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Temporal disorder and fluctuation theorem in chemical reactions David Andrieux and Pierre Gaspard

Summary: Temporal disorder and fluctuation theorem in chemical reactions
David Andrieux and Pierre Gaspard
Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles,
Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium
Received 10 January 2008; published 28 March 2008
We report the analytical study of a class of chemical reactions described as birth-and-death stochastic
processes ruled by a master equation compatible with the mass action law of chemical kinetics. We solve
analytically this master equation to find the generating functions of the fluctuating fluxes and of the Lebowitz-
Spohn action functional. These generating functions are explicitly shown to obey fluctuation theorems. In the
case of fluxes, we derive relations for the nonlinear response coefficients, extending Onsager's reciprocity
relations. Moreover, symmetry relations reminiscent of the fluctuation theorem are obtained for the finite-time
probability distributions of the fluxes. The temporal disorder of the stochastic process is also characterized and
related to the thermodynamic entropy production.
DOI: 10.1103/PhysRevE.77.031137 PACS number s : 05.70.Ln, 02.50.Ey, 82.60. s
Chemical reactions are dynamical processes evolving on
several scales. At the microscopic level, a reacting system is
composed of molecules of different species involved in in-
elastic collisions. During such collisions, the reactant mol-
ecules meet and form a transition complex, which thereafter


Source: Andrieux, David - Service de Physique Non-Linéaire and Mécanique Statistique, Université Libre de Bruxelles


Collections: Physics; Biology and Medicine