Finite-time fluctuation theorem for oscillatory lattices driven by a temperature gradient.

Abstract

The finite-time fluctuation theorem (FT) for the master functional, total entropy production, and medium entropy is studied in the one-dimensional Fermi-Pasta-Ulam-Tsingou-β (FPUT-β) chain coupled with two heat reservoirs at different temperatures. Through numerical simulations and theoretical analysis, we find that the nonequilibrium steady-state distribution of the one-dimensional FPUT-β chain violates the time-reversal symmetry. Thus, unlike the master functional, the total entropy production fails to satisfy the fluctuation relation for finite time. Meanwhile, we discuss the range of medium entropy production which obeys the conventional steady-state fluctuation theorem (SSFT) in the infinite time limit. Furthermore, we find that the generalized SSFT for medium entropy monotonically approaches the conventional SSFT as the time interval increases, irrespective of temperature difference, anharmonicity, and system size. Interestingly, the medium entropy production rate shows a nonmonotonic variation with anharomonicity, which comes from a competition mechanism of the phonon transport. Correspondingly, the difference between the generalized SSFT and the conventional SSFT shows similar nonmonotonic behaviors.