Arcsine Laws in Stochastic Thermodynamics

Abstract

We show that the fraction of time a thermodynamic current spends above its average value follows the arcsine law, a prominent result obtained by Lévy for Brownian motion. Stochastic currents with long streaks above or below their average are much more likely than those that spend similar fractions of time above and below their average. Our result is confirmed with experimental data from a Brownian Carnot engine. We also conjecture that two other random times associated with currents obey the arcsine law: the time a current reaches its maximum value and the last time a current crosses its average value. These results apply to, inter alia, molecular motors, quantum dots and colloidal systems.

11 pages, 11 figures

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Cited by in corpus (14)

• Generalised `Arcsine' laws for run-and-tumble particle in one dimension
• Distribution of the time of the maximum for stationary processes
• Time between the maximum and the minimum of a stochastic process
• Distribution of the Time Between Maximum and Minimum of Random Walks
• Extreme value statistics and arcsine laws for heterogeneous diffusion processes
• Arcsine Law and Multistable Brownian Dynamics in a Tilted Periodic Potential
• Aging arcsine law in Brownian motion and its generalization
• Occupation time of a system of Brownian particles on the line with steplike initial condition
• Experimental verification of Arcsine laws in mesoscopic non-equilibrium and active systems
• Gambling Carnot Engine
• Generalized arcsine laws for a sluggish random walker with subdiffusive growth
• Exact joint distributions of three global characteristic times for Brownian motion
• Heat Transport Hysteresis Generated through Frequency Switching of a Time-Dependent Temperature Gradient
• Short-time large deviations of first-passage functionals for high-order stochastic processes