ABSTRACT
This chapter extends the ensemble method to systems that exchange energy with their surroundings. It considers an ensemble based on a system that can exchange energy with its surroundings in the form of heat flow (a diathermic system). The resulting "canonical" ensemble is built by replicating a thermodynamic system that is in equilibrium with a thermal reservoir. The chapter finds the equilibrium distribution by maximizing the multiplicity, but this time with the additional constraint that the total energy of the ensemble. The equilibrium distribution is represented by another type of partition function, the "canonical partition function", in which the probabilities of microstates decay exponentially with energy. To connect to systems at constant pressure, the chapter introduces a third type of ensemble that allows volume change as well as heat flow by coupling to a mechanical reservoir. Maximizing this "isothermal–isobaric ensemble" using the Lagrange method produces an exponential decay with enthalpy, and is directly related to the Gibbs energy G.
