Representation of the Basic Laws of Thermodynamics in Quantum Mechanics

Abstract

We propose a representation of the basic laws, namely the zeroth, first, second and third law, in quantum thermodynamics. The zeroth law is represented by some parameters ( ) that specify respective quantum states. The parameters are the elements of thermodynamic state space . The introduction of such parameters is based on a probabilistic nature of quantum theory. A quantum analog of the first law can be established by utilizing these parameters. The notion of heat in quantum systems is clarified from the probabilistic point of view in quantum theory. The representation of the second law can be naturally described in terms of these parameters introduced for the respective quantum systems. In obtaining the representation of quantum thermodynamics, consistency between quantum theory and classical thermodynamics should have been preserved throughout our formulation of quantum thermodynamics. After establishing the representation of the second law, the third law is discussed briefly. The relationship between thermodynamic temperatures and the parameters in is also discussed.