On the relation of dynamics to statistical mechanics

Details On the relation of dynamics to statistical mechanics On the relation of dynamics to statistical mechanics

Dec 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977cemec..16..489p&link_type=abstract

Celestial Mechanics, vol. 16, Dec. 1977, p. 489-507. Research supported by the Robert A. Welch Foundation.

Physics

Condensed Matter

Statistical Mechanics

9

Classical Mechanics, Hamiltonian Functions, Statistical Mechanics, Thermodynamic Equilibrium, Thermodynamics, Energy Dissipation, Ergodic Process, Invariance, Kinetic Equations, Nonlinear Systems, Operators (Mathematics), Systems Stability

Scientific paper

The paper presents a new conceptual framework for the transition from dynamics to statistical mechanics. A central role is played by the collision operator, the destruction and creation operators, and their asymptotic behavior. A classification of invariants into regular and singular invariants follows if the asymptotic collision operator does not vanish identically. The nonvanishing of the collision operator is the dissipativity condition, and it is closely related to Poincare's theory of the nonexistence of uniform invariants. Nonequilibrium statistical mechanics provides a criterion for ergodic properties once the dissipativity condition is satisfied.

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