The physical systems are constituted by a very large number of components (moving particles, atoms, molecules). As a bridge between the macroscopic world of thermodynamic and the microscopic world of particles, the Statistical Mechanics tries to deduce/explain the macroscopic (large scale) properties of the systems based on the microscopic behavior of their components, since it results from a joint application of the laws of mechanics – classical or quantum, depending on context and work interests – and the probability theory. To avoid working with the motion equations of an unusually large number of components, we are forced to resort to the theory of probabilities to justify and reproduce the macroscopic regularities.
The study of equilibrium situations is an important preliminary requirement for the analysis of out-of-equilibrium cases, which are certainly very interesting, but often much more complicated. In addition, the statistical mechanics of equilibrium are well-founded, through the construction of the ‘Gibbs’ ensembles. Fixed the macroscopic parameters of a system, we have a state (macroscopic) of equilibrium, to which usually correspond many microscopic states (or microstates). It is the statistical mechanics of the identification of microscopic states of physical systems, the formulation of some hypothesis on the statistical weight of each of these states, and the establishment of a link between the microstates and a potential thermodynamic model that is capable of describing the macroscopic behavior of the system.
On the other hand, given a problem, the differences between the deterministic and the probabilistic approach are relatively significant. In the first, the data are estimated to find the best value for each input parameter and, after being processed by models analytical or numeric, provide only one result. In a probabilistic approach the uncertainties in the parameters and also in the models are clearly recognized. Input characteristics are defined as random variables, that is, some parameters assume any value within an admitted range. As a result, the results of the analysis models also show variations, so that A possible range of results is obtained, as well as their respective probabilities.
