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International Journal of Modern Physics B

ENTROPY INCREASE AND K-SYSTEMS IN QUANTUM THEORY

Walter E Thirring

Published Apr 1, 1990• 0 citations
Publisher

Abstract

It is shown that the relative entropy converges to its equilibrium value when the states converge strongly. This can happen only for subalgebras for which the clustering is uniform. It happens for K-systems for which this uniformity in clustering has the maximal extent which is possible.
DOI
10.1142/s0217979290000553

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We consider sequences of measurements implemented by positive operator valued measures (POVMs). Starting from the assumption that these sequences may be described as consistent and Markovian, even and especially for closed quantum systems, we identify properties of the equilibrium state that coincide with the properties of typical pure quantum states. We define a physical entropy that converges against the standard entropies in the approach to equilibrium. Furthermore, strict limits to its possible decrease are derived on the basis of Renyi entropies. It is demonstrated that Landauer's principle follows directly from these limits. Since the above assumptions are rather strong, we exemplify the fact that they may nevertheless apply by checking them numerically for some transition paths in a concrete model.
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A gauge-invariant C*-system is obtained as the fixed point subalgebra of the infinite tensor product of full matrix algebras under the tensor product unitary action of a compact group. In this paper, thermodynamics is studied in such systems and the chemical potential theory developed by Araki, Haag, Kastler and Takesaki is used. As a generalization of quantum spin system, the equivalence of the KMS condition, the Gibbs condition and the variational principle is shown for translation-invariant states. The entropy density of extremal equilibrium states is also investigated in relation to macroscopic uniformity.