Abstract: By now, the thermodynamics of fluid systems is well developed, but many issues related to solids still require discussion. In this work, six characteristic functions of classical thermodynamics are investigated in application to solid-state systems: energy, free energy, Gibbs energy, enthalpy, grand thermodynamic potential, and a new characteristic function recently discovered by the author, called the J-potential. The need to introduce such a potential appears in the thermodynamics of solid-state or mixed systems subjected to complex mechanical impacts, and also in colloidal science. Definitions are given for all six functions, fundamental thermodynamic equations are derived, and the conditions under which this function assumes the status of a thermodynamic potential are established.