Additivity of the entropy and definition of the temperature for quantum systems |
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Authors: | H Roos |
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Institution: | (1) Institute for Theoretical Physics, Groningen, The Netherlands |
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Abstract: | A closed quantum systemL is considered which is described by a microcanonical ensemble.L consists of two rather weakly interacting subsystemsL
1,L
2. In a rigorous way, the additivity of the entropy is proved by deriving an expression for the entropy density ofL in terms of the entropy densities ofL
1 andL
2. Rigorous implies that the thermodynamic limit is taken. In the second part, it is shown how a microcanonical state
of the composite system — provided this limit exists — gives rise to a canonical state
, when restricted toL
1, providedL
1 is very small as compared toL
2;
is defined as a limit of Gibbs states. This yields a definition of the equilibrium temperature –1.On leave of absence from the Institut für Theoretische Physik, Universität Göttingen. |
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Keywords: | |
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