Fluctuation symmetry in a two-state Markov model

Abstract

We show that the scaled cumulant generating and large deviation function, associated to a two-state 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.

arXiv comment4 pages, 3 figures

References in corpus (6)

• The large deviation approach to statistical mechanics
• Fluctuation theorems for stochastic dynamics
• Thermoelectric efficiency at maximum power in a quantum dot
• Fluctuation theorem and large deviation function for a solvable model of a molecular motor
• Fluctuation theorem for the effusion of an ideal gas
• Thermodynamics of a stochastic twin elevator

Cited by in corpus (5)

• Stochastic Efficiency: Five Case Studies
• Echo states for detailed fluctuation theorems
• Comment on "Generalized exclusion processes: Transport coefficients"
• Stochastic thermodynamics for Ising chain and symmetric exclusion process
• Stochastic functionals and fluctuation theorem for the multi-kangaroo process