  Irreversibility is one of the most intriguing concepts in physics. While
microscopic physical laws are perfectly reversible, macroscopic average
behavior has a preferred direction of time. According to the second law of
thermodynamics, this arrow of time is associated with a positive mean entropy
production. Using a nuclear magnetic resonance setup, we measure the
nonequilibrium entropy produced in an isolated spin-1/2 system following fast
quenches of an external magnetic field and experimentally demonstrate that it
is equal to the entropic distance, expressed by the Kullback-Leibler
divergence, between a microscopic process and its time-reverse. Our result
addresses the concept of irreversibility from a microscopic quantum standpoint.
