Gradient and GENERIC Systems in the Space of Fluxes, Applied to Reacting Particle Systems

Renger, D. R. Michiel

doi:10.3390/e20080596

Cited by 11 publications

(17 citation statements)

References 36 publications

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“…Next, we introduce the Legendre duality between flux and force for CRNs 4 , and summarize their relation to entropy production. The specific type of convex function introduced here was recently derived in the Macroscopic Fluctuation Theorem (MFT) [30][31][32][33][34].…”

Section: Legendre Duality Of Flux-forcementioning

confidence: 99%

Geometry of Nonequilibrium Chemical Reaction Networks and Generalized Entropy Production Decompositions

Kobayashi¹,

Loutchko²,

Kamimura³

et al. 2022

Preprint

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We derive the Hessian geometric structure of nonequilibrium chemical reaction networks (CRN) 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 structure, we can extend theories of nonequilibrium systems with quadratic dissipation functions to more general ones with nonquadratic ones, which are pivotal for studying chemical reaction networks. By applying generalized notions of orthogonality in Hessian geometry to chemical reaction networks, we obtain two generalized decompositions of the entropy production rate, each of which captures gradient-flow and minimumdissipation aspects in nonequilibrium dynamics.

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Section: Legendre Duality Of Flux-forcementioning

confidence: 99%

Geometry of Nonequilibrium Chemical Reaction Networks and Generalized Entropy Production Decompositions

Kobayashi¹,

Loutchko²,

Kamimura³

et al. 2022

Preprint

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“…•ċ, so that the force is indeed conservative as anticipated in Remark 2.4. In this case, (3.8) describes a nonlinear gradient flow, either in the space of concentrations [9] or in the space of integrated net fluxes [14].…”

Section: Remark 33 If Chemical Detailed Balance ← −mentioning

confidence: 99%

Orthogonality of fluxes in general nonlinear reaction networks

Renger¹,

Zimmer

2021

Discrete &Amp; Continuous Dynamical Systems - S

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We consider the chemical reaction networks and study currents in these systems. Reviewing recent decomposition of rate functionals from large deviation theory for Markov processes, we adapt these results for reaction networks. In particular, we state a suitable generalisation of orthogonality of forces in these systems, and derive an inequality that bounds the free energy loss and Fisher information by the rate functional.

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“…For the reaction part, we use the gradient structure which has been derived via a large-deviation principle from a microscopic Markov process in [MPR14]. We refer also to [Ren18], where our choice of gradient structure has been formally derived.…”

Section: Gradient Structure For the Linear Reaction Systemmentioning

confidence: 99%

EDP-convergence for a linear reaction-diffusion system with fast reversible reaction

Stephan¹

2020

Preprint

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We perform a fast-reaction limit for a linear reaction-diffusion system consisting of two diffusion equations coupled by a linear reaction. We understand the linear reaction-diffusion system as a gradient flow of the free energy in the space of probability measures equipped with a geometric structure, which contains the Wasserstein metric for the diffusion part and cosh-type functions for the reaction part. The fast-reaction limit is done on the level of the gradient structure by proving EDP-convergence with tilting. The limit gradient system induces a diffusion system with Lagrange multipliers on the linear slow-manifold. Moreover, the limit gradient system can be equivalently described by a coarse-grained gradient system, which induces a diffusion equation with a mixed diffusion constant for the coarse-grained slow variable.

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Gradient and GENERIC Systems in the Space of Fluxes, Applied to Reacting Particle Systems

Cited by 11 publications

References 36 publications

Geometry of Nonequilibrium Chemical Reaction Networks and Generalized Entropy Production Decompositions

Geometry of Nonequilibrium Chemical Reaction Networks and Generalized Entropy Production Decompositions

Orthogonality of fluxes in general nonlinear reaction networks

EDP-convergence for a linear reaction-diffusion system with fast reversible reaction

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