The functional generalization of the Boltzmann-Vlasov equation and its Gauge-like symmetry
arXiv:2309.05154 · doi:10.21468/SciPostPhys.16.3.070
Abstract
We argue that one can model deviations from the ensemble average in non-equilibrium statistical mechanics by promoting the Boltzmann equation to an equation in terms of {\em functionals} , representing possible candidates for phase space distributions inferred from a finite observed number of degrees of freedom. We find that, provided the collision term and the Vlasov drift term are both included, a gauge-like redundancy arises which does not go away even if the functional is narrow. We argue that this effect is linked to the gauge-like symmetry found in relativistic hydrodynamics \cite{bdnk} and that it could be part of the explanation for the apparent fluid-like behavior in small systems in hadronic collisions and other strongly-coupled small systems\cite{zajc}. When causality is omitted this problem can be look at via random matrix theory show, and we show that in such a case thermalization happens much more quickly than the Boltzmann equation would infer. We also sketch an algorithm to study this problem numerically
Discussion significantly extended and reorganized Accepted for publication, scipost Physics
References in corpus (17)
- The Color Glass Condensate
- The stickiness of sound: An absolute lower limit on viscosity and the breakdown of second order relativistic hydrodynamics
- Anomalous Viscosity of an Expanding Quark-Gluon Plasma
- On the equivalence between the Boltzmann equation and classical field theory at large occupation numbers
- Hydrodynamic attractors, initial state energy and particle production in relativistic nuclear collisions
- Resistive dissipative magnetohydrodynamics from the Boltzmann-Vlasov equation
- Hydrodynamic attractors in heavy ion collisions: a review
- Two-particle azimuthal correlations in photonuclear ultraperipheral Pb+Pb collisions at 5.02 TeV with ATLAS
- Quark-Gluon Plasmas and Thermalization
- Fluctuating relativistic dissipative hydrodynamics as a gauge theory
- Thermalization of non-abelian gauge theories at next-to-leading order
- Fluctuating Relativistic hydrodynamics from Crooks theorem
- Three dimensional Yukawa models and CFTs at strong and weak couplings
- Emergent symmetries of relativistic fluid dynamics from local ergodicity
- The eigenvalue spectrum of a large real antisymmetric random matrix with non-zero mean
- Fluctuations of the Elliptic Flow
- Quantum Field Theory in Large N Wonderland: Three Lectures