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I. General introduction II. The method of the most probable distribution III. Discussion of the Nernst theorem IV. Examples on the second section (a) Free mass-point (ideal monatomic gas) (b) Planck's oscillator (c) Fermi oscillator V. Fluctuations VI. The method of mean values VII. The n-particle problem VIII. Evaluation of the formulae. Limiting cases The entropy constant The failure of the classical theory. Gibb's paradox Digression: Annihilation of matter? Digression on the uncertainty relation Gas-degeneration proper Weak degeneration Medium degeneration Strong degeneration (a) Strong Fermi-Dirac degeneration (b) Strong Bose-Einstein degeneration IX. The problem of radiation Appendix