Finite-Temperature de Bruijn
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Finite-Temperature de Bruijn Identities: Fisher Information as the Spectral Gap of Blahut--Arimoto Dynamics
arXiv:2606.03813v1 Announce Type: new Abstract: We uncover a finite-temperature extension of de Bruijn's identity -- the classical relation $\frac{d}{dt}h(X+\sqrt{t}Z)=\frac{1}{2}J(X)$ connecting differential entropy and Fisher information. Our framework is the spectral theory of Blahut--Arimoto (BA) dynamics, recently developed by Wang~\cite{Wang2026} for the analysis of rate-distortion optimization. The central observation is elementary yet profound: for Gaussian sources, the spectral gap...