  Most natural and engineered processes, such as biomolecular reactions,
protein folding, and population dynamics, occur far from equilibrium and,
therefore, cannot be treated within the framework of classical equilibrium
thermodynamics. The Jarzynski equality holds the promise to calculate the
free-energy difference between two states from the Boltzmann-weighted
statistics of the irreversible work done along trajectories arbitrarily out of
equilibrium. This equality is the subject of intense activity. However, the
applicability of the Jarzynski equality to systems far from equilibrium such as
living matter has not been investigated yet. We present an experimental test of
the Jarzynski equality predictions on a paradigmatic physical model, i.e. a
Brownian particle held in an optical potential, coupled either to a thermal
bath or to an active bath. While in the thermal bath we find that the Jarzynski
equality correctly retrieves the free-energy difference from nonequilibrium
measurements, in the active bath the Jarzynski equality fails because of the
presence of non-Boltzmann statistics. We corroborate our experimental findings
with theoretical arguments and numerical simulations.
