  Two different physical systems are said to be thermodynamically equiv- alent
if one of the thermodynamic potentials of the first system is pro- portional to
the corresponding potential of the second system after expressing the state
variables of the first system in terms of those of the second by a
transformation reversible throughout the state pa- rameter domain. The
thermodynamic equivalence has a transitive nature so that physical systems
divide into classes of thermodynam- ically equivalent systems that have similar
phase diagrams. A first class of thermodynamically equivalent systems is formed
by the ideal classical and quantum Fermi gases, whatever the dimensions of the
confining spaces, and the one dimensional hard rod gas. A second class is
formed by the physical systems characterized by interactions that coincide by a
scaling of the distance and the coupling constant. A third class is formed by
the ideal Boses gases in arbitrary spatial dimensions. The thermodynamic
equivalence can also be defined in a more general way. By so doing the first
and the third class combine into a single class of thermodynamically equivalent
systems.
