Characterizing irreversibility in noise-driven dynamical systems with stream functions

Stochastic line integrals provide a useful means for quantitatively characterizing irreversibility and heat transfer in noise-driven dynamical systems. One realization is the stochastic area, recently studied theoretically and experimentally in coupled noise-driven linear electrical circuits [1,2]. For the case of stationary statistics in two-dimensional systems, we show that the stochastic area can be concisely expressed in terms of a stream function, the sign of which determines the orientation of probability current. We formulate an inhomogeneous boundary value problem for the stream function in which the source term depends on non-equilibrium driving terms (e.g., temperature difference for a system driven by multiple thermal noises.) The stream function allows determination of analytical expressions for the dependence of stochastic area growth rate on parameters of interest such as the system noise strengths and the character of system nonlinearity when present. In this talk we apply the stream function technique to the following systems: two masses moving in one spatial dimension and coupled by a linear or nonlinear spring with each mass driven by a distinct thermal noise source; and a nonlinear tunnel diode circuit model driven by multiple noise sources.

[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).