The Two-Particle Irreducible Effective Action for Classical Stochastic Processes

Tim Bode

doi:10.1088/1751-8121/ac73c6

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arXiv · 2111.14559

The Two-Particle Irreducible Effective Action for Classical Stochastic Processes

Tim Bode

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Abstract

By combining the two-particle-irreducible (2PI) effective action common in non-equilibrium quantum field theory with the classical Martin-Siggia-Rose formalism, self-consistent equations of motion for the first and second cumulants of non-linear classical stochastic processes are constructed. Such dynamical equations for correlation and response functions are important in describing non-equilibrium systems, where equilibrium fluctuation-dissipation relations are unavailable. The method allows to evolve stochastic systems from arbitrary Gaussian initial conditions. In the non-linear case, it is found that the resulting integro-differential equations can be solved with considerably reduced computational effort compared to state-of-the-art stochastic Runge-Kutta methods. The details of the method are illustrated by several physical examples.

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Tim Bode. 2021-11-29. The Two-Particle Irreducible Effective Action for Classical Stochastic Processes. https://doi.org/10.1088/1751-8121%2Fac73c6

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