The Gibbs free energy is a statistical mechanical potential that describes a system at constant temperature and pressure, and is defined as G = H - TS, where H is the enthalpy and S is the entropy.

In a reversible adiabatic process, the entropy of the system remains constant, ΔS = 0.

Boltzmann's theorem states that the entropy of a system is proportional to the logarithm of the number of possible microstates, S = k * ln(Ω).

The probability of finding a system in a microstate with energy E is given by the Boltzmann distribution, which is proportional to e^(−E/kT) and normalized by the partition function Z(T).

The microcanonical ensemble describes a closed system with a fixed number of particles (N), volume (V), and energy (E), and is characterized by a fixed energy and particle number.