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Irreversibility is one of the most intriguing concepts in physics. Whilemicroscopic physical laws are perfectly reversible, macroscopic averagebehavior has a preferred direction of time. According to the second law ofthermodynamics, this arrow of time is associated with a positive mean entropyproduction. Using a nuclear magnetic resonance setup, we measure thenonequilibrium entropy produced in an isolated spin-1/2 system following fastquenches of an external magnetic field and experimentally demonstrate that itis equal to the entropic distance, expressed by the Kullback-Leiblerdivergence, between a microscopic process and its time-reverse. Our resultaddresses the concept of irreversibility from a microscopic quantum standpoint.

Irreversibility and the arrow of time in a quenched quantum system