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Verfasst von:Koenigstein, Adrian [VerfasserIn]   i
 Steil, Martin J. [VerfasserIn]   i
 Wink, Nicolas [VerfasserIn]   i
 Grossi, Eduardo [VerfasserIn]   i
 Braun, Jens [VerfasserIn]   i
Titel:Numerical fluid dynamics for FRG flow equations: zero-dimensional QFTs as numerical test cases
Titelzusatz:II. Entropy production and irreversibility of RG flows
Verf.angabe:Adrian Koenigstein, Martin J. Steil, Nicolas Wink, Eduardo Grossi, Jens Braun
E-Jahr:2022
Jahr:13 September 2022
Umfang:22 S.
Fussnoten:Gesehen am 28.09.2022
Titel Quelle:Enthalten in: Physical review
Ort Quelle:Woodbury, NY : Inst., 2016
Jahr Quelle:2022
Band/Heft Quelle:106(2022), 6, Artikel-ID 065013, Seite 1-22
ISSN Quelle:2470-0029
Abstract:We demonstrate that the reformulation of renormalization group (RG) flow equations as nonlinear heat equations has severe implications on the understanding of RG flows in general. We demonstrate by explicitly constructing an entropy function for a zero-dimensional Z2-symmetric model that the dissipative character of generic nonlinear diffusion equations is also hard-coded in the functional RG equation. This renders RG flows manifestly irreversible, revealing the semigroup property of RG transformations on the level of the flow equation itself. Additionally, we argue that the dissipative character of RG flows, its irreversibility and the entropy production during the RG flow may be linked to the existence of a so-called C−/A-function. In total, this introduces an asymmetry in the so-called RG time—in complete analogy to the thermodynamic arrow of time—and allows for an interpretation of infrared actions as equilibrium solutions of dissipative RG flows equations. The impossibility of resolving microphysics from macrophysics is evident in this framework. Furthermore, we directly link the irreversibility and the entropy production in RG flows to an explicit numerical entropy production, which is manifest in diffusive and non-linear partial differential equations (PDEs) and a standard mathematical tool for the analysis of PDEs. Using exactly solvable zero-dimensional Z2-symmetric models, we explicitly compute the (numerical) entropy production related to the total variation nonincreasing property of the PDE during RG flows toward the infrared limit. Finally, we discuss generalizations of our findings and relations to the C−/A-theorem as well as how our work may help to construct truncations of RG flow equations in the future, including numerically stable schemes for solving the corresponding PDEs.
DOI:doi:10.1103/PhysRevD.106.065013
URL:Bitte beachten Sie: Dies ist ein Bibliographieeintrag. Ein Volltextzugriff für Mitglieder der Universität besteht hier nur, falls für die entsprechende Zeitschrift/den entsprechenden Sammelband ein Abonnement besteht oder es sich um einen OpenAccess-Titel handelt.

Volltext ; Verlag: https://doi.org/10.1103/PhysRevD.106.065013
 Volltext: https://link.aps.org/doi/10.1103/PhysRevD.106.065013
 DOI: https://doi.org/10.1103/PhysRevD.106.065013
Datenträger:Online-Ressource
Sprache:eng
K10plus-PPN:1817232002
Verknüpfungen:→ Zeitschrift

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