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-ro...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.展开更多
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. NSFC91329301 and NSFC9152930016） and grants from the State Key Laboratory of Oncogenes and Related Genes （Grant No. 90-10-11）.
文摘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.
