The functional renormalization group is equivalent to a diffeomorphism-modified Ricci flow on the information metric of coupling space, with the log effective action generating diffeomorphisms and an F-entropy serving as the driving Lyapunov functional toward a Ricci soliton.
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Functional Renormalization Group as a Ricci Flow: An $\mathcal{F}$-Entropy Perspective on Information Metric Dynamics
The functional renormalization group is equivalent to a diffeomorphism-modified Ricci flow on the information metric of coupling space, with the log effective action generating diffeomorphisms and an F-entropy serving as the driving Lyapunov functional toward a Ricci soliton.