Arcsine Laws in Stochastic Thermodynamics
We show that the fraction of time that a thermodynamic current spends above its average value follows
the arcsine law, a prominent result obtained by Levy 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.