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Abstract: Theoretical studies of nonequilibrium systems are complicated by the lack ofa general framework. In this work we first show that a transformationintroduced by Ao recently J. Phys. A {\bf 37}, L25 2004 is related toprevious works of Graham Z. Physik B {\bf 26}, 397 1977 and Eyink {\it etal.} J. Stat. Phys. {\bf 83}, 385 1996, which can also be viewed as thegeneralized application of the Helmholtz theorem in vector calculus. We thenshow that systems described by ordinary stochastic differential equations withwhite noise can be mapped to thermostated Hamiltonian systems. A steady-stateof a dissipative system corresponds to the equilibrium state of thecorresponding Hamiltonian system. These results provides a solid theoreticalground for corresponding studies on nonequilibrium dynamics, especially onnonequilibrium steady state. The mapping permits the application of establishedtechniques and results for Hamiltonian systems to dissipative non-Hamiltoniansystems, those for thermodynamic equilibrium states to nonequilibrium steadystates. We discuss several implications of the present work.



Author: Jianhua Xing

Source: https://arxiv.org/







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