A second look at the second law of thermodynamics

The essence of the second law of thermodynamics is the statement that all adiabatic processes (slow or violent, reversible or not) can be quantified by a unique entropy function, S, on the equilibrium states of all macroscopic systems, whose increase is a necessary and sufficient condition for such a process to occur. It is one of the few really fundamental physical laws in the sense that no deviation, however tiny, is permitted and its consequences are far reaching. Since the entropy principle is independent of any statistical mechanical model, it ought to be derivable from a few logical principles without recourse to Carnot cycles, ideal gases and other assumptions about such things as 'heat', 'hot' and 'cold', 'temperature', 'reversible processes', etc. Indeed, temperature is a consequence of entropy rather than the other way around. In this lecture on joint work with Jakob Yngvason, the foundations of the subject and the construction of entropy from a few simple, physical principles will be presented. (For background, see: Notices of the Amer. Math. Soc. 45, p.571 (1998), Physics Today 53, p.32 (April 2000) and Physics Reports 310, p.1 (1999).)