A thermodynamical formalism describing mechanical interactions

Abstract

The dynamical behavior of an overdamped mechanical model devoid of any usual thermal effects is analyzed by a formalism that is similar to usual thermodynamics, and completely independent of any ad hoc assumption of a probability distribution of states in phase space of the mechanical model. It leads to the definition of a new entropy function, which does not coincide with the usual thermodynamical entropy. The new step making the difference to previous studies of this system is the identification of two non-equivalent mechanical interaction mechanisms, which are defined and identified as work and pseudo-heat. Together with the introduced effective temperature θ, they make it possible to characterize the equivalent to isothermal, adiabatic, isobaric, and isochoric processes. Three statements, formally analogous to the zeroth, first, and second law of thermodynamics, are issued. The statement of the second law results from the asymmetry in the way energy can be exchanged along the two processes. A Carnot cycle is defined, for which the efficiency is expressed in terms of θ in the operating pseudo-heat reservoirs. The analogous Clausius theorem for the system operating an arbitrary reversible cycle is proved, leading to the new entropy function. Consequences of the extension of thermodynamic formalism to mechanical models with different processes of transferring energy are discussed.