THERMODYNAMICS OF CRAWFORD ENERGY EQUIPARTITION JOURNEYS

Energy equipartition ''journeys'' proposed originally in the context of relativistic mechanics [F. S. Crawford, Am. J. Phys. 61, 317-326 (1993)] are examined thermodynamically. Equipartition is between ideal gases separated by an insulating piston. Each journey alternates slow adiabatic volume changes and zero-work adiabatic piston resettings effected by a benevolent Maxwell's demon until temperature and pressure equalities exist. For the systems considered, reversible adiabatic thermodynamic processes are equivalent to slow mechanically adiabatic, constant-action processes. Because phase space mixing is assumed implicitly in thermodynamics, the piston jiggling step needed in Crawford's mechanics-based treatment is unnecessary. Zero-work journeys maximize the gas system's entropy change, and maximum work output journeys leave that entropy unchanged. Thermodynamics confirms Crawford's result for the piston's effective spring constant, and statistical mechanics enables rigorous justification of his interesting recursion relation for the moments of q = momentum X velocity.