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Condensed Matter > Statistical Mechanics
Title: First passage time of a given level and value of overjump for fluctuations of trajectory observables
(Submitted on 26 Jun 2023 (v1), last revised 14 Nov 2023 (this version, v6))
Abstract: The process of fluctuations of trajectory observables of stochastic systems is associated with processes with independent increments from the risk theory. Boundary problems are considered: first-passage times (times when a certain value of the variable is first reached), overjumps at the moments of the first-passage times to reach positive and negative levels. A correspondence between the expressions of the theory of random processes and thermodynamics of trajectories is established, as well as deviations from such a correspondence for the process of fluctuations of trajectory observables. Relations between the general regularities of the 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, the possibilities of combining the approaches of the theory of random processes and statistical physics are indicated.
Submission history
From: Vasiliy Ryazanov [view email][v1] Mon, 26 Jun 2023 12:56:36 GMT (492kb)
[v2] Tue, 27 Jun 2023 19:41:59 GMT (497kb)
[v3] Wed, 5 Jul 2023 10:44:17 GMT (501kb)
[v4] Mon, 23 Oct 2023 15:54:16 GMT (505kb)
[v5] Fri, 10 Nov 2023 10:45:30 GMT (539kb)
[v6] Tue, 14 Nov 2023 17:40:44 GMT (537kb)
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