Nonequilibrium inhomogeneous processes: a nonlinear stochastic description

Abstract

An alternative interpretation of the Langevin-type stochastic equation has been established. As an obvious, simple and natural alternative to both Ito's and Stratonovich's rules, the present interpretation rule has never before been reported. Under the new rule, an equivalent nonlinear stochastic description of the master equation for the general inhomogeneous process under the condition of small transition lengths is obtained. The advantage of the present interpretation over the existing ones is that under the present rule, the nonlinear Langevin equation for an inhomogeneous nonequilibrium process has exactly the same form as the linear one corresponding to its relevant homogeneous process. Therefore, under the condition of small transition lengths, a simple approach for obtaining the mesoscopic descriptions of an inhomogeneous process from the ones known for the relevant homogeneous process is established.