  This article is a short version of a longer article to appear in Physics
Reports (cond-mat/9708200). The essential postulates of classical
thermodynamics are formulated, from which the second law is deduced as the
principle of increase of entropy in irreversible adiabatic processes that take
one equilibrium state to another. The entropy constructed here is defined only
for equilibrium states and no attempt is made to define it otherwise.
Statistical mechanics does not enter these considerations. One of the main
concepts that makes everything work is the comparison principle (which, in
essence, states that any two states of the same chemical composition can be
connected by an adiabatic process) and we show that it can be derived from some
assumptions about the pressure and thermal equilibrium. Temperature is derived
from entropy, but at the start not even the concept of `hotness' is assumed.
Our formulation offers a certain clarity and rigor that goes beyond most
textbook discussions of the second law.
