Fluctuation symmetry in a two-state Markov model

Abstract

We show that the scaled cumulant generating and large deviation function, associated to a twostate Markov process involving two processes, obey a symmetry relation reminiscent of the fluctuation theorem, independent from any conditions on the transition rates. The Legendre transform leading from the scaled cumulant generating function to the large deviation function is performed in an ingenious way, avoiding the sign problem associated to taking a square root. Applications to the theory of random walks and to the stochastic thermodynamics for a quantum dot are presented.PACS. 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion -05.70.Ln Nonequilibrium and irreversible thermodynamics

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