## ::Statistical mechanics

### ::concepts

Ensemble::system State::center Systems::states Energy::quantum Which::first About::physics

**Statistical mechanics** is a branch of theoretical physics that studies, using probability theory, the average behaviour of a mechanical system where the state of the system is uncertain.<ref name="gibbs"/><ref name="tolman"/><ref name="balescu"/><ref group=note>The term *statistical mechanics* is sometimes used to refer to only *statistical thermodynamics*. This article takes the broader view. By some definitions, *statistical physics* is an even broader term which statistically studies any type of physical system, but is often taken to be synonymous with statistical mechanics.</ref>

The classical view of the universe was that its fundamental laws are mechanical in nature, and that all physical systems are therefore governed by mechanical laws at a microscopic level. These laws are precise equations of motion that map any given initial state to a corresponding future state at a later time. There is however a disconnection between these laws and everyday life experiences, as we do not find it necessary (nor even theoretically possible) to know exactly at a microscopic level the simultaneous positions and velocities of each molecule while carrying out processes at the human scale (for example, when performing a chemical reaction). Statistical mechanics is a collection of mathematical tools that are used to fill this disconnection between the laws of mechanics and the practical experience of incomplete knowledge.

A common use of statistical mechanics is in explaining the thermodynamic behaviour of large systems. Microscopic mechanical laws do not contain concepts such as temperature, heat, or entropy, however, statistical mechanics shows how these concepts arise from the natural uncertainty that arises about the state of a system when that system is prepared in practice. The benefit of using statistical mechanics is that it provides exact methods to connect thermodynamic quantities (such as heat capacity) to microscopic behaviour, whereas in classical thermodynamics the only available option would be to just measure and tabulate such quantities for various materials. Statistical mechanics also makes it possible to *extend* the laws of thermodynamics to cases which are not considered in classical thermodynamics, for example microscopic systems and other mechanical systems with few degrees of freedom.<ref name="gibbs"/> This branch of statistical mechanics which treats and extends classical thermodynamics is known as **statistical thermodynamics** or **equilibrium statistical mechanics**.

Statistical mechanics also finds use outside equilibrium. An important subbranch known as **non-equilibrium statistical mechanics** deals with the issue of microscopically modelling the speed of irreversible processes that are driven by imbalances. Examples of such processes include chemical reactions, or flows of particles and heat. Unlike with equilibrium, there is no exact formalism that applies to non-equilibrium statistical mechanics in general and so this branch of statistical mechanics remains an active area of theoretical research.

**Statistical mechanics sections**

Intro Principles: mechanics and ensembles Statistical thermodynamics Non-equilibrium statistical mechanics Applications outside thermodynamics History See also Notes References External links

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