Computation of energy exchanges by combining information theory and a key thermodynamic relation: Physical applications

By considering a simple thermodynamic system, in thermal equilibrium at a temperature T and in the presence of an external parameter A, we focus our attention on the particular thermodynamic (macroscopic) relation dU=TdS+δW. Using standard axioms from information theory and the fact that the microscopic energy levels depend upon the external parameter A, we show that all usual results of statistical mechanics for reversible processes follow straightforwardly, without invoking the Maximum Entropy principle. For the simple system considered herein, two distinct forms of heat contributions appear naturally in the Clausius definition of entropy, TdS=δQ(T)+δQ(A)=CA(T)dT+CT(A)dA. We give a special attention to the amount of heat δQ(A)=CT(A)dA, associated with an infinitesimal variation dA at fixed temperature, for which a “generalized heat capacity”, CT(A)=T(∂S/∂A)T, may be defined. The usefulness of these results is illustrated by considering some simple thermodynamic cycles.