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SUMMARY:Beyond Linear Response: Equivalence between Thermodynamic Geometry
  and Optimal Transport - Adrianne Zhong\, UC Berkeley
DTSTART:20241105T130000Z
DTEND:20241105T140000Z
UID:TALK220432@talks.cam.ac.uk
CONTACT:Balázs Németh
DESCRIPTION:A fundamental result of thermodynamic geometry is that the opt
 imal\, minimal-work protocol that drives a nonequilibrium system between t
 wo thermodynamic states in the slow-driving limit is given by a geodesic o
 f the friction tensor\, a Riemannian metric defined on control space. For 
 overdamped dynamics in arbitrary dimensions\, we demonstrate that thermody
 namic geometry is equivalent to 𝐿2 optimal transport geometry defined o
 n the space of equilibrium distributions corresponding to the control para
 meters. We show that obtaining optimal protocols past the slow-driving or 
 linear response regime is computationally tractable as the sum of a fricti
 on tensor geodesic and a counterdiabatic term related to the Fisher inform
 ation metric. These geodesic-counterdiabatic optimal protocols are exact f
 or parametric harmonic potentials\, reproduce the surprising nonmonotonic 
 behavior recently discovered in linearly biased double well optimal protoc
 ols\, and explain the ubiquitous discontinuous jumps observed at the begin
 ning and end times.
LOCATION:Center for Mathematical Sciences\, Lecture room MR4
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