme combined with substrate at time t. We suppose e and p to be negligibly small compared with a and x. Then by the laws of mass action dP = k1 (a x) (e p) -k2p-k3p,
1,207 citations