Fluctuating relativistic dissipative hydrodynamics as a gauge theory

Relativistic fluids, hydrodynamic frames and their Galilean versus Carrollian avatars

“…We have made that choice here, and we will not further discuss this side of hydrodynamic-frame invariance, but rather focus on the kinematical aspects. More information can be found in the already quoted literature, and in particular in [10][11][12][13][14][15][16][17][18][19].…”

“…We will not delve in analyzing the effects induced on thermodynamic observables by the local Lorentz transformations (for that see e.g. [10][11][12][13][14][15][16][17][18][19]85]), but will conclude this discussion with some remarks. At the first place, as already stressed, there is no microscopic definition of the entropy current.…”

“…A comprehensive presentation of the subject can be found in [3][4][5][6], where the main difficulties, namely causality, stability and shock structure, are discussed in length. 1 More recent progress has been reported in [9][10][11][12][13][14][15][16][17][18][19], showing that the debate is still ongoing. It is worth stressing that the above phenomenological descriptions of out-of-equilibrium phenomena are enshrined by relativistic kinetic theory.…”

Linear response hydrodynamics of a relativistic dissipative fluid with spin

“…We indeed expect the introduction of correlations between microstates with no equilibrium counterpart since the deviation from the environment (Ψ−sector), at the local level, has no meaningful hydrodynamic approach. This assumption and local causality require [23] the inclusion of additional degrees of freedom breaking the symmetries associated with the equilibrium but having relaxational dynamics (although fluctuations mean these are not uniquely defined [17]). Microscopic interactions are responsible for the relaxation of degrees of freedom and the second law of thermodynamics means that in the absence of backreaction [6] dynamics should be relaxational with respect to their source.…”

“…The advantages, as written earlier, are a direct connection with microscopic entropy and, since conservation laws do not dictate the dynamics, a bypassing of the pseudo-gauge issue. The disadvantage is that away from the ideal limit free energy is not maximized exactly so a Schwinger-Keldysh formalism, and a precise fluctuation-dissipation relation, are needed to hold for the dynamics to be well-defined [17].…”