Inequivalence of ensembles in statistical mechanics

Abstract

For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that all these ensembles may not yield the same results even in the thermodynamic limit except at high temperatures. An investigation of the coupling between systems suggest that the state of thermodynamic equilibrium is a special case of statistical equilibrium. As a byproduct of this analysis we have obtained a general form for probability density function in an interval.