Measurement of detailed balance violation in noise-driven linear circuits

In the context of noise-driven dynamical systems, detailed balance implies the equality of transition rates between pairs of system states, and also the vanishing of probability current everywhere in the system phase space under steady-state conditions. We report here on the measurement of the violation of detailed balance in coupled, noise-driven linear electronic circuits; in particular, we study two nominally identical RC circuits that are coupled either via variable capacitance or with more general linear coupling. The time-dependent voltages across each of the two primary capacitors serve as our dynamical variables, and the system is driven by two independent noise sources with independently variable amplitudes. Detailed balance violation is quantitatively detected by two methods: 1) explicit construction of the probability current density, and 2) by constructing the time-dependent area tensor as recently introduced in Ref. [1]. In comparing the two methods, we find that the area tensor is relatively simple to implement, computationally inexpensive, and provides a highly accurate means for detecting violations of detailed balance.

[1] A. Ghanta, J. C. Neu, & S. Teitsworth, Phys. Rev. E 95, 032128 (2017).