Timeline for The relations between the Perelman's entropy functional and notions of entropy from statistical mechanics

8 events

when toggle format	what		by	license	comment
Feb 25, 2015 at 21:25	vote	accept	Sepideh Bakhoda
Nov 23, 2013 at 18:17	answer	added	user41263		timeline score: 10
May 19, 2013 at 0:43	answer	added	Robert Haslhofer		timeline score: 9
May 18, 2013 at 18:55	answer	added	Carlo Beenakker		timeline score: 7
May 18, 2013 at 15:39	comment	added	Deane Yang		Although it might seem like nothing more than a formal correspondence, the power of using entropy-type functionals for certain types of elliptic and parabolic PDE's indicates strongly to me that there is a deeper connection to the physical and information theoretic definitions of entropy than what we currently understand.
May 18, 2013 at 15:25	comment	added	Carlo Beenakker		it seems to be little more than a formal correspondence, judging from page 11 of arxiv.org/abs/math.DG/0211159
May 18, 2013 at 14:43	comment	added	Deane Yang		The more standard notions of entropy, notably Boltzmann and Shannon are roughly of the form $\int u\log u\,d\mu$ and if in Perelman's definiton you set $u = e^{-f}$ you get one term like this. The gradient term looks to me more like Fisher information, which can be viewed as the derivative of entropy with respect to time under Brownian motion. I suppose that the scalar curvature arises because everything is on a curved instead of flat space. The constant term arises from normalization. But this is all just my speculation.
May 18, 2013 at 14:33	history	asked	Sepideh Bakhoda	CC BY-SA 3.0