  The second law of thermodynamics is a fundamental law of Nature. It is almost
universally associated with the Clausius inequality that lower bounds a change
in entropy by the ratio of supplied heat and temperature. However, this result
presupposes that a system is in contact with a heat bath that drives it to a
thermal state. For isolated systems that are moved from an initial equilibrium
state by a dissipative heat exchange, the Clausius inequality has been
predicted to be reversed. We here experimentally investigate the nonequilibrium
thermodynamics of an isolated dilute gas of ultracold Cesium atoms that can be
either thermalized or pushed out of equilibrium by means of laser cooling
techniques. We determine in both cases the phase-space dynamics by tracing the
evolution of the gas with position-resolved fluorescence imaging, from which we
evaluate all relevant thermodynamic quantities. Our results confirm the
validity of the usual Clausius inequality for the first process and of the
reversed Clausius inequality for the second transformation.
