Journal Article10.1103/REVMODPHYS.50.221
General properties of entropy
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TL;DR: This paper discusses properties of entropy, as well as related concepts such as relative entropy, skew entropy, dynamical entropy, etc, in detail with reference to their implications in statistical mechanics, to get a glimpse of systems with infinitely many degrees of freedom.
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Abstract: It is rather paradoxical that, although entropy is one of the most important quantities in physics, its main properties are rarely listed in the usual textbooks on statistical mechanics. In this paper we try to fill this gap by discussing these properties, as, for instance, invariance, additivity, concavity, subadditivity, strong subadditivity, continuity, etc., in detail, with reference to their implications in statistical mechanics. In addition, we consider related concepts such as relative entropy, skew entropy, dynamical entropy, etc. Taking into account that statistical mechanics deals with large, essentially infinite systems, we finally will get a glimpse of systems with infinitely many degrees of freedom.
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Mixed State Entanglement and Quantum Error Correction
Charles H. Bennett,Charles H. Bennett,Charles H. Bennett,David P. DiVincenzo,David P. DiVincenzo,David P. DiVincenzo,John A. Smolin,John A. Smolin,John A. Smolin,William K. Wootters,William K. Wootters,William K. Wootters +11 more
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References
Sur L'intégrale de Configuration Pour Les Systèmes De Particules À Une Dimension
TL;DR: In this paper, the free energy of a one-dimensional system of particles is calculated for the case of non-vanishing incompressibility radius of the particles and a finite range of the forces.
Inequality with Applications in Statistical Mechanics
TL;DR: In this paper, it was shown that for Hermitian matrices (or more generally for completely continuous self-adjoint linear operators in Hilbert space) A and B, Tr (eA+B ) ≤ Tr(eAeB ), and the inequality was shown to be sharper than the convexity property (0 ≤ α ≤ 1).
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