Elliott H. Lieb and Jakob Yngvason
The Mathematics and Physics of the Second Law of Thermodynamics
(387K, plain TeX, 93pp. 8eps figures, gzipped tar file)
ABSTRACT. The essential postulates of classical thermodynamics are formu-
lated, 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
given any two states of the same chemical composition at least
one is adiabatically accessible from the other) 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 for-
mulation offers a certain clarity and rigor that goes beyond most
textbook discussions of the second law.