Publications

We determine the conditions under which the nonlinear Maxwell-Cattaneo theory of charge transport admits a local Gaussian Schwinger-Keldysh embedding with a particular modified dynamical KMS symmetry. We show that treating the additional vector as intrinsically dissipative fundamentally modifies the entropy-current analysis: the hydrostatic generating functional no longer fixes all entropy-current improvements, which must instead be supplied independently. Subsequently we discuss the additional constraints not contained in the hydrodynamic analysis that are imposed by the modified KMS transformation becoming a symmetry of the action. We both interpret and supply the corresponding stochastic quasi-hydrodynamics.

Modern effective field theories of dissipative hydrodynamics, built on the Schwinger-Keldysh formalism, include thermal noise that is not Gaussian. The resultant higher-order noise vertices are constrained by symmetries, but otherwise treated as free parameters. We show explicitly that symmetry constraints alone do not guarantee these vertices yield a genuine probability distribution. Requiring a probability interpretation yields sharp bounds between cumulants that are invisible to the symmetry analysis. The bounds are optimal: their boundaries are attained by explicit positive distributions, and constructive completions are provided for both negative- and positive-kurtosis noise data. This gives closed-form nonlinear response and an exact sampling algorithm, whose Monte Carlo implementation reproduces the exact cumulants and nonlinear fluctuation-dissipation relations. Confronted with microscopic results, the framework places a sharp lower bound on the time step required for a positive stochastic completion of a quartic model of the Brownian particle used in the literature, while holographically computed SU(2) noise vertices pass a nontrivial continuum fourth-order positivity test.

This note provides a comprehensive examination of the various approaches to formulating relativistic hydrodynamics, with a particular emphasis on the canonical approach. Relativistic hydrodynamics plays a crucial role in understanding the behavior of fluids in high-energy astrophysical phenomena and heavy-ion collisions. The canonical approach is explored in detail, highlighting its foundational principles, mathematical formulations, and practical implications in modeling relativistic fluid dynamics. Following this, we delve into linear response theory, elucidating its relevance in the context of hydrodynamics. We analyze the response of relativistic fluids to external perturbations, discussing the theoretical framework and key results. This dual focus aims to bridge the gap between theoretical foundations and practical applications, offering a robust perspective on the dynamic interplay between relativistic hydrodynamics and linear response theory.