Thermodynamical relations for systems in contact with finite heat baths

We obtain the relations between macroscopic thermodynamical properties and microscopic ensemble averages of a system in contact with a heat bath which has a finite number of degrees of freedom. Our approach is based on the geometry of the accessible phase space of the system. By using a suitable definition of temperature for such kind of system (energy equipartition theorem), it is shown that the relations obtained here have the same dependence on the system's partition function Z1 as in Boltzmann–Gibbs statistics.