Axiomatics of classical statistical mechanics - Kurth, Rudolf (Mineola: Dover Publications, 2019)
"Requiring only familiarity with the elements of calculus and analytical geometry, this monograph constructs classical statistical mechanics as a deductive system, based on the equations of motion and the basic postulates of probability. The book consists chiefly of theorems and proofs that are expressed in a manner that reveals the theory's logical structure. A chapter on mathematical tools makes the treatment as self-contained as possible."--
The theorems of V. Neumann and Birkhoff; the ergodic hypothesis -- The initial distribution of probability in the phase space. A formal description of the concept of probability -- On the application of the concept of probability -- Probability distributions which depend on time. Mechanical systems with general equations of motion -- Hamiltonian and newtonian systems -- The initial value problem -- The approach of mechanical systems towards states of statistical equilibrium -- Time-independent probability distributions. Fluctuations in statistical equilibrium -- Gibbs's canonic probability distribution -- Statistical thermodynamics. The equation of state -- The fundamental laws of thermodynamics -- Entropy and probability.
Originally published: New York : Pergamon Press, 1960, as volume 11 in the International series of monographs in pure and applied mathematics.
Includes bibliographical references and index.
Keywords: Statistical mechanics