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The term statistical physics encompasses statistical approaches to classical mechanics and quantum mechanics. Statistical mechanics is then often used as a synonym. When the context requires a distinction, one uses the terms classical statistical mechanics and quantum statistical mechanics.
A statistical approach can work well in classical systems when the number of degrees of freedom (and so the number of variables) is so large that exact solution is not possible, or not really useful. Statistical mechanics can also describe work in non-linear dynamics, chaos theoryChaos theory in mathematics and physics, deals with the behaviour of certain nonlinear dynamical systems that (under certain conditions) exhibit the phenomenon known as chaos most famously characterised by sensitivity to initial conditions (see butterfly, thermal physics, fluid dynamicsFluid dynamics is the study of fluids ( liquids and gases) in motion, and the effect of the fluid motion on fluid boundaries, such as solid containers or other fluids. Fluid dynamics is a branch of fluid mechanics, and has a number of subdisciplines, incl (particularly at low Knudsen numberThe Knudsen number Kn is the ratio of the molecular mean free path length to a representative physical length scale. It is defined as: where T, temperature (K) k, Boltzmann's constant P, total pressure (Pa) See also Fluid dynamics Mach number Reynolds nums), or plasma physicsPlasma physics is the field of physics which studies the dynamic behaviour of plasmas. Briefly, it is the study of the statistical properties of a field of charged particles, called a plasma. Sometimes called "the fourth state of matter" (besides solid, l.
Although some problems in statistical physics can be solved analytically using approximations and expansions, most current research utilizes the large processing power of modern computers to simulate or approximate solutions. A common approach to statistical problems is to use a Monte Carlo simulation, to yield insight into the dynamics of a complex system.