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Statistical mechanics is a branch of physics that studies the average behaviour of a mechanical system composed of identical or equivalent subunits.〔〔〔〔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.〕 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.〔 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. ==Principles: mechanics and ensembles== In physics there are two types of mechanics usually examined: classical mechanics and quantum mechanics. For both types of mechanics, the standard mathematical approach is to consider two ingredients: # The complete state of the mechanical system at a given time, mathematically encoded as a phase point (classical mechanics) or a pure quantum state vector (quantum mechanics). # An equation of motion which carries the state forward in time: Hamilton's equations (classical mechanics) or the time-dependent Schrödinger equation (quantum mechanics) Using these two ingredients, the state at any other time, past or future, can in principle be calculated. Whereas ordinary mechanics only considers the behaviour of a single state, statistical mechanics introduces the statistical ensemble, which is a large collection of virtual, independent copies of the system in various states. The statistical ensemble is a probability distribution over all possible states of the system. In classical statistical mechanics, the ensemble is a probability distribution over phase points (as opposed to a single phase point in ordinary mechanics), usually represented as a distribution in a phase space with canonical coordinates. In quantum statistical mechanics, the ensemble is a probability distribution over pure states,〔The probabilities in quantum statistical mechanics should not be confused with quantum superposition. While a quantum ensemble can contain states with quantum superpositions, a single quantum state cannot be used to represent an ensemble.〕 and can be compactly summarized as a density matrix. As is usual for probabilities, the ensemble can be interpreted in different ways:〔 * an ensemble can be taken to represent the various possible states that a ''single system'' could be in (epistemic probability, a form of knowledge), or * the members of the ensemble can be understood as the states of the systems in experiments repeated on independent systems which have been prepared in a similar but imperfectly controlled manner (empirical probability), in the limit of an infinite number of trials. These two meanings are equivalent for many purposes, and will be used interchangeably in this article. However the probability is interpreted, each state in the ensemble evolves over time according to the equation of motion. Thus, the ensemble itself (the probability distribution over states) also evolves, as the virtual systems in the ensemble continually leave one state and enter another. The ensemble evolution is given by the Liouville equation (classical mechanics) or the von Neumann equation (quantum mechanics). These equations are simply derived by the application of the mechanical equation of motion separately to each virtual system contained in the ensemble, with the probability of the virtual system being conserved over time as it evolves from state to state. One special class of ensemble is those ensembles that do not evolve over time. These ensembles are known as ''equilibrium ensembles'' and their condition is known as ''statistical equilibrium''. Statistical equilibrium occurs if, for each state in the ensemble, the ensemble also contains all of its future and past states with probabilities equal to the probability of being in that state.〔Statistical equilibrium should not be confused with ''mechanical equilibrium''. The latter occurs when a mechanical system has completely ceased to evolve even on a microscopic scale, due to being in a state with a perfect balancing of forces. Statistical equilibrium generally involves states that are very far from mechanical equilibrium.〕 The study of equilibrium ensembles of isolated systems is the focus of statistical thermodynamics. Non-equilibrium statistical mechanics addresses the more general case of ensembles that change over time, and/or ensembles of non-isolated systems. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「statistical mechanics」の詳細全文を読む スポンサード リンク
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