What does statistical mechanics mean?

Statistical mechanics consists of the study of the particular laws which govern the behavior and properties of macroscopic bodies, that is to say, bodies made up of a very large number of separate particles (atoms and molecules). The number of particles is of the order of 1023, the Avogadro number. From microscopic point of view, complete information about the system can be obtained by setting up the equations of motion and then solving them. In general, equations of motion are second order differential equations in both classical and quantum case (and twice the number of first order differential equations in Hamiltonian formulation). Their solutions will have two constants of integration for each equation of motion, corresponding to each particle, to be determined from the initial conditions of individual particles. This is simply a tremendous task involving a lot of paperwork and is simply a near impossibility. But a new type of regularity can be found by relating the macroscopic description to a few variables based on statistical laws, which arise due to the large number of particles involved. These laws become quite meaningless if applied to a single particle or even a mechanical system with very few degrees of freedom. The development and exposition of these laws constitute the subject matter of statistical mechanics, which arise due to the large number of particles involved The importance of statistical mechanics lies in the fact that, in nature, we are dealing all the time with macroscopic bodies (matter in a bulk) whose behavior can’t be described by pure mechanical methods and which in fact do obey statistical laws The science of statistical mechanics has the special function of providing reasonable method for treating the behavior of mechanical systems under circumstances such that out knowledge of the condition of the system is less than the maximal knowledge which would be theoretically possible. The principles of ordinary mechanics may be regarded as allowing us to make precise predictions as to the future state of a mechanical system from a precise knowledge of it is initial state. On the other hand, the principles of statistical mechanics are to be regarded as permitting us to make reasonable predictions as to the future condition of a system, which may be expected to hold on the average, starting from an incomplete knowledge of it is initial state. Since our actual contacts with the physical world are such that we never do have the maximal knowledge of systems regarded as theoretically allowable, the idea of the precise state of a system is in any case an abstract limiting concept. Hence the methods of ordinary mechanics really apply to somewhat highly idealized situations, and the methods of statistical mechanics provide a significant supplement in the direction of decreased abstraction and closer correspondence between theoretical methods and actual experience. Even in the case of simple systems of only a few degrees of freedom, where our lack of maximal knowledge is not due to difficulties arising from the complexity of the system, the methods of statistical mechanics may be applied to a system whose initial state is not completely specified .

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