Constraints on fluid dynamics from equilibrium partition functions

By Nabamita Banerjee, J. Bhattacharya, Sayantani Bhattacharyya, Sachin Jain, Shiraz Minwalla, Tarun Sharma. 2012

330 citations recorded by the source corpus.

A bstractWe study the thermal partition function of quantum field theories on arbitrary stationary background spacetime, and with arbitrary stationary background gauge fields, in the long wavelength expansion. We demonstrate that the equations of relativistic hydrodynamics are significantly constrained by the requirement of consistency with any partition function. In examples at low orders in the derivative expansion we demonstrate that these constraints coincide precisely with the equalities between hydrodynamical transport coefficients that follow from the local form of the second law of thermodynamics. In particular we recover the results of Son and Surowka on the chiral magnetic and chiral vorticity flows, starting from a local partition function that manifestly reproduces the field theory anomaly, without making any reference to an entropy current. We conjecture that the relations between transport coefficients that follow from the second law of thermodynamics agree to all orders in the derivative expansion with the constraints described in this paper.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ec3566551dd44a0e06a48b4132dd7a5e3c77c95d

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Citations in the corpus

First-order relativistic hydrodynamics is stable (2019, background): “Analogous consistency conditions for two-derivative terms in the constitutive relations were worked out in [25, 26].”
(Non)-renormalization of the chiral vortical effect coefficient (2012, methodology): “In order to see the connection between the 3-dimensional Chern-Simons term and the CVE, we dimensionally reduce the theory on the compactified time direction [5].”
Effective field theory of dissipative fluids (2015, background): “This is precisely the prescription recently analyzed in detail in [13, 14].”
Anomalous transport of Weyl fermions in Weyl semimetals (2013, methodology): “Since the effects are non-dissipative they can also be obtained from effective action approaches [45, 46] or using Ward identities [47].”
Generalized global symmetries and dissipative magnetohydrodynamics (2016, background): “[10,45] that, in general, such considerations can be extended to higher orders in the derivative expansion and provide an alternative route to deriving the constraints on transport that arise from the local form of the second law.”
Relativistic magnetohydrodynamics (2017, background): “J H E P 0 5 ( 2 0 1 7 ) 0 0 1 velocity uα and the chemical potential μ are functions of the Killing vector and the external sources [5, 6]”
Holographic Quantum Matter (2016, background): “While we will follow the conventional description [485], the reader may be interested in more modern treatments that dispense of (421) as an additional postulate [68; 151; 326; 422].”