Path-integral formalism for classical Brownian motion in a general environment

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Abstract
The path-integral formalism for classical Brownian motion in a general environment is derived from the first principles of microdynamics by using the path-integral formulation of classical mechanics. The classical influence functional, which contains a nonlocal dissipation term and a colored noise term, is introduced. We show that there exists a classical fluctuation-dissipation relation. We also compare this classical influence functional theory with the well-known quantum influence-functional theory.

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