Experimental metrics for detection of detailed balance violation

We report on the measurement of detailed balance violation in a coupled, noise-driven linear electronic circuit consisting of two nominally identical RC elements that are coupled via a variable capacitance. The state variables are the time-dependent voltages across each of the two primary capacitors, and the system is driven by independent noise sources in series with each of the resistances. From the recorded time histories of these two voltages, we quantify violations of detailed balance by three methods: (1) explicit construction of the probability current density, (2) constructing the time-dependent stochastic area, and (3) constructing statistical fluctuation loops. In comparing the three methods, we find that the stochastic area is relatively simple to implement and computationally inexpensive and provides a highly sensitive means for detecting violations of detailed balance.