Microscopic expression of entransy

Boltzmann found that a proportional relation exists between the entropy and the logarithm of the microstate number in an approximate non-interaction particle system. The relation was expressed as the Boltzmann's entropic equation by Planck later. Boltzmann's work gives a microphysical interpretation of entropy. In this paper, a microscopic expression of entransy is introduced for an ideal gas system of monatomic molecules. The changes of the microstate number, the entropy and the entransy of the system are analyzed and discussed for an isolated ideal gas system of monatomic molecules going through the initial stage of unequilibriun thermal state to the thermal equilibrium state. It is found that the microstate number and the entropy always increase in the process, while the entransy decreases. The microstate number is a basic physical quantity which could measure the disorder degree of the system. The irreversibility of a thermal equilibrium process is attributed to the increase in microstate number. Entropy and entransy both are single value functions of the microstate number and they both could reflect the change of the state for the system. Therefore, both entropy and entransy could describe the irreversibility of thermal processes.