SDE decomposition and A-type stochastic interpretation in nonequilibrium processes
SDE decomposition and A-type stochastic interpretation in nonequilibrium processes作者机构：Key Laboratory of Systems Biomedicine Ministry of Education Shanghai Center for Systems Biomedicine Shanghai Jiao Tong University Shanghai 200240 China Department of Physics and Astronomy Shanghai-Jiao Tong University Shanghai 200240 China
出 版 物：《Frontiers of physics》 (物理学前沿（英文版）)
年 卷 期：2017年第12卷第6期
页 面：1-9页
核心收录：
主 题：nonequilibrium statistical physics nonequilibrium potential Lyapunov function,nonlinear stochastic dynamics systems biology
摘 要：An innovative theoretical framework for stochastic dynamics based on the decomposition of a stochas- tic differential equation （SDE） into a dissipative component, a detailed-balance-breaking component, and a dual-role potential landscape has been developed, which has fruitful applications in physics, engineering, chemistry, and biology. It introduces the A-type stochastic interpretation of the SDE beyond the traditional Ito or Stratonovich interpretation or even the a-type interpretation for multi- dimensional systems. The potential landscape serves as a Hmniltonian-like function in nonequilibrimn processes without detailed balance, which extends this important concept from equilibrium statistical physics to the nonequilibrium region. A question on the uniqueness of the SDE decomposition was recently raised. Our review of both the mathematical and physical aspects shows that uniqueness is guaranteed. The demonstration leads to a better understanding of the robustness of the novel frame- work. In addition, we discuss related issues including the limitations of an approach to obtaining the potential function from a steady-state distribution.
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