  We show that the fraction of time a thermodynamic current spends above its
average value follows the arcsine law, a prominent result obtained by L\'evy
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.
