TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.3.070
TI  - The functional generalization of the Boltzmann-Vlasov equation and its gauge-like symmetry
PY  - 2024/03/11
UR  - https://www.scipost.org/SciPostPhys.16.3.070
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 3
SP  - 070
A1  - Torrieri, Giorgio
AB  - 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 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 [Ann. Phys. 442, 168902 (2022)] 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 [Annu. Rev. Nucl. Part. Sci. 68, 211 (2018)]. When causality and Lorentz invariance are 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.
ER  -

@Article{10.21468/SciPostPhys.16.3.070,
	title={{The functional generalization of the Boltzmann-Vlasov equation and its gauge-like symmetry}},
	author={Giorgio Torrieri},
	journal={SciPost Phys.},
	volume={16},
	pages={070},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.3.070},
	url={https://scipost.org/10.21468/SciPostPhys.16.3.070},
}