2 Circulation Distribution, Entropy Production and Irreversibility of Finite Markov Chains with Continuous Parameter

Jiang, Da-Quan; Qian, Min; Qian, Minping

doi:10.1007/978-3-540-40957-1_3

Cited by 3 publications

(12 citation statements)

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“…According to the theory of cycle representation and cycle fluxes for Markov process [16,20,21], one can trace along every sample path, and calculate the time-averaged number of times that a particular cycle c formed by time t. Then letting the time t go to infinity the limit defines the cycle flux ω c for c. In the CME, the system is at equilibrium (time-reversible) if and only if ω c = ω c − for every cycle c [16,20], in which c − is the reversed cycle of c. Furthermore, the ratio…”

Section: B Kinetic Cycle Net Cycle Flux and One-way Cycle Fluxesmentioning

confidence: 99%

“…with − i being the reversed reaction of the reaction i and r is the corresponding transition rates. The exact expression of cycle fluxes and the corresponding cycle decomposition of probability fluxes are given in Appendix B, cited from [16,20].…”

Section: B Kinetic Cycle Net Cycle Flux and One-way Cycle Fluxesmentioning

confidence: 99%

“…The steady-state mesoscopic entropy production rate (mesoEPR) in the counting space can be expressed by all the cycle fluxes [16]…”

Section: Steady-state Entropy Production Ratementioning

confidence: 99%

“…In this section we will list the exact expression of cycle fluxes in the context of a general continuous-time Markov jumping process with countable states, including the chemical-master-equation model on the counting space. The detailed derivation can be referred to [16,20].…”

Section: Appendix B: Expressions Of Cycle Fluxes and Cycle Decompositmentioning

confidence: 99%

“…The one-way flux of each reaction cycle is defined through the cycle fluxes in the counting space of the corresponding chemical-master-equation model [14] describing the stochastic kinetics of molecular numbers. Our theory is based on the general mathematical results on cycle fluxes of a Markov process [15,16]: We prove Eq. 1for each reaction cycle by summing over all the corresponding stochastic cycles in the counting space and derive the entropy production rate in terms of the one-way cycle fluxes.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Universal relation between thermodynamic driving force and one-way fluxes in a nonequilibrium chemical reaction with complex mechanism

Peng

Qian

Beard

et al. 2020

Phys. Rev. Research

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In nonequilibrium chemical reaction systems, a fundamental relationship between unbalanced kinetic one-way fluxes and thermodynamic chemical driving forces is believed to exist. However, in fact, the formula for this fundamental relation, in general, and the very definition of kinetic one-way fluxes in nonlinear chemical reaction networks, are still missing. 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. This work provides a concrete mathematical/physical basis for a long-hold belief in chemical kinetics. It gives an equivalent definition of the free energy difference in nonequilibrium chemical reaction networks and unifies the stochastic and macroscopic nonequilibrium chemical thermodynamics in a very broad setting.

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Section: B Kinetic Cycle Net Cycle Flux and One-way Cycle Fluxesmentioning

confidence: 99%

Section: B Kinetic Cycle Net Cycle Flux and One-way Cycle Fluxesmentioning

confidence: 99%

“…The steady-state mesoscopic entropy production rate (mesoEPR) in the counting space can be expressed by all the cycle fluxes [16]…”

Section: Steady-state Entropy Production Ratementioning

confidence: 99%

Section: Appendix B: Expressions Of Cycle Fluxes and Cycle Decompositmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Universal relation between thermodynamic driving force and one-way fluxes in a nonequilibrium chemical reaction with complex mechanism

Peng

Qian

Beard

et al. 2020

Phys. Rev. Research

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Universal Relation Between Thermodynamic Driving Force and One-Way Fluxes in a Nonequilibrium Chemical Reaction with Complex Mechanism

Peng,

Qian,

Beard

et al. 2019

Preprint

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In nonequilibrium chemical reaction systems, a fundamental relationship between unbalanced kinetic oneway 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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The limit of mesoscopic one-way fluxes in a nonequilibrium chemical reaction with complex mechanism

Chen¹,

Gao²,

Qiao³

et al. 2021

Preprint

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Peng et al. (2020) formulated one-way fluxes for a general chemical reaction far from equilibrium, with arbitrary complex mechanisms, multiple intermediates, and internal kinetic cycles. Species are classified into internal Y ′ s and external X ′ s. They defined the limit of mesoscopic one-way fluxes when the volume of the tank reactor tends to infinity as macroscopic one-way fluxes, but a rigorous proof of existence of the limit is still awaiting. In this article, we fill this gap under a mild hypothesis: the Markov chain associated with the chemical master equation has finite states and any two rows in the stoichiometric matrices for the internal species Y ′ s are not identical. In fact, an explicit expression of the limit is obtained.

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2 Circulation Distribution, Entropy Production and Irreversibility of Finite Markov Chains with Continuous Parameter

Cited by 3 publications

References 0 publications

Universal relation between thermodynamic driving force and one-way fluxes in a nonequilibrium chemical reaction with complex mechanism

Universal relation between thermodynamic driving force and one-way fluxes in a nonequilibrium chemical reaction with complex mechanism

Universal Relation Between Thermodynamic Driving Force and One-Way Fluxes in a Nonequilibrium Chemical Reaction with Complex Mechanism

The limit of mesoscopic one-way fluxes in a nonequilibrium chemical reaction with complex mechanism

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