We slightly extend the fluctuation theorem obtained in \cite{LS} for sums of generators, considering continuous-time Markov chains on a finite state space whose underlying graph has multiple edges and no loop. This extended frame is suited when analyzing chemical systems. As simple corollary we derive in a different method the fluctuation theorem of D. Andrieux and P. Gaspard for the fluxes along the chords associated to a fundamental set of oriented cycles \cite{AG2}.
We associate to each random trajectory an oriented cycle on the graph and we decompose it in terms of a basis of oriented cycles. We prove a fluctuation theorem for the coefficients in this decomposition. The resulting fluctuation theorem involves the cycle affinities, which in many real systems correspond to the macroscopic forces. In addition, the above decomposition is useful when analyzing the large deviations of additive functionals of the Markov chain. As example of application, in a very general context we derive a fluctuation relation for the mechanical and chemical currents of a molecular motor moving along a periodic filament.
Entropic Fluctuation Theorems for the Spin-Fermion Model
Institut de Mathématiques de Toulouse, UMR5219Université de Toulouse, CNRS, UPS IMT（图卢兹数学研究所）；Département de Mathématiques, CNRS UMR 8088Cergy Paris Université（塞吉巴黎大学）；Dipartimento di MatematicaPolitecnico di Milano（米兰理工大学）；Université de Toulon, CNRS, CPT, UMR 7332（土伦大学）；Aix-Marseille Université, CNRS, CPT, UMR 7332（艾克斯-马赛大学）
Entropic fluctuations in XY chains and reflectionless Jacobi matrices
We study the entropic fluctuations of a general XY spin chain where initially the left(x<0)/right(x>0) part of the chain is in thermal equilibrium at inverse temperature Tl/Tr. The temperature differential results in a non-trivial energy/entropy flux across the chain. The Evans-Searles (ES) entropic functional describes fluctuations of the flux observable with respect to the initial state while the Gallavotti-Cohen (GC) functional describes these fluctuations with respect to the steady state (NESS) the chain reaches in the large time limit. We also consider the full counting statistics (FCS) o…
