Symmetries of generating functionals of Langevin processes with colored multiplicative noise
Camille Aron, Giulio Biroli, Leticia F. Cugliandolo
TL;DR
This paper investigates the symmetries of generating functionals in Langevin processes with colored multiplicative noise, unifying different formalisms and deriving key relations like fluctuation theorems and Schwinger-Dyson equations.
Contribution
It provides a comprehensive analysis of symmetries in Langevin processes with colored noise using multiple formalisms, linking them to fundamental physical relations.
Findings
Unified treatment of Martin-Siggia-Rose-Janssen-deDominicis and supersymmetric formalisms.
Derived relations include fluctuation theorems, fluctuation-dissipation theorems, and Schwinger-Dyson equations.
Identified invariances in the vanishing friction limit for Newtonian dynamics.
Abstract
We present a comprehensive study of the symmetries of the generating functionals of generic Langevin processes with multiplicative colored noise. We treat both Martin-Siggia-Rose-Janssen-deDominicis and supersymmetric formalisms. We summarize the relations between observables that they imply including fluctuation relations, fluctuation-dissipation theorems, and Schwinger-Dyson equations. Newtonian dynamics and their invariances follow in the vanishing friction limit.
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