Arcsine Laws in Stochastic Thermodynamics

Area of Science:

• Statistical mechanics
• Non-equilibrium thermodynamics
• Stochastic processes

Background:

• Brownian motion and stochastic processes are fundamental in physics.
• Understanding the behavior of thermodynamic currents is crucial for analyzing energy conversion in small systems.
• The arcsine law, a key result from Lévy, describes specific behaviors in Brownian motion.

Purpose of the Study:

• To investigate the statistical properties of thermodynamic currents.
• To determine if the arcsine law applies to thermodynamic currents.
• To explore the implications of these findings for various nanoscale systems.

Main Methods:

• Theoretical analysis of stochastic currents.
• Application of Lévy's arcsine law to thermodynamic processes.
• Experimental validation using a Brownian Carnot engine.

Main Results:

• The fraction of time a thermodynamic current spends above its average value follows the arcsine law.
• Stochastic currents are more likely to exhibit long persistent streaks above or below their average.
• Experimental data from a Brownian Carnot engine confirmed the theoretical predictions.

Conclusions:

• The arcsine law governs the temporal behavior of thermodynamic currents.
• This universality extends beyond Brownian motion to systems like molecular motors, quantum dots, and colloidal systems.
• Further conjectures suggest the arcsine law also applies to the first passage time and last passage time of currents.