Link between Continuous and Discrete Descriptions of Noise in Nonlinear Resistive Electrical Components

TL;DR

This paper explores the connection between continuous and discrete noise models in nonlinear resistive electrical components, revealing thermodynamic constraints and conditions for their equivalence, especially at low voltages.

Contribution

It demonstrates how thermodynamics constrains noise modeling, linking stochastic differential equations and Markovian master equations in nonlinear resistive devices.

Findings

Thermodynamics dictates the use of the Hänggi-Klimontovich prescription in noise modeling.

A generalized Johnson-Nyquist relation is derived for nonlinear resistive components.

The discrete and continuous noise models are shown to be compatible under thermodynamic principles at low voltages.

Abstract

We consider the modeling of noise in a nonlinear, classical, resistive electrical component using two models: i) a continuous description based on a stochastic differential equation with a white thermal Gaussian noise; ii) a discrete, shot noise model based on a Markovian master equation. We show that thermodynamics imposes in i) the use of the H\"anggi-Klimontovich (H-K) prescription when the noise depends on bias voltage, and implies a generalized Johnson-Nyquist relation for the noise where the conductance is replaced by the ratio mean current over voltage. In ii) we show that the discrete description compatible with thermodynamics leads to the continuous one of i) with again the H-K prescription. Here the generalized Johnson-Nyquist relation for noise is recovered only at low voltage, when the continuous description is valid.