Axiomatics of classical statistical mechanics Rudolf Kurth.

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.

Introduction. Statement of the problem -- Mathematical tools. Sets -- Mapping -- Point sets in the n-dimensional vector space Rn -- Topological mapping in vector spaces -- Systems of ordinary differential equations -- The lebesgue measure -- The Lebesgue integral -- Hubert spaces -- The phase flows of mechanical systems. Mechanical systems -- Phase flow; Liouville's theorem -- Stationary measure-conserving phase flow; Poincaré's, Hopf's and Jacobi's theorems.

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.

"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."--