Thermodynamic Probability

the number of processes by which the state of a physical system can be realized. In thermodynamics a system is characterized by specific values of density, pressure, temperature, and other measurable quantities. The enumerated values determine the state of the system as a whole (its macrostate). However, for the same density, temperature, and so on, the system’s particles can be distributed in space by different processes and can have different momenta. Each given particle distribution is called a microstate of the system. The thermodynamic probability (denoted by W) is equal to the number of micro-states which realize a given macrostate, from which it follows that W ^ 1. The thermodynamic probability is connected with one of the basic macroscopic characteristics of the system, the entropy S, by the Boltzmann relation S = k ln W, where k is Boltzmann’s constant.

The thermodynamic probability is not a probability in a mathematical sense. It is used in statistical physics to determine the properties of systems which are in thermodynamic equilibrium (for which the thermodynamic probability attains a maximum value). Of importance in the calculation of the thermodynamic probability is whether the system’s particles are distinguishable or indistinguishable. Consequently, classical and quantum mechanics lead to different expressions for the thermodynamic probability.