Fluctuation Theorem For Low-dimensional Nonlinear Lattices

We studied the non-equilibrium steady state fluctuation theorem and the transient fluctuation theorem of the nonlinear interaction system.For the non-equilibrium steadystate fluctuation theorem,we use the one-dimensional FPU-β chain and the one-dimensionalΦ4 chain coupled with two thermal reservoirs of different temperatures as the physical model to study the fluctuating nature of main functional,total entropy production and environmental entropy production.Through numerical simulation and theoretical analysis,we found that the non-equilibrium steady-state distribution of the nonlinear interaction system does not satisfy the time reversal symmetry.Therefore,unlike the main functional,the total entropy production does not conform to the steady-state fluctuation theorem in a finite time window.It also shows that the total entropy production is not equivalent to the main functional.Through the exponential decay property of the probability distribution of the fluctuation of the boundary term of the main functional,we discuss the range of the fluctuation of environmental entropy in the long-term limit in accordance with the traditional steady-state fluctuation theorem.By numerically calculating the fluctuations produced by environmental entropy in different time windows,we find that for systems with different nonlinear strengths and sizes,the consistency of the generalized steady-state fluctuation theorem produced by environmental entropy as the time window increases monotonically approaches the traditional one.Fluctuation theorem,and the greater the distance from the equilibrium state,the faster it approaches the traditional fluctuation theorem.For the transient fluctuation theorem,we take the one-dimensional FPU-β chain as the physical model,and proceed from the generalized form of the fluctuation theorem to analyze the transient process of a one-dimensional nonlinear interaction system that introduces external disturbances.The physical quantities(work,main functional,and total entropy production)conform to the time-reversed odd symmetry(the initial states of the transient processes we studied are all equilibrium states),so that these physical quantities conform to the generalized fluctuation theorem.And according to the introduction of disturbance properties,we analyze and discuss the manifestation of the transient fluctuation relationship of different physical quantities.