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.

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