Thermodynamical equivalence of physical systems

Abstract: 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.