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On quantum informational thermodynamics with macrostates defined with respect to several operators

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Szafnicki B.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS INTRODUCTION.................................................................................................................................................................................. 5 Chapter 1. PRELIMINARIES.............................................................................................................................................................. 7 § 1.1. Basic concepts of quantum mechanics.............................................................................................................................. 7 § 1.2. Basic concepts of quantum informational thermodynamics........................................................................................... 8 Chapter 2. THE ENTROPY OF A SYSTEM OF COMMUTING OPERATORS............................................................................ 9 § 2.1. Definitions.................................................................................................................................................................................. 9 5 2.2. The entropy of a system of operators with finite simple spectra..................................................................................... 10 §2.3. The entropy and the generalized temperature.................................................................................................................... 18 § 2.4. Thermodynamically regular systems of operators............................................................................................................ 22 Chapter 3. THE MOTION OP PHYSICAL SYSTEMS...................................................................................................................... 26 § 3.1. Basic notions and definitions................................................................................................................................................. 26 § 3.3. Some property of the entropy of moving systems............................................................................................................... 28 § 3.4. Macrostates invariant under motion...................................................................................................................................... 31 Chapter 4. MACROSTATES WITH RESPECT TO p-STATISTICAL MOMENTS OF THE OPERATOR A.............................. 35 §4.1. Basic concepts.......................................................................................................................................................................... 35 §4.2. Some properties of the entropy $S_A(\bar{Φ}(\bar{M}))$.................................................................................................. 36 Chapter 5. INFORMATIONAL THERMODYNAMICS IN THE CASE OF A SYSTEM OF NON-COMMUTING OPERATORS........................................................................................................................................................................................ 39 REFERENCES.................................................................................................................................................................................... 43

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1 Szafnicki B.

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On quantum informational thermodynamics with macrostates defined with respect to several operators