Statistical mechanics treats the detailed state of a system (its quantum state or, in classical models, its position in phase space) as unknown and subject to statistical uncertainties; entropy is a measure of this uncertainty. Statistical mechanics describes the distribution of states in an equilibrium system at a given temperature (describing either the distribution of probabilities of quantum states or the probability density function in phase space), and can be used to derive thermodynamic properties from properties at the molecular level. These equilibrium results are useful in nanomechanical design.

The study of the collective behavior of large numbers of interacting particles. Properties of interest include those describing time-dependent, irreversible process. The basic principles of this discipline were laid down in the nineteenth century by Ludwig Boltzmann, James Clerk Maxwell, and Josiah Willard Gibbs.

"...the mechanics of large assemblies of (relatively) simple systems such as molecules in a gas, atoms in a crystal, photons in a laser beam, stars in a galaxy, cars on a highway, people in a social group, and so on. The main purpose of this science is to understand the behavior of the assembly as a whole in terms of the behavior of its constituents." [1

field theory for people with low energy