Seminar Details
2025-02-25 (14h) : Noise modelling and analysis of nonlinear circuits and systems: From statistical mechanics to nonlinear dynamics
At Maxwell building (Shannon room)
Organized by Mathematical Engineering
Speaker :
Michele Bonnin (Polytechnico di Torino)
Abstract :
The theory of random fluctuations in linear systems does not extend to the internal noise in nonlinear systems. In this talk, we will review the standard methods for modeling internal noise in linear circuits and systems. After examining the thermodynamic requirements for a consistent model, it will be demonstrated that applying linear-system methods to nonlinear systems leads to circuit behaviors that violate thermodynamic principles. A series of tests will be introduced to assess whether a given noise model for nonlinear devices aligns with accepted thermodynamic principles. We will explore the validity of Gaussian and shot-noise models for nonlinear devices, as well as the limitations and shortcomings of approaches based on Langevin and Fokker-Planck equations. Additionally, a stochastic description using the master equation will be presented, which relates to the one-time probability density of Markov processes governing the fluctuating electrical quantities. Finally, we will discuss the implications of these findings for emerging computational paradigms such as neuromorphic and reservoir computing.