13 Facts About Statistical mechanics

In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities.

Statistical mechanics arose out of the development of classical thermodynamics, a field for which it was successful in explaining macroscopic physical properties—such as temperature, pressure, and heat capacity—in terms of microscopic parameters that fluctuate about average values and are characterized by probability distributions.

Statistical mechanics fills this disconnection between the laws of mechanics and the practical experience of incomplete knowledge, by adding some uncertainty about which state the system is in.

Whereas ordinary mechanics only considers the behaviour of a single state, statistical mechanics introduces the statistical ensemble, which is a large collection of virtual, independent copies of the system in various states.

Statistical mechanics equilibrium occurs if, for each state in the ensemble, the ensemble contains all of its future and past states with probabilities equal to the probability of being in that state.

Whereas statistical mechanics proper involves dynamics, here the attention is focussed on statistical equilibrium.

For example, recent studies shows that the theory of statistical mechanics can be built without the equal a priori probability postulate.

The field of non-equilibrium statistical mechanics is concerned with understanding these non-equilibrium processes at the microscopic level.

In principle, non-equilibrium statistical mechanics could be mathematically exact: ensembles for an isolated system evolve over time according to deterministic equations such as Liouville's equation or its quantum equivalent, the von Neumann equation.

Non-equilibrium Statistical mechanics is therefore an active area of theoretical research as the range of validity of these additional assumptions continues to be explored.

One approach to non-equilibrium statistical mechanics is to incorporate stochastic behaviour into the system.

Since equilibrium statistical mechanics is mathematically well defined and more amenable for calculations, the fluctuation–dissipation connection can be a convenient shortcut for calculations in near-equilibrium statistical mechanics.

Statistical mechanics was initiated in the 1870s with the work of Boltzmann, much of which was collectively published in his 1896 Lectures on Gas Theory.