Lieb E.H., Yngvason J.
The Physics and Mathematics of the Second Law of Thermodynamics 
(956K, ps)

ABSTRACT.  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.