Orthogonality of fluxes in general nonlinear reaction networks

D. R. Michiel Renger; Johannes Zimmer

doi:10.3934/dcdss.2020346

Article Contents

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

This issue Previous Article Global Hopf bifurcation in networks with fast feedback cycles Next Article Weak sequential stability for a nonlinear model of nematic electrolytes

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: July 1, 2019

Revised: November 1, 2019

Early access: May 12, 2020

Published online: January 1, 2021

Abstract / Introduction Full Text(HTML) Related Papers Cited by

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.

Keywords:

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

Citation:

Full Text(HTML)

Related Papers

Cited by

References

[1]	S. Adams, N. Dirr, M. Peletier and J. Zimmer, Large deviations and gradient flows, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 371 (2013), 17pp. doi: 10.1098/rsta.2012.0341.
[2]	D. F. Anderson and T. G. Kurtz, Continuous time Markov chain models for chemical reaction networks, in Design and Analysis of Biomolecular Circuits, Springer, NY, 2011, 3–42. doi: 10.1007/978-1-4419-6766-4_1.
[3]	L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio and C. Landim, Macroscopic fluctuation theory, Rev. Modern Phys., 87 (2015), 593-636. doi: 10.1103/RevModPhys.87.593.
[4]	B. Hilder, M. A. Peletier, U. Sharma and O. Tse, An inequality connecting entropy distance, Fisher Information and large deviations, Stochastic Process. Appl., 130 (2020), 2596-2638. doi: 10.1016/j.spa.2019.07.012.
[5]	M. Kaiser, R. L. Jack and J. Zimmer, Canonical structure and orthogonality of forces and currents in irreversible Markov chains, J. Stat. Phys., 170 (2018), 1019-1050. doi: 10.1007/s10955-018-1986-0.
[6]	T. G. Kurtz, Solutions of ordinary differential equations as limits of pure jump Markov processes, J. Appl. Probability, 7 (1970), 49-58. doi: 10.2307/3212147.
[7]	C. Maes, Frenetic bounds on the entropy production, Phys. Rev. Lett., 119 (2017). doi: 10.1103/PhysRevLett.119.160601.
[8]	C. Maes and K. Netočný, Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states, Europhys. Lett. EPL, 82 (2008), 6pp. doi: 10.1209/0295-5075/82/30003.
[9]	A. Mielke, R. I. A. Patterson, M. A. Peletier and D. R. M. Renger, Non-equilibrium thermodynamical principles for chemical reactions with mass-action kinetics, SIAM J. Appl. Math., 77 (2017), 1562-1585. doi: 10.1137/16M1102240.
[10]	A. Mielke, M. A. Peletier and D. R. M. Renger, On the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusion, Potential Anal., 41 (2014), 1293-1327. doi: 10.1007/s11118-014-9418-5.
[11]	L. Onsager and S. Machlup, Fluctuations and irreversible processes, Phys. Rev. (2), 91 (1953), 1505-1512. doi: 10.1103/PhysRev.91.1505.
[12]	R. I. A. Patterson and D. R. M. Renger, Large deviations of jump process fluxes, Math. Phys. Anal. Geom., 22 (2019), 32pp. doi: 10.1007/s11040-019-9318-4.
[13]	D. R. M. Renger, Flux large deviations of independent and reacting particle systems, with implications for macroscopic fluctuation theory, J. Stat. Phys., 172 (2018), 1291-1326. doi: 10.1007/s10955-018-2083-0.
[14]	D. R. M. Renger, Gradient and GENERIC systems in the space of fluxes, applied to reacting particle systems, Entropy, 20 (2018). doi: 10.3390/e20080596.
[15]	J. Schnakenberg, Network theory of microscopic and macroscopic behavior of master equation systems, Rev. Modern Phys., 48 (1976), 571-585. doi: 10.1103/RevModPhys.48.571.