A Novel Dissipation Property of the Master Equation

Liu Hong Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, P.R. China Chen Jia Beijing Computational Science Research Center, Beijing 100094, P.R. China Yi Zhu Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, P.R. China Wen-An Yong Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, P.R. China

TBD mathscidoc:2204.43008

2015.11
Recent studies have shown that the entropy production rate for the master equation consists of two nonnegative terms: the adiabatic and non-adiabatic parts, where the non-adiabatic part is also known as the dissipation rate of a Boltzmann-Shannon relative entropy. In this paper, we provide some nonzero lower bounds for the relative entropy, the entropy production rate, and its adiabatic and non-adiabatic parts. These nonzero lower bounds not only reveal some novel dissipative properties for general nonequilibrium processes which are much stronger than the second law of thermodynamics, but also impose some new constraints on thermodynamic constitutive relations. Moreover, we also provide a mathematical application of these nonzero lower bounds by studying the long-time behavior of the master equation. Extensions to the Tsallis statistics are also discussed, including the nonzero lower bounds for the Tsallis-type relative entropy and its dissipation rate.
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@inproceedings{liu2015a,
  title={A Novel Dissipation Property of the Master Equation},
  author={Liu Hong, Chen Jia, Yi Zhu, and Wen-An Yong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220421114046081349084},
  year={2015},
}
Liu Hong, Chen Jia, Yi Zhu, and Wen-An Yong. A Novel Dissipation Property of the Master Equation. 2015. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220421114046081349084.
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