Fluctuation-dissipation relations for steady-state systems

¹ Virginia Polytechnic Institute and State University - Blacksburg, VA, 24061-0406, USA
² State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences P. O. Box 2735, Beijing 100190, China
³ Kavli Institute for Theoretical Physics China, Chinese Academy of Sciences P. O. Box 2735, Beijing 100190, China
⁴ Center for Advanced Study, Tsinghua University - Beijing 100084, China

^(a) jxing@vt.edu

Received: 23 July 2012
Accepted: 21 September 2012

Abstract

The fluctuation-dissipation (FD) theorem is a fundamental result for systems near thermodynamic equilibrium. It states that the nonequilibrium relaxation dynamics is related to the spontaneous fluctuation at equilibrium. Recently we have shown that the dynamics of a dissipative system described by stochastic differential equations can be mapped to that of a thermostated Hamiltonian system, with a nonequilibrium steady state of the former corresponding to the equilibrium state of the latter. In present manuscript, the corresponding FD theorem is derived in the way parallel to the procedure for deriving the near equilibrium FD theorem, based on this mapping. The analytical results in the present approach are in good agreement with numerical results. We find some previous results are special cases of the current relations. We also suggest further studies exploiting the analogy between a general dissipative system appearing in other science branches and a Hamiltonian system.