Statistical mechanics aims at studying the macroscopic parameters of a system in equilibrium from a knowledge of the microscopic properties of its constituent particles using the laws of mechanics. This is different from the approach of thermodynamics which aims at studying a macroscopic system in equilibrium from macroscopic phenomenological standpoint without considering the microscopic constituents of the system.

Statistical physics is the branch of physics where a scheme to calculate the free energy is formulated. In statistical physics, we use the fact that matter consists of atoms. On the basis of a knowledge of the microscopic laws that govern the motion of atoms and most importantly an additional law of statistical physics, it gives a general expression for the free energy. Since statistical physics starts from the microscopic level, it can discuss not only thermal equilibrium states, but also non equilibrium states. Small deviations from thermal equilibrium can be discussed by the use of linear response theory, and we can discuss such effects as electrical or thermal conductivity. However, the statistical physics of non equilibrium states is not yet well established, especially for states far from equilibrium. It is an actively investigated branch of physics even today.

In statistical mechanics we study the physical systems consisting of very large number of particles. The simplest system of interest is a perfect gas in thermal equilibrium. From the macroscopic point of view it appears to be a continuum. A complete set of thermodynamic variables, characterizing its equilibrium state, is the energy E, volume V and the number of molecules N. The N, although referred to molecules for convenience, is a macroscopic variable because it is directly related to the mass of the gas. From the microscopic point of view, the gas (matter) consists of discrete particles, like atoms or molecules.

We know that, a proper thermodynamic system is made up or composed of an assembly of molecules or atoms, its macroscopic behavior can be explained in terms of the microscopic behavior of its constituent particles. This basic tenet provides the foundation for the subject of statistical thermodynamics. Clearly, statistical methods are mandatory as even 1 cm^{3} of a perfect gas contains some 10^{19} molecules or atoms.

By definition, the *Boltzmann constant is equal to the gas constant (R) divided by the Avogadro constant (N*_{A}). It is denoted by the symbol k_{B}_{}. The value for k_{B} is equal to 1.380×10^{-23} JK^{-1}

It is a general belief that physics is a science where fundamental laws of nature are established. A student being introduced to physics first encounters the fundamental theories, for instance Newtonian mechanics, electrodynamics and the theory of relativity, and see in these the ideals of a scientific theory. In statistical mechanics it seems that statistics has to be taken serious. However, when one inspects theories on statistical mechanics to see how they present the concepts of probability theory. A physicist who is confronted with the interpretation of experimental results for a thesis, or who wishes to analyze the effects of complex systems in his or her later profession, will almost inevitably find that this cannot be done without the application of statistical methods. Limited information about the dynamics of a system and uncontrollable influences on the system often mean that is can only be considered as a statistical system. And apart from that, when analyzing experimental data, one always has to take into account that any measured value has an uncertainty expressed by its error. One should not only expect limited knowledge but one should also know how to deal with it. One has to be acquainted with mathematical tools allowing one to quantify uncertainties both in the knowledge about a system to be modeled as well as in the knowledge that can be inferred from experimental data of a system. These tools are probability theory and statistics. Statistics plays a special role in the description and analysis of complex systems; a physicist will need statistics not only in the context of statistical mechanics.

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