Fluctuation theorems for discrete kinetic models of molecular motors

Motivated by discrete kinetic models for non-cooperative molecular motors on periodic tracks, we consider random walks (also not Markov) on quasi one dimensional (1d) lattices, obtained by gluing several copies of a fundamental graph in a linear fashion. We show that, for a suitable class of quasi-1d lattices, the large deviation rate function associated to the position of the walker satisfies a Gallavotti–Cohen symmetry for any choice of the dynamical parameters defining the stochastic walk. This class includes the linear model considered in Lacoste et al (2008 Phys. Rev. E 78 011915). We also derive fluctuation theorems for the time-integrated cycle currents and discuss how the matrix approach of Lacoste et al (2008 Phys. Rev. E 78 011915) can be extended to derive the above Gallavotti–Cohen symmetry for any Markov random walk on $Z$ with periodic jump rates. Finally, we review in the present context some large deviation results of Faggionato and Silvestri (2017 Ann. Inst. Henri Poincaré 53 46–78) and give some specific examples with explicit computations. (paper: classical statistical mechanics, equilibrium and non-equilibrium)