关于一维非线性晶格热传导的有限时间涨落定理

Finite-time Fluctuation Theorem for Heat Conduction in One-dimensional Nonlinear Lattices

研究了与两个不同温度的热库耦合的一维非线性晶格的主泛函、总熵产生与环境熵产生的涨落.通过理论分析发现一维非线性晶格处于非平衡稳态时其状态分布不满足时间反演对称性,这意味着总熵产生与主泛函不等价,因此总熵产生在有限时间窗口下不符合稳态涨落关系.对一维φ4模型的数值模拟计算结果表明,对于任意给定的温差和非线性,环境熵产生的广义稳态涨落定理(SSFT)随时间窗口的增大均单调趋近于传统SSFT,且动力学过程不可逆性越强,广义SSFT越快趋近于传统SSFT.

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 onedimensional 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 onedimensional 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.