Year: 2026
Type: preprint
Abstract: One of the longstanding open questions in linear response theory concerns its true range of validity. Determining when the linear approximation can be trusted typically requires knowledge of second-order corrections, which are often difficult to compute explicitly. In this letter, I propose a self-consistent criterion for the validity of linear response, formulated in terms of a typical length scale that emerges from the fluctuation-response inequality within the theory itself. The result applies to classical open systems. I illustrate the criterion with explicit examples of Brownian particles in harmonic traps, and classical open systems presenting Kibble-Zurek mechanism. Finally, I discuss the physical meaning of this typical length, providing both thermodynamic and information-theoretic interpretations.
Source: arXiv (Cornell University)
Author: Nazé, Pierre
Institution: Universidade Federal do Pará
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7129530201
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