非平衡态统计物理的随机数学理论

Stochastic Theory of Nonequilibrium Statistical Physics

非平衡态热力学和统计物理理论从20世纪70至80年代开始进入了蓬勃发展的阶段,特别是其中的随机模型可以用来描述亚宏观尺度的生物物理过程,恰好契合了现代物理化学和生物化学高精度实验技术的发展潮流.本文将回顾过去三十多年里非平衡态统计物理随机数学理论的发展,包括非平衡态热力学理论的起源、非平衡定态的随机数学理论、非平衡暂态的随机数学理论以及非平衡定态的初步相变理论等.在这套随机数学理论中,随机过程的时间可逆性、熵产生率和环流是最核心的概念,而寻求在随机轨道层面热力学第一定律和第二定律的对应形式是最重要的目标.这套数学物理理论能够很好地被应用于细胞层面重要的生物化学过程,通过严格的数学论证探寻其中重要的规律,以期对处于非平衡态的生命现象得到更深刻的认识和理解.

Nonequilibrium thermodynamics and statistical physics entered a stage of vig- orous development since 1970s. The stochastic models involved can be used to describe the mesoscopic-scale biophysical processes, which well fit the development of advanced experimental techniques in modern physical chemistry and biochemistry. This paper reviews the stochastic theory of non-equilibrium statistical physics in the past more than thirty years, including the origin of nonequilibrium thermodynamics, nonequilibrium-steady-state theory, nonequilibrium- transient-state theory, nonequilibrium-phase-transition theory, and so on. The time reversibility of stochastic processes, entropy production and circulation are the central concepts within such a stochastic theory, and the most important goals here are to pursue the corresponding expressions of the first law and the second law of thermodynamics. This branch of mathematical physics can be applied to the important biochemical processes at the cellular and subcellular levels, both exploring novel results and achieving deeper understanding for nonequilibrium phenomenon of living entities.