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Statistical Physics Volume 5 von Lifshitz, E. M. (eBook)

  • Verlag: Elsevier Reference Monographs
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Statistical Physics

A lucid presentation of statistical physics and thermodynamics which develops from the general principles to give a large number of applications of the theory.

Produktinformationen

    Format: ePUB
    Kopierschutz: AdobeDRM
    Seitenzahl: 563
    Sprache: Englisch
    ISBN: 9780080570464
    Verlag: Elsevier Reference Monographs
    Größe: 5746 kBytes
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Statistical Physics

CHAPTER I THE FUNDAMENTAL PRINCIPLES OF STATISTICAL PHYSICS

Publisher Summary

Statistical physics is the study of special laws that govern the behavior and properties of macroscopic bodies. The general character of these laws does not depend on the mechanics that describes the motion of the individual particles in a body, but their substantiation demands a different argument in the two cases. Information concerning the motion of a mechanical system is obtained by constructing and integrating the equations of motion of the system that are equal in number to its degrees of freedom. These statistical laws resulting from the presence of a large number of particles forming the body cannot be reduced to mechanical laws. They cease to have meaning when applied to mechanical systems with a small number of degrees of freedom. Thus, although the motion of systems with a large number of degrees of freedom obeys the same laws of mechanics as that of systems consisting of a small number of particles, the existence of many degrees of freedom results in laws of a different kind.
§ 1 Statistical distributions

Statistical physics , often called for brevity simply statistics , consists in the study of the special laws which govern the behaviour and properties of macroscopic bodies (that is, bodies formed of a very large number of individual particles, such as atoms and molecules). To a considerable extent the general character of these laws does not depend on the mechanics (classical or quantum) which describes the motion of the individual particles in a body, but their substantiation demands a different argument in the two cases. For convenience of exposition we shall begin by assuming that classical mechanics is everywhere valid.

In principle, we can obtain complete information concerning the motion of a mechanical system by constructing and integrating the equations of motion of the system, which are equal in number to its degrees of freedom. But if we are concerned with a system which, though it obeys the laws of classical mechanics, has a very large number of degrees of freedom, the actual application of the methods of mechanics involves the necessity of setting up and solving the same number of differential equations, which in general is impracticable. It should be emphasised that, even if we could integrate these equations in a general form, it would be completely impossible to substitute in the general solution the initial conditions for the velocities and coordinates of all the particles.

At first sight we might conclude from this that, as the number of particles increases, so also must the complexity and intricacy of the properties of the mechanical system, and that no trace of regularity can be found in the behaviour of a macroscopic body. This is not so, however, and we shall see below that, when the number of particles is very large, new types of regularity appear.

These statistical laws resulting from the very presence of a large number of particles forming the body cannot in any way be reduced to purely mechanical laws. One of their distinctive features is that they cease to have meaning when applied to mechanical systems with a small number of degrees of freedom. Thus, although the motion of systems with a very large number of degrees of freedom obeys the same laws of mechanics as that of systems consisting of a small number of particles, the existence of many degrees of freedom results in laws of a different kind.

The importance of statistical physics in many other branches of theoretical physics is due to the fact that in Nature we continually encounter macroscopic bodies whose behaviour can not be fully described by the methods of mechanics alone, for the reasons mentioned above, and which obey statistical laws.

In proceeding to formulate the fundamental probl

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