A Gallavotti-Cohen-Evans-Morriss Like Symmetry for a Class of Markov Jump Processes

Andre Cardoso Barato (1) , Raphael Chetrite (2) , Haye Hinrichsen (3) , David Mukamel (4)

1 ICTP - Abdus Salam International Centre for Theoretical Physics [Trieste]
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 Fakultät für Physik und Astronomie [Würzburg]
4 Weizmann Institute

We investigate a new symmetry of the large deviation function of certain timeintegrated currents in non-equilibrium systems. The symmetry is similar to the well-known Gallavotti-Cohen-Evans-Morriss-symmetry for the entropy production, but it concerns a different functional of the stochastic trajectory. The symmetry can be found in a restricted class of Markov jump processes, where the network of microscopic transitions has a particular structure and the transition rates satisfy certain constraints. We provide three physical examples, where time-integrated observables display such a symmetry. Moreover, we argue that the origin of the symmetry can be traced back to time-reversal if stochastic trajectories are grouped appropriately.

Mots clés: Fluctuation relations; Jump processes; Large deviation theory

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Probabilités [math.PR]; Mécanique statistique [cond-mat.stat-mech]

Andre Cardoso Barato, Raphael Chetrite, Haye Hinrichsen, David Mukamel. A Gallavotti-Cohen-Evans-Morriss Like Symmetry for a Class of Markov Jump Processes. Journal of Statistical Physics, 2012, 146, pp.294-313. ⟨10.1007/s10955-011-0389-2⟩. ⟨hal-00762149⟩