"The statistical ensemble that represents the possible states of a mechanical system in thermal equilibrium with a heat bath at a fixed temperature."
An ensemble of systems that are in thermal equilibrium with each other.
Statistical Mechanics: A branch of physics that deals with the application of statistics to the study of thermodynamic properties of matter.
Ensembles: A collection of all possible states of a system that are compatible with some given set of constraints.
Microcanonical Ensemble: An ensemble that specifies the exact values of energy, volume, and the number of particles in the system.
Canonical Ensemble: An ensemble that specifies the exact value of temperature, volume, and the number of particles in the system.
Grand Canonical Ensemble: An ensemble that specifies the exact value of temperature, volume, and the chemical potential.
Boltzmann Distribution: A probability distribution that relates the number of particles in a given energy state to the temperature of the system.
Partition Function: A mathematical function that describes the statistical behavior of a system in equilibrium.
Helmholtz Free Energy: A thermodynamic function that describes the maximum amount of work a system can perform in a closed system.
Internal Energy: The total energy contained within a system.
Entropy: A measure of the level of disorder or randomness in a system.
Gibbs Free Energy: A thermodynamic function that describes the maximum amount of work that can be performed by a system at constant temperature and pressure.
Equilibrium: A state in which there are no net changes in the macroscopic properties of a system over time.
Ideal gas canonical ensemble: This ensemble models a system of non-interacting particles that obey the ideal gas law.
Quantum canonical ensemble: This ensemble models a system of particles that obey the laws of quantum mechanics. The energy levels of the particles are discrete and quantized.
Classical canonical ensemble: This ensemble models a system of particles that obey classical mechanics. The energy levels of the particles are continuous.
Ising Model canonical ensemble: This ensemble models a system of interacting magnetic spins.
Bose-Einstein canonical ensemble: This ensemble models a system of bosons, which are particles that obey Bose-Einstein statistics.
Fermi-Dirac canonical ensemble: This ensemble models a system of fermions, which are particles that obey Fermi-Dirac statistics.
"The absolute temperature (symbol: T). The ensemble typically also depends on mechanical variables such as the number of particles in the system (symbol: N) and the system's volume (symbol: V)."
"Both influence the nature of the system's internal states."
"P = e^( (F - E) / (kT) )"
"The total energy of the microstate."
"First, it provides a normalization factor for the probability distribution. Second, many important ensemble averages can be directly calculated from the function F(N, V, T)."
"P = (1/Z)e^(-E/(kT))"
"The canonical partition function is e^(-F/(kT))."
"In 1884."
"Gibbs in 1902."
"The statistical ensemble that represents the possible states of a mechanical system in thermal equilibrium with a heat bath at a fixed temperature."
"The absolute temperature (symbol: T)."
"The number of particles in the system (symbol: N) and the system's volume (symbol: V)."
"P = e^( (F - E) / (kT) )"
"The total energy of the microstate."
"It provides a normalization factor for the probability distribution."
"Z = e^(-F/(kT))"
"First described by Boltzmann in 1884."
"Gibbs in 1902."
"By using the function F(N, V, T) derived from the free energy."