The Boltzmann equation, also often known as the Boltzmann transport equation, devised by Ludwig Boltzmann, describes the statistical distribution of one particle in a fluid. It is one of the most important equations of non-equilibrium statistical mechanics, the area of statistical mechanics that deals with systems far from thermodynamic equilibrium; for instance, when there is an applied temperature gradient or electric field. The Boltzmann equation is used to study how a fluid transports physical quantities such as heat and charge, and thus to derive transport properties such as electrical conductivity, Hall conductivity, viscosity, and thermal conductivity. The Boltzmann equation is an equation for the time t evolution of the distribution function 'f' in one-particle phase space, where x and p are position and momentum, respectively.

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