The second law of thermodynamics as variation on a theme of Caratheodory

This paper revisits the second law of thermodynamics via certain modifications of the axiomatic foundation provided by the celebrated 1909 work of Caratheodory. It is shown that his postulate of adiabatic inaccessibility represents one of several constraints on the energy balance that serve to establish the existence of thermostatic entropy as a foliation of state space, with temperature representing a force of constraint. To achieve the thermostatic version of the second law, as embodied in the postulates of Clausius and Gibbs, work principles are proposed to define thermostatic equilibrium and stability in terms of the convexity properties of internal energy, entropy and related thermostatic potentials. Comparisons are made with the classic work of Coleman and Noll on thermostatic equilibrium in simple continua, resulting in a few unresolved differences. Perhaps the most novel aspect of the current work is an extension to irreversible processes by means of a non-equilibrium entropy derived from recoverable work, which generalizes similar ideas in continuum viscoelasticity. This definition of entropy calls for certain revisions of modern theories of continuum thermomechanics by Coleman, Noll and others that are based on a generally inaccessible entropy and undefined temperature.

Automated summary

This paper revisits the second law of thermodynamics by modifying the axiomatic foundation provided by Caratheodory in 1909. It proposes a new interpretation of thermodynamic entropy and establishes work principles for defining thermodynamic equilibrium and stability based on the convexity properties of internal energy, entropy, and related thermodynamic potentials. The most novel aspect is the extension to irreversible processes through a non-equilibrium entropy derived from recoverable work.