On baricenters of heating measures and thermodynamical inequalities (Q1322048)

This paper exploits the concept of the accumulation function of Serrin and of the heating measure [\textit{M. Silhavy}, Arch. Ration. Mech. Anal. 81, 221-243 (1983; Zbl 0517.73002)] to obtain representations of thermodynamical functions solely in terms of total work and heat and a finite number of temperatures. For the first time, the accounting for heat in terms of temperature allowed by the accumulation function or the heating measure is accomplished without recourse to a field description of processes. As a result, the author obtains optimal bounds on the efficiency of cycles and on the work in any process the system may perform. The temperatures appearing in these bounds are directly related to baricenters (in a measure-theoretical sense) of heat absorption and emission. The relationship between these bounds and the statements of the laws of thermodynamics is explored in a wide range of circumstances.