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.
Highlights
Thermodynamics is one of the theories which have high universality since thermodynamics as itself has been unchanged even if we have a well-developed quantum theory
When we consider the thermodynamics for quantum systems, the important is the change in entropy since entropy is a constant of motion under the unitary transformation generated by a system Hamiltonian [6] [7]
We propose a representation of the thermodynamical laws for quantum system in terms of the respective parameters and develop a theory of quantum thermodynamics based on the axiomatic theory of classical thermodynamics by Lieb and Yngvason [3]
Summary
Thermodynamics is one of the theories which have high universality since thermodynamics as itself has been unchanged even if we have a well-developed quantum theory. The first term iEidpi implies there exists a non-mechanical source that induces a change in the internal energy of the system since a change in quantum states is in general determined by the unitary operator which does not change the definite probability. We propose a representation of the thermodynamical laws for quantum system in terms of the respective parameters and develop a theory of quantum thermodynamics based on the axiomatic theory of classical thermodynamics by Lieb and Yngvason [3]. In their formulation, the second law refers to the possible adiabatic transition of any two states in a state space.
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