zbMATH — the first resource for mathematics

Effective field theory of dissipative fluids. II: Classical limit, dynamical KMS symmetry and entropy current. (English) Zbl 1382.81205
Summary: In this paper we further develop the fluctuating hydrodynamics proposed in our Paper I [ibid. 2017, No. 9, Paper No. 95, 82 p. (2017; Zbl 1382.81199)] in a number of ways. We first work out in detail the classical limit of the hydrodynamical action, which exhibits many simplifications. In particular, this enables a transparent formulation of the action in physical spacetime in the presence of arbitrary external fields. It also helps to clarify issues related to field redefinitions and frame choices. We then propose that the action is invariant under a $$Z_2$$ symmetry to which we refer as the dynamical KMS symmetry. The dynamical KMS symmetry is physically equivalent to the previously proposed local KMS condition in the classical limit, but is more convenient to implement and more general. It is applicable to any states in local equilibrium rather than just thermal density matrix perturbed by external background fields. Finally we elaborate the formulation for a conformal fluid, which contains some new features, and work out the explicit form of the entropy current to second order in derivatives for a neutral conformal fluid.

MSC:
 81T60 Supersymmetric field theories in quantum mechanics 82B10 Quantum equilibrium statistical mechanics (general) 76Y05 Quantum hydrodynamics and relativistic hydrodynamics 94A17 Measures of information, entropy
Full Text:
References:
 [1] M. Crossley, P. Glorioso and H. Liu, Effective field theory of dissipative fluids, arXiv:1511.03646 [INSPIRE]. · Zbl 1382.81199 [2] Dubovsky, S.; Gregoire, T.; Nicolis, A.; Rattazzi, R., Null energy condition and superluminal propagation, JHEP, 03, 025, (2006) · Zbl 1226.83090 [3] S. Dubovsky, L. Hui, A. Nicolis and D.T. Son, Effective field theory for hydrodynamics: thermodynamics and the derivative expansion, Phys. Rev.D 85 (2012) 085029 [arXiv:1107.0731] [INSPIRE]. · Zbl 1226.83090 [4] Endlich, S.; Nicolis, A.; Porto, RA; Wang, J., Dissipation in the effective field theory for hydrodynamics: first order effects, Phys. Rev., D 88, 105001, (2013) [5] S. Dubovsky, L. Hui and A. Nicolis, Effective field theory for hydrodynamics: Wess-Zumino term and anomalies in two spacetime dimensions, Phys. Rev.D 89 (2014) 045016 [arXiv:1107.0732] [INSPIRE]. · Zbl 1388.83352 [6] Endlich, S.; Nicolis, A.; Rattazzi, R.; Wang, J., The quantum mechanics of perfect fluids, JHEP, 04, 102, (2011) · Zbl 1250.81116 [7] A. Nicolis and D.T. Son, Hall viscosity from effective field theory, arXiv:1103.2137 [INSPIRE]. · Zbl 1388.83360 [8] A. Nicolis, Low-energy effective field theory for finite-temperature relativistic superfluids, arXiv:1108.2513 [INSPIRE]. · Zbl 1390.81382 [9] L.V. Delacrétaz, A. Nicolis, R. Penco and R.A. Rosen, Wess-Zumino Terms for Relativistic Fluids, Superfluids, Solids and Supersolids, Phys. Rev. Lett.114 (2015) 091601 [arXiv:1403.6509] [INSPIRE]. · Zbl 1388.83352 [10] Geracie, M.; Son, DT, Effective field theory for fluids: Hall viscosity from a Wess-Zumino-Witten term, JHEP, 11, 004, (2014) [11] Grozdanov, S.; Polonyi, J., Viscosity and dissipative hydrodynamics from effective field theory, Phys. Rev., D 91, 105031, (2015) [12] Harder, M.; Kovtun, P.; Ritz, A., On thermal fluctuations and the generating functional in relativistic hydrodynamics, JHEP, 07, 025, (2015) · Zbl 1388.83352 [13] Kovtun, P.; Moore, GD; Romatschke, P., Towards an effective action for relativistic dissipative hydrodynamics, JHEP, 07, 123, (2014) [14] Haehl, FM; Loganayagam, R.; Rangamani, M., The eightfold way to dissipation, Phys. Rev. Lett., 114, 201601, (2015) · Zbl 1388.81456 [15] Haehl, FM; Loganayagam, R.; Rangamani, M., Adiabatic hydrodynamics: the eightfold way to dissipation, JHEP, 05, 060, (2015) · Zbl 1388.81456 [16] Haehl, FM; Loganayagam, R.; Rangamani, M., The fluid manifesto: emergent symmetries, hydrodynamics and black holes, JHEP, 01, 184, (2016) · Zbl 1388.83350 [17] Haehl, FM; Loganayagam, R.; Rangamani, M., Topological σ-models & dissipative hydrodynamics, JHEP, 04, 039, (2016) · Zbl 1388.83351 [18] F.M. Haehl, R. Loganayagam and M. Rangamani, Schwinger-Keldysh formalism. Part I: BRST symmetries and superspace, JHEP06 (2017) 069 [arXiv:1610.01940] [INSPIRE]. · Zbl 1380.81369 [19] F.M. Haehl, R. Loganayagam and M. Rangamani, Schwinger-Keldysh formalism. Part II: thermal equivariant cohomology, JHEP06 (2017) 070 [arXiv:1610.01941] [INSPIRE]. · Zbl 1380.81370 [20] N. Andersson and G.L. Comer, A covariant action principle for dissipative fluid dynamics: From formalism to fundamental physics, Class. Quant. Grav.32 (2015) 075008 [arXiv:1306.3345] [INSPIRE]. · Zbl 1328.83028 [21] Floerchinger, S., Variational principle for theories with dissipation from analytic continuation, JHEP, 09, 099, (2016) · Zbl 1390.81382 [22] D. Nickel and D.T. Son, Deconstructing holographic liquids, New J. Phys.13 (2011) 075010 [arXiv:1009.3094] [INSPIRE]. [23] Boer, J.; Heller, MP; Pinzani-Fokeeva, N., Effective actions for relativistic fluids from holography, JHEP, 08, 086, (2015) · Zbl 1388.83360 [24] Crossley, M.; Glorioso, P.; Liu, H.; Wang, Y., Off-shell hydrodynamics from holography, JHEP, 02, 124, (2016) · Zbl 1388.83344 [25] J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, Clarendon Press, Oxford U.K. (2002). · Zbl 0865.00014 [26] P. Gao and H. Liu, Emergent Supersymmetry in Local Equilibrium Systems, arXiv:1701.07445 [INSPIRE]. · Zbl 1384.81134 [27] K. Jensen, N. Pinzani-Fokeeva and A. Yarom, Dissipative hydrodynamics in superspace, arXiv:1701.07436 [INSPIRE]. [28] P. Glorioso and H. Liu, The second law of thermodynamics from symmetry and unitarity, arXiv:1612.07705 [INSPIRE]. [29] Banerjee, N.; Bhattacharya, J.; Bhattacharyya, S.; Jain, S.; Minwalla, S.; Sharma, T., Constraints on fluid dynamics from equilibrium partition functions, JHEP, 09, 046, (2012) · Zbl 1397.82026 [30] Jensen, K.; Kaminski, M.; Kovtun, P.; Meyer, R.; Ritz, A.; Yarom, A., Towards hydrodynamics without an entropy current, Phys. Rev. Lett., 109, 101601, (2012) [31] Haack, M.; Yarom, A., Universality of second order transport coefficients from the gauge-string duality, Nucl. Phys., B 813, 140, (2009) · Zbl 1194.81207 [32] Shaverin, E.; Yarom, A., Universality of second order transport in Gauss-Bonnet gravity, JHEP, 04, 013, (2013) · Zbl 1342.83306 [33] Grozdanov, S.; Starinets, AO, On the universal identity in second order hydrodynamics, JHEP, 03, 007, (2015) · Zbl 1317.83068 [34] S. Grozdanov and A.O. Starinets, Zero-viscosity limit in a holographic Gauss-Bonnet liquid, Theor. Math. Phys.182 (2015) 61 [Teor. Mat. Fiz.182 (2014) 76]. · Zbl 1226.83090 [35] E. Shaverin, A breakdown of a universal hydrodynamic relation in Gauss-Bonnet gravity, arXiv:1509.05418 [INSPIRE]. · Zbl 1342.83306 [36] P. Romatschke, Relativistic Viscous Fluid Dynamics and Non-Equilibrium Entropy, Class. Quant. Grav.27 (2010) 025006 [arXiv:0906.4787] [INSPIRE]. · Zbl 1184.83026 [37] Bhattacharyya, S., Constraints on the second order transport coefficients of an uncharged fluid, JHEP, 07, 104, (2012) [38] Bhattacharyya, S., Entropy current from partition function: one example, JHEP, 07, 139, (2014)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.