Virial expansionThe virial expansion is a model of thermodynamic equation of state. This model expresses the pressure P of a gas in local equilibrium as a power series of the density. This equation may be represented in terms of the compressibility factor, , as This equation was first proposed by Kamerlingh Onnes. The terms A, B and C, represent the virial coefficients. The leading coefficient, A, is defined as the constant value of 1, which enforces that the equation reduces to the ideal gas expression as the gas density approaches zero.
Identical particlesIn quantum mechanics, identical particles (also called indistinguishable or indiscernible particles) are particles that cannot be distinguished from one another, even in principle. Species of identical particles include, but are not limited to, elementary particles (such as electrons), composite subatomic particles (such as atomic nuclei), as well as atoms and molecules. Quasiparticles also behave in this way.
Fermi–Dirac statisticsFermi–Dirac statistics (F–D statistics) is a type of quantum statistics that applies to the physics of a system consisting of many non-interacting, identical particles that obey the Pauli exclusion principle. A result is the Fermi–Dirac distribution of particles over energy states. It is named after Enrico Fermi and Paul Dirac, each of whom derived the distribution independently in 1926 (although Fermi derived it before Dirac). Fermi–Dirac statistics is a part of the field of statistical mechanics and uses the principles of quantum mechanics.
Bose–Einstein statisticsIn quantum statistics, Bose–Einstein statistics (B–E statistics) describes one of two possible ways in which a collection of non-interacting, indistinguishable particles may occupy a set of available discrete energy states at thermodynamic equilibrium. The aggregation of particles in the same state, which is a characteristic of particles obeying Bose–Einstein statistics, accounts for the cohesive streaming of laser light and the frictionless creeping of superfluid helium.
Phase spaceIn dynamical systems theory and control theory, a phase space or state space is a space in which all possible "states" of a dynamical system or a control system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. It is the direct product of direct space and reciprocal space. The concept of phase space was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré, and Josiah Willard Gibbs.