首页>
外文OA文献
>Mathematical foundation of nonequilibrium fluctuation–dissipation theorems for inhomogeneous diffusion processes with unbounded coefficients
【2h】
Mathematical foundation of nonequilibrium fluctuation–dissipation theorems for inhomogeneous diffusion processes with unbounded coefficients
Nonequilibrium fluctuation-dissipation theorems (FDTs) are one of the mostimportant advances in stochastic thermodynamics over the past two decades. Herewe provide a rigourous mathematical theory of two types of nonequilibrium FDTsfor inhomogeneous diffusion processes with unbounded drift and diffusioncoefficients by using the Schauder estimates for partial differential equationsof parabolic type and the theory of weak generators. The FDTs proved in thispaper apply to any forms of nonlinear external perturbations. Furthermore, weprove the uniqueness of the conjugate observables and clarify the precisemathematical conditions and ranges of applicability for the two types of FDTs.Examples are also given to illustrate the main results of this paper.
展开▼
