Thermodynamic insights from a one-particle gas

Abstract

Fundamentals of thermodynamics are introduced and illuminated using a model ‘‘gas’’ consisting of a single particle of mass m and kinetic energy E in a one-dimensional box of length L. Constancy of the classical action, 𝒜=2√2mE L under slow, mechanically reversible changes in L reflects the symmetry of reversibility. Heat is defined in terms of work using adiabatic paths to connect an arbitrary pair of states. The ensemble average of 𝒜 increases for many irreversible mechanical processes that break the reversibility symmetry, and entropy can be linked to ln(𝒜). Although not strictly ‘‘thermodynamic,’’ this model helps clarify the statistical nature of the second law of thermodynamics and illuminates the very essence of thermodynamics, namely, the invisible mixing of energy within systems.