Thermodynamics and Statistical Mechanics

Thermodynamics relates temperature, energy, and pressure quantities based on a few underlying physical assumptions, while statistical mechanics instead proceeds from the principle that a system with many degrees of freedom transitions randomly between all accessible configurations consistent with its macroscopic properties. The behaviour of a statistical mechanical system is characterized by the average properties of a large number of independent realizations or replicas, termed a statistical ensemble. The laws of thermodynamics together with the definitions of ΔW and ΔS indicate that in a thermally isolated system with fixed volume, the system energy is a unique function of the entropy and volume. Materials can exist in several phases, such as solid, liquid, gas, or different crystalline structures. At fixed temperature and pressure, the global equilibrium state corresponds to the phase that minimizes the Gibbs free energy. This chapter also discusses the photons and phonons heat engines, Carnot cycle and Bose-Einstein condensation.

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