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Relation between stochastic processes and thermodynamics of trajectories

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  • Ryazanov, V.V.

Abstract

The process of fluctuations of trajectory observables of stochastic systems is related to processes with independent increments from risk theory. The first-passage times of variables of the thermodynamics of trajectories, in particular, dynamic activity, are considered. A correspondence between expressions of the theory of random processes and thermodynamics of trajectories, as well as deviations from such a correspondence for the process of fluctuations of trajectory observables, are established. The connections between general regularities of first-passage times in the theory of random processes and thermodynamics of trajectories are discussed. A more complete use of the theory of random processes in physical problems is proposed, and the possibilities of combining approaches of the theory of random processes and statistical physics are indicated.

Suggested Citation

  • Ryazanov, V.V., 2025. "Relation between stochastic processes and thermodynamics of trajectories," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 674(C).
    • Handle: RePEc:eee:phsmap:v:674:y:2025:i:c:s0378437125004121
    DOI: 10.1016/j.physa.2025.130760
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Garrahan, Juan P., 2018. "Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 504(C), pages 130-154.
    4. Robert L. Jack, 2020. "Ergodicity and large deviations in physical systems with stochastic dynamics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(4), pages 1-22, April.
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