Bounding Variance and Skewness of Fluctuations in Nonlinear Mesoscopic Systems with Stochastic Thermodynamics

TL;DR

This paper investigates the limitations of Gaussian noise approximations in nonlinear mesoscopic systems, revealing that fluctuations often exceed classical predictions and are influenced by skewness, highlighting the need for a thermodynamically consistent stochastic theory.

Contribution

It demonstrates that variance in nonlinear systems surpasses classical predictions due to skewness, challenging Gaussian assumptions and proposing a thermodynamically consistent stochastic framework.

Findings

Variance exceeds classical predictions controlled by skewness.

Symmetric fluctuations obey extended Johnson-Nyquist formula.

Gaussian approximation is physically inconsistent for certain nonlinear models.

Abstract

Fluctuations arising in nonlinear dissipative systems (diode, transistors, chemical reaction, etc.) subject to an external drive (voltage, chemical potential, etc.) are well known to elude any simple characterization such as the fluctuation-dissipation theorem (also called Johnson-Nyquist law, or Einstein's law in specific contexts). Using results from stochastic thermodynamics, we show that the variance of these fluctuations exceeds the variance predicted by a suitably extended version of Johnson-Nyquist's formula, by an amount that is controlled by the skewness (third moment) of the fluctuations. As a consequence, symmetric fluctuations necessarily obey the extended Johnson-Nyquist formula. This shows the physical inconsistency of Gaussian approximation for the noise arising in some nonlinear models, such as MOS transistors or chemical reactions. More generally, this suggests the need for a stochastic nonlinear systems theory that is compatible with the teachings of thermodynamics.