partition function describes the statistical properties of a system in thermodynamic equilibrium.[citation needed] Partition functions are functions of...

generalizes its use in statistical mechanics and quantum field theory: Partition function (statistical mechanics) Partition function (quantum field theory)...

systems, is a generalization of the definition of a partition function in statistical mechanics. It is a special case of a normalizing constant in probability...

the value of the wave function. Statistical mechanics links the empirical thermodynamic properties of a system to the statistical distribution of an ensemble...

function (statistical mechanics) Derivation of the partition function Partition of an interval Partition of a set Ordered partition Partition refinement...

In statistical mechanics, the translational partition function, q T {\displaystyle q_{T}} is that part of the partition function resulting from the movement...

Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. In quantum mechanics a statistical ensemble (probability...

system might be in. In other words, a statistical ensemble is a set of systems of particles used in statistical mechanics to describe a single system. The...

\left(\exp(z_{1})+\cdots +\exp(z_{n})\right)} . The softmax function was used in statistical mechanics as the Boltzmann distribution in the foundational paper...

versions of statistical mechanics partition functions, giving rise to a close connection between these two areas of physics. Partition functions can rarely...

_{j=1}^{M}f_{j}(y|\{x_{k}\})} is a normalization constant (see partition function (statistical mechanics)). This is related to (but quite different from) a mixture...

In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic...

rotational partition function relates the rotational degrees of freedom to the rotational part of the energy. The total canonical partition function Z {\displaystyle...

McQuarrie, Statistical Mechanics, Harper & Row, 1973 G. Herzberg, Infrared and Raman Spectra, Van Nostrand Reinhold, 1945 Partition function (mathematics)...

or impossible. In statistical mechanics, entropy is formulated as a statistical property using probability theory. The statistical entropy perspective...

In statistical mechanics, the transfer-matrix method is a mathematical technique which is used to write the partition function into a simpler form. It...

In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution) is a probability distribution or probability measure...

Fermi–Dirac statistics is a part of the field of statistical mechanics and uses the principles of quantum mechanics. Fermi–Dirac statistics applies to identical...

classical mechanics, such as: statics, dynamics, kinematics, continuum mechanics (which includes fluid mechanics), statistical mechanics, etc. Mechanics: A branch...

system's dynamics. Common examples are the partition function of statistical mechanics, the Hamiltonian, and the function which acts as a bridge between two sets...

Carlo in statistical physics refers to the application of the Monte Carlo method to problems in statistical physics, or statistical mechanics. The general...

oscillator, and in statistical mechanics, to find its partition function. Although no elementary function exists for the error function, as can be proven...

short-ranged. In statistical mechanics, the properties of a system of noninteracting particles are described using the partition function. For N noninteracting...

group. It typically arises as a partition function, in the sense of statistical mechanics, many-body quantum mechanics or quantum field theory, as the...

characteristic state function or Massieu's potential in statistical mechanics refers to a particular relationship between the partition function of an ensemble...

In statistical mechanics, a canonical ensemble is the statistical ensemble that represents the possible states of a mechanical system in thermal equilibrium...

Langevin functions are a pair of special functions that appear when studying an idealized paramagnetic material in statistical mechanics. These functions are...

2kT}\right)}.\end{aligned}}} This is the partition function of one harmonic oscillator. Because, statistically, heat capacity, energy, and entropy of the...

analytical mechanics, or theoretical mechanics is a collection of closely related formulations of classical mechanics. Analytical mechanics uses scalar...

the statistical mechanics of black-body radiation led to the development of the theory of quantum mechanics, the effort to understand the statistical mechanics...