从达尔文动力学看非平衡统计力学和热力学
Nonequilibrium Statistical Mechanics and Thermodynamics from Darwinian Dynamics: a Primer
摘要：
本文探讨了达尔文动力学的物理意义.我们首先说明非平衡统计力学是如何自然产生的。证明了热力学的前三定律，即第零定律、第一定律和第二定律，除了第三定律外，都可以从达尔文动力学中得到遵循。无法推导出第三定律表明达尔文动力学属于“经典”领域。具体地说，第二定律是从动力学的角度证明的。本文详细讨论了两类电流动力学方程：一类是基于Feynman-Kac公式的方程，另一类是Einstein关系的推广。两者都可以直接进行实验测试。我们的论证表明，达尔文动力学在逻辑上是进入热力学的一个简单而直接的起点，是对物理学中占主导地位的保守动力学的补充。
英文摘要：
We present here an exploration on on the physical implications of the Darwinian dynamics. We first show that how the nonequilibrium statistical mechanics emerges naturally. We then show that the first three laws of the thermodynamics, the Zeroth Law, the First Law and the Second Law can be followed from the Darwinian dynamics, except the Third Law. The inability to derive the Third Law indicates that the Darwinian dynamics belongs to the "classical" domain. Specifically, the Second Law is proved from the dynamical point of view. Two types of current dynamical equalities are explicitly discussed in the paper: one is based on Feynman-Kac formula and one is a generalization of the Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that the Darwinian dynamics is logically a simple and straightforward starting point to get into thermodynamics and is complementary to the conservative dynamics dominated in physics.
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