nLab statistical mechanics

Statistical mechanics is the theoretical study of systems with a large number of degrees of freedom, and in particular statistical features of ensembles of large systems. An ensemble is a theoretical term denoting a collection of similar large systems under consideration, where statistical features of the ensemble are considered. Alternatively, an ensemble may be a probability distribution of similar physical systems. Statistical mechanics wants to extract a small number of relevant “macroscopical” features of a physical system determined as the average over an ensemble. One may consider ensembles with fixed features, such as the number of particles or the total energy, and in which hypothetically an ergodic hypothesis is true: after sufficient passage of time the system will evolve in a system which is arbitrary close to any given member of the ensemble.

Related entries

• thermodynamics, ergodic theory

• Brownian motion

• Liouville's equation

• Langevin equation

• stochastic process

• dissipation, fluctuation-dissipation theorem

• random matrix theory

• Euclidean field theory

• KMS state

• Schwinger-Keldysh formalism

category: physics