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A probable probability distribution of a series nonequilibrium states in a simple system out of equilibrium

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  • Gao, Haixia
  • Li, Ting
  • Xiao, Changming

Abstract

When a simple system is in its nonequilibrium state, it will shift to its equilibrium state. Obviously, in this process, there are a series of nonequilibrium states. With the assistance of Bayesian statistics and hyperensemble, a probable probability distribution of these nonequilibrium states can be determined by maximizing the hyperensemble entropy. It is known that the largest probability is the equilibrium state, and the far a nonequilibrium state is away from the equilibrium one, the smaller the probability will be, and the same conclusion can also be obtained in the multi-state space. Furthermore, if the probability stands for the relative time the corresponding nonequilibrium state can stay, then the velocity of a nonequilibrium state returning back to its equilibrium can also be determined through the reciprocal of the derivative of this probability. It tells us that the far away the state from the equilibrium is, the faster the returning velocity will be; if the system is near to its equilibrium state, the velocity will tend to be smaller and smaller, and finally tends to 0 when it gets the equilibrium state.

Suggested Citation

  • Gao, Haixia & Li, Ting & Xiao, Changming, 2016. "A probable probability distribution of a series nonequilibrium states in a simple system out of equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 354-358.
    • Handle: RePEc:eee:phsmap:v:450:y:2016:i:c:p:354-358
    DOI: 10.1016/j.physa.2015.12.119
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