Experimental verification of a reversed Clausius inequality in an isolated system

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.