The Elusive Object of Desire: In Pursuit of the Kinetic Equations and the Second Law

Abstract

It is impossible to overrate the important contribution which statistical mechanics makes to our contemporary understanding of the physical world. Cutting across the hierarchy of theories which describe the constitution of things, and related in subtle and not yet fully understood ways to the fundamental dynamical theories, it provides the essential framework for describing the dynamical evolution of systems where large domains of initial conditions lead to a wide variety of possible outcomes distributed in a regular and predictable way. For the special case of the description of systems in equilibrium, the theory provides a systematic formalism which can be applied in any appropriate situation to derive the macroscopic equation of state. Here the usual Gibbsian ensembles, especially microcanonical and canonical, function as a general schematism into which each particular case can be fit. In the more general case of nonequilibrium the situation is less clear.