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SUMMARY:Noether's theorem and hyperforces in statistical mechanics - Sophi
 e Hermann (Sorbonne University)
DTSTART:20250506T120000Z
DTEND:20250506T130000Z
UID:TALK229933@talks.cam.ac.uk
CONTACT:Sarah Loos
DESCRIPTION:Noether's theorem is familiar to most physicists due its funda
 mental role in linking the existence of conservation laws to the underlyin
 g symmetries of a physical system. I will present how Noether's reasoning 
 also applies within statistical mechanics to thermal systems\, where fluct
 uations are paramount. Exact identities ("sum rules") follow thereby from 
 functional symmetries. The obtained sum rules contain both\, well-known re
 lations\, such as the first order term of the Yvon-Born-Green (YBG) hierar
 chy (i.e. the spatially resolved force balance)\, as well as previously un
 known identities\, relating different correlations in many-body systems. T
 he identification of the underlying Noether concept enables their systemat
 ic \nderivation. Since Noether's theorem is quite general it is possible t
 o generalize to arbitrary thermodynamic observables. This generalization y
 ields sum rules \nfor hyperforces\, i.e. the mean product between the cons
 idered observable and the relevant forces that act in the system. Simulati
 ons of a range of simple and complex liquids demonstrate the fundamental r
 ole of these \ncorrelation functions in the characterization of spatial st
 ructure\, such as quantifying spatially inhomogeneous self-organization. F
 inally\, we show that the considered phase-space-shifting is a gauge trans
 formation in \nequilibrium statistical mechanics.
LOCATION:Center for Mathematical Sciences\, Lecture room MR4
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