Right Type Departmental Bulletin Paper

For systems in equilibrium ， it has been established as the βuctuαtion-dissipαtion theorem that the magnitude of fluctuations is equal to the the response function against a small perturbation multiplied by. the temperature of the system. On the other hand ， for systems maintained at a non-equilibrium steady state by external driving forces ， ithas been realized that the similar relation does not hold in general even in an isothermal case. In the present paper ， we show that there is an equality betweeen an extent of violation of the fluctuation-dissipation relation (FDR) and the rate of energy dissipation into the environment for non-equilibrium systems that can be described by La時evinequations [1]. As a simple example ， we consider a system where N spherical colloidal particles in a three dimensional aqueous solution are driven by an constant external force f ex [2]. Let us denote the coordinat 邸 ofthe particles by r = {ぬ}(i ニ 0， ・ ，3N-1) ， where 九 三 (X3μ，X3μ+1，X3μ+2) represents the position of the j.t-th particle (μ ニ 0， ・ ，N-1). Then ， a widely used model describing the motion of the particles is provided as [3] γぬ(t) = Fdr(t)) +ふ(t)+εff(t) ， 、 ? ， ， ， ， ，?? ， ，? 、 、 where γis the企ictioncoefficient of a particle an