Abstract: The fluctuations of master functional, total entropy production and medium entropy production of the one-dimensional nonlinear lattices coupled to two heat reservoirs at different temperatures are studied. The theoretical analysis reveals that the non-equilibrium steady state distribution of one-dimensional nonlinear lattices fail to satisfy the time reversal symmetry, which means that the total entropy production is inequivalent to the main functional. Thus the total entropy production fails to satisfy the steady-state fluctuation relation for finite time. Furthermore, through numerical simulations in one-dimensional φ⁴ lattices, we find that the generalized steady-state fluctuation theorem (SSFT) for medium entropy production monotonically approaches to the conventional SSFT as the time interval increases for any given temperature difference and nonlinearity. The stronger the irreversibility of the dynamical process, the faster the generalized SSFT approaches to the conventional SSFT.

Key words: steady-state fluctuation theorem, master functional, entropy production, finite time interval, heat conduction