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arXiv:cond-mat/0012056

Zeroth and Second Laws of Thermodynamics Simultaneously Questioned in the Quantum Microworld

Vladislav Čápek

Published Dec 5, 2000• 0 citations
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Abstract

Several models of quantum open systems are known at present to violate, according to principles of the standard quantum theory of open systems, the second law of thermodynamics. Here, a new and rather trivial model of another type is suggested describing mechanism that violates, according to the same principles, the zeroth and the second laws of thermodynamics simultaneously. Up to a technically minor modification, the model resembles some models already known, solved by standard means, and properly understood. Universal validity of two basic principles of thermodynamics in strictly quantum situations is thus simultaneously called in question.

DOI
10.48550/arxiv.cond-mat/0012056

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Several models of quantum open systems are known at present to violate, according to principles of the standard quantum theory of open systems, the second law of thermodynamics. Here, a new and rather trivial model of another type is suggested describing mechanism that violates, according to the same principles, the zeroth and the second laws of thermodynamics simultaneously. Up to a technically minor modification, the model resembles some models already known, solved by standard means, and properly understood. Universal validity of two basic principles of thermodynamics in strictly quantum situations is thus simultaneously called in question.
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Abstract Thermodynamics was developed when it was still unclear whether the microworld had an atomic substructure. The objective here is to investigate the relationship between the process of a quantum measurement and the second law of thermodynamics. It is necessary to make the ideas of heat and work explicit in this approach. It is possible to study the correspondence between information entropy and thermodynamic entropy. Finally, a model is proposed in such a way as to resemble an experimental example for the discussion.
It is proposed a representation of the basic laws (i.e. the zeroth, first, second and third laws) in thermodynamics for quantum systems in the pure and mixed ensembles, respectively. We show that the basic laws are represented by parameters that specify respective quantum states. The parameters are the elements of the thermodynamic state space Mθ and the state space Mϑ of the mixed ensemble for quantum systems. The introduction of such parameters is based on a probabilistic nature of quantum theory. Consistency between quantum theory and classical thermodynamics is preserved throughout the formulation for the representation of the thermodynamical laws in quantum systems (quantum thermodynamics). The present theory gives the mathematical foundations of quantum thermodynamics.
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.