Orthogonality of fluxes in general nonlinear reaction networks

D. R. Michiel Renger; Johannes Zimmer

doi:10.3934/dcdss.2020346

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2021, Volume 14, Issue 1: 205-217. Doi: 10.3934/dcdss.2020346

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Orthogonality of fluxes in general nonlinear reaction networks

D. R. Michiel Renger^1, and
Johannes Zimmer^2,

1.
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany
2.
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, United Kingdom

Dedicated, in gratitude, to Alex Mielke on the occasion of his 60th birthday

Received: June 30, 2019

Revised: October 31, 2019

Early access: May 2020

Published: January 2021

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Abstract

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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Mathematics Subject Classification: Primary: 82C35; Secondary: 82C31, 60J27.

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