Experimental metrics for detection of detailed balance violation

TL;DR

This paper investigates how to detect violations of detailed balance in a coupled electronic circuit driven by noise, comparing three methods and highlighting the stochastic area as an effective detection tool.

Contribution

It introduces and compares three methods for quantifying detailed balance violation, emphasizing the efficiency and sensitivity of the stochastic area approach.

Findings

Stochastic area method is simple and computationally inexpensive.

All three methods can detect detailed balance violations.

Stochastic area provides high sensitivity for detection.

Abstract

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) by constructing the time-dependent stochastic area, and 3) by constructing statistical fluctuation loops. In comparing the three methods, we find that the stochastic area is relatively simple to implement, computationally inexpensive, and provides a highly sensitive means for detecting violations of detailed balance.