The Science of $ΘΔ^{cs}$

Abstract

There is a long tradition of thinking of thermodynamics, not as a theory of fundamental physics (or even a candidate theory of fundamental physics), but as a theory of how manipulations of a physical system may be used to obtain desired effects, such as mechanical work. On this view, the basic concepts of thermodynamics, heat and work, and with them, the concept of entropy, are relative to a class of envisaged manipulations. This view has been dismissed by many philosophers of physics, in my opinion too hastily. This paper is a sketch and defense of a science of manipulations and their effects on physical systems. This is, I claim, the best way to make sense of thermodynamics as it is found in textbooks and as it is practiced. I call this science thermo-dynamics (with hyphen), or $ΘΔ^{cs}$, for short, to highlight that it may be different from the science of thermodynamics, as the reader conceives it. Even if one is not convinced that it is the best way to make sense of thermodynamics as it is practiced, it should be non-controversial that $ΘΔ^{cs}$ is a legitimate science. An upshot of the discussion is a clarification of the roles of the Gibbs and von Neumann entropies. Given the definition of statistical thermo-dynamic entropy, it can be proven that, under the assumption of availability of thermodynamically reversible processes, these functions are the unique (up to an additive constant) functions that represent thermo-dynamic entropy. Light is also shed on the use of coarse-grained entropies.}