Husimi function and Wehrl entropy in thermo field dynamics

Abstract

Using the quantum phase space technique and the information-theory like the Wehrl entropy, the Husimi function and the Wehrl entropy of the quantum pure states and the corresponding mixed states in thermo field dynamics are studied. It is found that the Husimi function and the Wehrl entropy of the thermal coherent state agree with that of the corresponding mixed states. And the Wehrl entropy of thermal coherent state is not related with the displacement factor. Therefore for a quantum system, the quantum fluctuations of the observable quantities and corresponding uncertainty relation are also not related with the displacement factor in the thermal coherent state.