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

Seria
Rozprawy Matematyczne tom/nr w serii: 78 wydano: 1970
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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
Słowa kluczowe
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Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 78
Liczba stron
44
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom LXXVIII
Daty
wydano
1970
Twórcy
Bibliografia
  • [1] L. Dubikajtis, R. S. Ingarden and A. Kossakowski, On regularity of information, Bull. Acad. Polon. Sci., Sér. sci. math., astr. et phys. 16 (1968), pp. 55-56.
  • [2] P. R. Halmos, Introduction to Hilbert space and the theory of spectral multiplicity, New York 1951.
  • [3] R. S. Ingarden, A simplified axiomatic definition of information, Bull. Acad. Polon. Sci., Sér. sci. math., astr. et phys. 11 (1963), pp. 209-212.
  • [4] R. S. Ingarden, Information theory and variational principles in statistical theories, ibidem 11 (1963), pp. 541-547.
  • [5] R. S. Ingarden, Physics and Techniques of Low Temperatures, Proc. 3rd Reg. Conf. held in Prague 1963, Prague 1964, p. 45.
  • [6] R. S. Ingarden, The higher order temperatures and zeroth principle of thermodynamics, Bull. Acad. Polon. Sci., Sér. sci. math., astr. et phys. 13 (1965), pp. 69-72.
  • [7] R. S. Ingarden, The density operator and information thermodynamics, Acta Phys, Polon. 27 (1966), pp. 179-196.
  • [8] R. S. Ingarden, Information Theory and Thermodynamics of Light, Part II, Principles of Information Thermodynamics, Fortsch. Phys. 13 (1965), pp. 755-805.
  • [9] R. S. Ingarden and A. Kossakowski, Statistical thermodynamics with higher order temperatures for ideal gases of bosons and fermions, Acta Phys. Polon. 28 (1965), pp. 499-511.
  • [10] R. S. Ingarden and A. Kossakowski, An axiomatic definition of information in quantum mechanics, Bull. Acad. Polon. Sci., Sér. sci. math., astr. et phys. 16 (1968), pp. 61-68.
  • [11] R. S. Ingarden and K. Urbanik, Information as a fundamental notion of statistical physics, Bull. Acad. Polon. Sci., Sér. sci. math., astr. et phys. 9 (1961), pp. 313-316.
  • [12] R. S. Ingarden and K. Urbanik, Information without Probability, Colloq. Math. 9 (1962), pp. 131-150.
  • [13] R. S. Ingarden and K. Urbanik, Quantum informational thermodynamics, Acta Phys. Polon. 21 (1962), pp. 281-304.
  • [14] E. T. Jaynes, Information theory and statistical mechanics, Phys. Rev. 106 (1957), pp. 620-630.
  • [15] A. Kossakowski, Bloch equation with higher order temperatures, Bull. Acad. Polon. Sci., Sér. sci. math., astr. et phys. 13 (1965), pp. 367-368.
  • [16] A. Kossakowski, On the quantum informational thermodynamics, ibidem 17 (1969), pp. 263-267.
  • [17] A. Kossakowski, On a measure relative information in quantum mechanics, ibidem 17 (1969), pp. 77-79.
  • [18] L. D. Landau and E. M. Lifshitz, Quantum mechanics (in Russian), Moscow-Leningrad 1948.
  • [19] J. von Neumann, Mathematische, Grundlagen der Quantenmechanik, Berlin 1932, English translation Princeton 1955.
  • [20] F. Riesz et B. Sz. Nagy, Leçons d'analyse fonctionnelle, Budapest 1965.
  • [21] K. Urbanik, The principle of increase of entropy for spin operators, Bull. Acad. Polon. Sci., Sér. sci. math., astr. et phys. 10 (1962), pp. 349-352.
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