Stochastic Dynamical Structure (SDS) of Nonequilibrium Processes in the Absence of Detailed Balance. III: potential function in local stochastic dynamics and in steady state of Boltzmann-Gibbs type distribution function

摘要: From a logic point of view this is the third in series to solve problem absence detailed balance. This paper will be denoted as SDS III. The existence dynamical potential with both local and global meanings general nonequilibrium processes has been controversial. Following an earlier explicit construction by one us (Ao, J. Phys. {\bf A37}, L25 '04, arXiv:0803.4356, referred II), present we show rigorously its for generic class situations physical biological sciences. meaning function demonstrated via special stochastic differential equation steady-state novel form Fokker-Planck equation, zero mass limit. We also give procedure obtain any given equation. No balance condition required our demonstration. For first time here formula describe noise induced shift drift force comparing steady state distribution, phenomenon extensively observed numerical studies. comparison two well known integration methods, Ito Stratonovich, are made ready. Such was elsewhere Life Rev. 2} (2005) 117. q-bio/0605020).