# Fluctuation theorems for discrete kinetic models of molecular motors

## TL;DR

This paper establishes fluctuation theorems and Gallavotti-Cohen symmetry for large deviations in discrete kinetic models of molecular motors, extending previous matrix approaches to non-Markovian and non-cooperative random walks on quasi 1D lattices.

## Contribution

It introduces a class of quasi 1D lattice models where fluctuation theorems hold, extending existing matrix methods to non-Markovian and non-cooperative stochastic processes.

## Key findings

- Gallavotti-Cohen symmetry holds for a broad class of quasi 1D lattice models.
- Fluctuation theorems are derived for time-integrated cycle currents.
- Explicit examples with computations illustrate the theoretical results.

## Abstract

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 \cite{LLM1}. We also derive fluctuation theorems for the time-integrated cycle currents and discuss how the matrix approach of \cite{LLM1} can be extended to derive the above Gallavotti-Cohen symmetry for any Markov random walk on $\mathbb{Z}$ with periodic jump rates. Finally, we review in the present context some large deviation results of \cite{FS1} and give some specific examples with explicit computations.