Eight physical systems of thermodynamics, statistical mechanics, and computer simulations

The equilibrium properties of a pure substance can be described in at least eight distinct ways in thermodynamics and in statistical mechanics. These eight different descriptions are interrelated to one another through a Laplace-Legendre transformation scheme. The only existing scheme defines three systems which lack useful application. We present an alternative, more natural description which incorporates two novel thermodynamic functions and three relatively new statistical mechanics ensemble theories that have been put to practical use in computer simulations.