This connection has been addressed in detail in two papers by Samuel and Chowdury: "Geometric flows and black hole entropy" and "Energy, entropy and the Ricci flow". For a discussion of both these papers, see chapter 6 of "On the Emergence Theme of Physics" by Robert Carroll.

Perelman has given a gradient formulation for the Ricci flow, introducing an "entropy function" which increases monotonically along the flow. We pursue a thermodynamic analogy and apply Ricci flow ideas to general relativity. We investigate whether Perelman's entropy is related to (Bekenstein-Hawking) geometric entropy as familiar from black hole thermodynamics. From a study of the fixed points of the flow we conclude that Perelman entropy is not connected to geometric entropy. However, we notice that there is a very similar flow which does appear to be connected to geometric entropy. The new flow may find applications in black hole physics suggesting for instance, new approaches to the Penrose inequality.

Perelman himself wrote about his entropy formula for the Ricci flow that "The interplay of statistical physics and (pseudo)-riemannian geometry occurs in the subject of Black Hole Thermodynamics, developed by Hawking et al. Unfortunately, this subject is beyond my understanding at the moment."

Subsequently, this connection has been explored in some detail in two papers by Samuel and Chowdury: "Geometric flows and black hole entropy" and "Energy, entropy and the Ricci flow". For a discussion of both these papers, see chapter 6 of "On the Emergence Theme of Physics" by Robert Carroll.

Perelman has given a gradient formulation for the Ricci flow, introducing an "entropy function" which increases monotonically along the flow. We pursue a thermodynamic analogy and apply Ricci flow ideas to general relativity. We investigate whether Perelman's entropy is related to (Bekenstein-Hawking) geometric entropy as familiar from black hole thermodynamics. From a study of the fixed points of the flow we conclude that Perelman entropy is not connected to geometric entropy. However, we notice that there is a very similar flow which does appear to be connected to geometric entropy. The new flow may find applications in black hole physics suggesting for instance, new approaches to the Penrose inequality.

This question has been addressed in detail in two papers by Samuel and Chowdury: "Geometric flows and black hole entropy" and "Energy, entropy and the Ricci flow". For a critical discussion of both these papers, see chapter 6 of "On the Emergence Theme of Physics" by Robert Carroll.

Perelman has given a gradient formulation for the Ricci flow, introducing an "entropy function" which increases monotonically along the flow. We pursue a thermodynamic analogy and apply Ricci flow ideas to general relativity. We investigate whether Perelman's entropy is related to (Bekenstein-Hawking) geometric entropy as familiar from black hole thermodynamics. From a study of the fixed points of the flow we conclude that Perelman entropy is not connected to geometric entropy. However, we notice that there is a very similar flow which does appear to be connected to geometric entropy. The new flow may find applications in black hole physics suggesting for instance, new approaches to the Penrose inequality.

This connection has been addressed in detail in two papers by Samuel and Chowdury: "Geometric flows and black hole entropy" and "Energy, entropy and the Ricci flow". For a discussion of both these papers, see chapter 6 of "On the Emergence Theme of Physics" by Robert Carroll.

Perelman has given a gradient formulation for the Ricci flow, introducing an "entropy function" which increases monotonically along the flow. We pursue a thermodynamic analogy and apply Ricci flow ideas to general relativity. We investigate whether Perelman's entropy is related to (Bekenstein-Hawking) geometric entropy as familiar from black hole thermodynamics. From a study of the fixed points of the flow we conclude that Perelman entropy is not connected to geometric entropy. However, we notice that there is a very similar flow which does appear to be connected to geometric entropy. The new flow may find applications in black hole physics suggesting for instance, new approaches to the Penrose inequality.