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Novel dissipative properties of the master equation
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When the detailed balance condition is satisfied, the master equation is equivalent to Kirchoff’s law of the RC circuit, where pi is the charge on the ith capacitor, μi is the capacitance of the ith capacitor, and μiqij is the conductivity between the ith and jth capacitors.
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Recent studies have shown that the entropy production rate for the master equation consists of two non-negative terms: the adiabatic and non-adiabatic parts, where the non-adiabatic part is also known as the free energy dissipation rate. In this paper, we present some nonzero lower bounds for the free energy, the entropy production rate, and its adiabatic and non-adiabatic parts. These nonzero lower bounds not only reveal some novel dissipative properties for nonequilibrium dynamics which are much stronger than the second law of thermodynamics, but also impose some new constraints on thermodynamic constitutive relations. Moreover, we also give a mathematical application of the 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 free energy and its dissipation rate.
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