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In statistical mechanics, a canonical ensemble is a statistical ensemble that represents the possible states of a mechanical system in thermal equilibrium with a heat bath at a fixed temperature.

The grand canonical ensemble is used to represent the statistical behavior of a system in contact with a reservoir that can exchange both energy and particles.

The thermodynamic limit refers to the behavior of large macroscopic systems, where the number of particles and the volume approach infinity, but the density of particles remains constant.

A microstate is a specific detailed microscopic configuration of a system that a system may occupy with certain probability when in thermodynamic equilibrium.

The partition function is a sum over all possible microstates of a system, weighted by their Boltzmann factors $e^{-\beta E}$, and it plays a central role in statistical mechanics by encapsulating all thermodynamic information of a system.

In statistical mechanics, entropy represents the measure of the number of specific ways in which a thermodynamic system may be arranged, commonly understood as a measure of disorder.

The Boltzmann distribution is a probability distribution that gives the probability that a system will be in a certain state as a function of that state's energy and the temperature of the system.

A macrostate refers to the macroscopic properties of a system, like temperature and pressure, which describe the thermodynamic equilibrium state without concern for the individual microscopic configurations.

The equipartition theorem states that for a thermodynamic system in equilibrium, the total energy is divided equally among its degrees of freedom and each degree of freedom contributes $\frac{1}{2}k_BT$ to the energy.