Abstract
Systems composed of many particles involve a very large number of degrees of freedom, and it is most often uninteresting—not to say hopeless—to try to describe in a detailed way the microscopic state of the system. The aim of statistical physics is rather to restrict the description of the system to a few relevant macroscopic observables, and to predict the average values of these observables, or the relations between them.
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Notes
- 1.
The fundamental theory describing the dynamics of particles at the atomic scale is actually quantum mechanics rather than classical mechanics. However, classical mechanics is in many cases of interest a reasonable approximation. We shall thus remain in the framework of classical mechanics for the purpose of the present booklet.
- 2.
For a more detailed introduction to the Hamiltonian formalism, see, e.g., Ref. [5].
- 3.
The concept of energy, introduced here on a specific example, plays a fundamental role in physics. Though any precise definition of the energy is necessarily formal and abstract, the notion of energy can be thought of intuitively as a quantity that can take very different forms (kinetic, electromagnetic or gravitational energy, but also internal energy exchanged through heat transfers) in such a way that the total amount of energy remains constant. Hence an important issue is to describe how energy is transferred from one form to another. For instance, in the case of the particle attached to a spring, the kinetic energy \(E_c\) and potential energy U of the spring are continuously exchanged, in a reversible manner. In the presence of friction forces, kinetic energy would also be progressively converted, in an irreversible way, into internal energy, thus raising the temperature of the system.
- 4.
We do not follow here the evolution of the constant c under renormalization, and rather focus on the evolution of the physically relevant coupling constant J.
References
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T.L. Hill, An Introduction to Statistical Thermodynamics (Dover, New York, 1986)
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Bertin, E. (2012). Equilibrium Statistical Physics. In: A Concise Introduction to the Statistical Physics of Complex Systems. SpringerBriefs in Complexity. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23923-6_1
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