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First-passage time and change of entropy

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  • V. V. Ryazanov

    (Institute for Nuclear Research)

Abstract

The first-passage time is proposed as an independent thermodynamic parameter of the statistical distribution that generalizes the Gibbs distribution. The theory does not include the determination of the first-passage statistics itself. A random process is set that describes a physical phenomenon. The first-passage statistics is determined from this random process. The thermodynamic parameter conjugated to the first-passage time is the same as the Laplace transform parameter of the first-passage time distribution in the partition function. The corresponding partition function is divided into multipliers, one of which is associated with the equilibrium parameters, and the second one with the parameters of the first-passage time distribution. The thermodynamic parameter conjugated to the first-passage time can be expressed in terms of the deviation of the entropy from the equilibrium value. Thus, all moments of the distribution of the first-passage time are expressed in terms of the deviation of the entropy from its equilibrium value and the external forces acting on the system. By changing the thermodynamic forces, it is possible to change the first-passage time. Graphic abstract

Suggested Citation

  • V. V. Ryazanov, 2021. "First-passage time and change of entropy," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(12), pages 1-19, December.
    • Handle: RePEc:spr:eurphb:v:94:y:2021:i:12:d:10.1140_epjb_s10051-021-00246-0
    DOI: 10.1140/epjb/s10051-021-00246-0
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    References listed on IDEAS

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    1. Molini, A. & Talkner, P. & Katul, G.G. & Porporato, A., 2011. "First passage time statistics of Brownian motion with purely time dependent drift and diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 1841-1852.
    2. V. V. Ryazanov, 2009. "Lifetime distributions in the methods of non-equilibrium statistical operator and superstatistics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 72(4), pages 629-639, December.
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