Carnot's Entropy

The goal of this work is simple and traditional: to provide a formalization and generalization of the notion of entropy in the spirit of Carnot. The tools we employ to achieve our objective are quite novel however. We have no need for state spaces, paths in state spaces, path integration,cycles in state spaces, systems in equilibrium, quasi-static transformations, the usual dynamical notion of reversibility, or even, the first law of thermodynamics. Instead, we rely on a primitive notion of process and the effects a process has on a system, typically, on the surroundings of a system. Carnot cycles are replaced in our framework by bithermal processes. We recover that the efficiency of a bithermal process is maximal when the process is reversible and maximal efficiency is determined by the temperature of the reservoirs. We also derive that all cyclic processes are dissipative, at best isentropic. The formalism assigns a degree of irreversibility to every process. The argument we present is quite general. It does not assume systems to be at equilibrium; it simply requires systems to have a state at the beginning and at the end of the process.