Stochastic Line Integrals as Metrics of Irreversibility and Heat Transfer

Stochastic line integrals provide a powerful tool for quantitatively characterizing irreversibility and detailed balance violation in noise-driven dynamical systems. A particular realization of such integrals, the stochastic area, was recently introduced for linear systems and has been tested experimentally in coupled linear electrical circuits [1,2]. In this talk, we provide a framework for understanding general properties of stochastic line integrals and clarify their implementation for experiments and simulations as well as their utility as metrics for quantifying non-equilibrium behavior. Theoretical results are supported by numerical studies of an overdamped, two-dimensional mass-spring system driven out of equilibrium. In this case, the stochastic area can be concisely expressed in terms of a streamfunction the sign of which determines the orientation of probability current loops. Furthermore, the stream function allows one to analytically understand the dependence of stochastic area on key parameters such as the noise strength (equivalently temperature) for both nonlinear and linear springs.
[1] A. Ghanta, J. Neu, and S. Teitsworth, Phys. Rev. E 95, 032128 (2017).
[2] J. P. Gonzalez, J. Neu, and S. Teitsworth, Phy. Rev. E 99, 022143 (2019).