Statistical mechanics is a branch of physics that applies probability theory to the study of matter at the microscopic level, allowing for the understanding of the macroscopic properties of matter based on the behavior of its constituent particles.

The Maxwell-Boltzmann distribution describes the distribution of particles among different energy levels in a classical system, where particles are distinguishable and can occupy the same energy level multiple times.

In statistical mechanics, entropy is a measure of the disorder or randomness of a system. The higher the disorder, the higher the entropy.

The canonical ensemble is used to describe a system in thermal equilibrium, where the system is in contact with a heat bath and can exchange energy with it.

In statistical mechanics, temperature is a measure of the average kinetic energy of particles in a system. The higher the temperature, the higher the average kinetic energy of the particles.

The spontaneous tendency of a system to move towards a state of higher entropy is known as entropy increase. This is a fundamental principle in statistical mechanics and is often referred to as the second law of thermodynamics.

In statistical mechanics, the probability of a particular microstate is known as the microstate probability. It is the probability of finding the system in that particular microstate.

In statistical mechanics, the partition function is a mathematical function that is directly proportional to the thermodynamic properties of a system. It provides a complete description of the statistical behavior of the system.

The microcanonical ensemble is used to describe a system with a fixed number of particles and volume but variable energy. It is also known as the constant energy ensemble.

In statistical mechanics, the free energy is directly proportional to the probability of a particular macrostate. The higher the free energy, the higher the probability of the macrostate.

The grand canonical distribution is used to describe the statistical distribution of particles in a system with a fixed chemical potential. It is also known as the grand ensemble.

The isothermal-isobaric ensemble is used to describe a system with a fixed number of particles and temperature but variable volume. It is also known as the constant temperature-constant pressure ensemble.

In statistical mechanics, the chemical potential is directly proportional to the average number of particles in a system. The higher the chemical potential, the higher the average number of particles.

The canonical distribution is used to describe the statistical distribution of particles in a system with a fixed number of particles, volume, and temperature. It is also known as the constant temperature ensemble.

In statistical mechanics, the internal energy is the average energy of a system. It is the sum of the kinetic and potential energies of all the particles in the system.