可微动力系统中熵流率与 Lyapunov 指数的谱界
Spectral bounds on the entropy flow rate and Lyapunov exponents in differentiable dynamical systems
AI总结：
本文利用经典密度矩阵与局部稳定性矩阵的谱性质，推导确定性恒温多粒子系统熵流率、Lyapunov 指数及输运系数的可计算上下界，并以电场中带电粒子的电导率为例说明。
摘要：
某些微观动力学在宏观上也是不可逆的，会耗散能量并产生熵。对于与确定性恒温器相互作用的多粒子系统，耗散到环境中的热力学熵速率等于相空间收缩的平均速率。本文利用这一等式以及经典密度矩阵的性质，借助局部稳定性矩阵的谱特性，推导出熵流率的上界和下界。这些界是对连续时间动力系统中 Lyapunov 指数和相空间收缩率更基本界的推广。它们表示由系统的底层动力学和确定性恒温器所设定的熵产生、传热及输运系数的最大和最小速率。由于这些宏观耗散极限源自密度矩阵和局部稳定性矩阵，因此可通过分子动力学进行数值计算。作为示例，我们证明这些界适用于受电场作用的带电粒子系统的电导率。
英文摘要：
Some microscopic dynamics are also macroscopically irreversible, dissipating energy and producing entropy. For many-particle systems interacting with deterministic thermostats, the rate of thermodynamic entropy dissipated to the environment is the average rate at which phase space contracts. Here, we use this identity and the properties of a classical density matrix to derive upper and lower bounds on the entropy flow rate with the spectral properties of the local stability matrix. These bounds are an extension of more fundamental bounds on the Lyapunov exponents and phase space contraction rate of continuous-time dynamical systems. They are maximal and minimal rates of entropy production, heat transfer, and transport coefficients set by the underlying dynamics of the system and deterministic thermostat. Because these limits on the macroscopic dissipation derive from the density matrix and the local stability matrix, they are numerically computable from the molecular dynamics. As an illustration, we show that these bounds are on the electrical conductivity for a system of charged particles subject to an electric field.
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