Lifshitz hydrodynamics at generic z from a moving black brane

Abstract A Lifshitz black brane at generic dynamical critical exponent z > 1, with non-zero linear momentum along the boundary, provides a holographic dual description of a non-equilibrium steady state in a quantum critical fluid, with Lifshitz scale invariance but without boost symmetry. We consider moving Lifshitz branes in Einstein-Maxwell-Dilaton gravity and obtain the non-relativistic stress tensor complex of the dual field theory via a suitable holographic renormalisation procedure. The resulting black brane hydrodynamics and thermodynamics are a concrete holographic realization of a Lifshitz perfect fluid with a generic dynamical critical exponent.

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Nambu-Goldstone modes in non-equilibrium systems from AdS/CFT correspondence

Journal of High Energy Physics ◽

10.1007/jhep04(2021)040 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Shuta Ishigaki ◽

Masataka Matsumoto

Keyword(s):

Field Theory ◽

Steady State ◽

Dispersion Relation ◽

Dissipative System ◽

Constant Current ◽

Theory Approach ◽

Linear Dispersion ◽

Diffusive Behavior ◽

Goldstone Modes ◽

Non Equilibrium

Abstract We investigate dispersion relation of Nambu-Goldstone modes in a dissipative system realized by the AdS/CFT correspondence. We employ the D3/D7 model which represents $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory coupled to $$ \mathcal{N} $$ N = 2 flavor fields. If we consider massless quarks in the presence of an external magnetic field, the system exhibits the phase transition associated with the spontaneous symmetry breaking of the chiral symmetry. We find that the Nambu-Goldstone modes show a diffusive behavior in the dispersion relation, which agrees with that found with the effective field theory approach. We also study a non-equilibrium steady state which has a constant current flow in the presence of an external electric field. In a non-equilibrium steady state, we find that the Nambu-Goldstone modes show a linear dispersion in the real part of the frequency in addition to the diffusive behavior. Moreover, we analyze the linear dispersion of the Nambu-Goldstone modes in the hydrodynamic approximation. As a result, we find that the linear dispersion can be written as the analytic functions of quantities in the dual field theory. Our results imply that such a linear dispersion is a characteristic behavior of Nambu-Goldstone modes in a non-equilibrium steady state.

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Supradegeneracy and the Second Law of Thermodynamics

Journal of Non-Equilibrium Thermodynamics ◽

10.1515/jnet-2019-0051 ◽

2020 ◽

Vol 45 (2) ◽

pp. 121-132

Author(s):

Daniel P. Sheehan

Keyword(s):

Steady State ◽

Statistical Mechanics ◽

Population Inversion ◽

Laboratory Experiments ◽

Second Law Of Thermodynamics ◽

Second Law ◽

Boltzmann Factor ◽

Energy Currents ◽

Non Equilibrium

AbstractCanonical statistical mechanics hinges on two quantities, i. e., state degeneracy and the Boltzmann factor, the latter of which usually dominates thermodynamic behaviors. A recently identified phenomenon (supradegeneracy) reverses this order of dominance and predicts effects for equilibrium that are normally associated with non-equilibrium, including population inversion and steady-state particle and energy currents. This study examines two thermodynamic paradoxes that arise from supradegeneracy and proposes laboratory experiments by which they might be resolved.

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Non-equilibrium effective field theory and second sound

Journal of High Energy Physics ◽

10.1007/jhep04(2021)213 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Michael J. Landry

Keyword(s):

Field Theory ◽

Effective Field Theory ◽

Sound Wave ◽

Effective Field ◽

Second Sound ◽

Gauge Symmetries ◽

Sound Modes ◽

State Of Matter ◽

The Difference ◽

Non Equilibrium

Abstract We investigate the phenomenon of second sound in various states of matter from the perspective of non-equilibrium effective field theory (EFT). In particular, for each state of matter considered, we find that at least two (though sometimes multiple) qualitatively different EFTs exist at finite temperature such that there is always at least one EFT with a propagating second-sound wave and at least one with no such second-sound wave. To aid in the construction of these EFTs, we use the method of cosets developed for non-equilibrium systems. It turns out that the difference between the EFTs with and without second-sound modes can be understood as arising from different choices of a new kind of inverse Higgs constraint. Finally, we demonstrate that it is possible to bypass the need for new inverse Higgs constraints by formulating EFTs on a new kind of manifold that is like the usual fluid worldvolume, but with reduced gauge symmetries.

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Modules or Mean-Fields?

Entropy ◽

10.3390/e22050552 ◽

2020 ◽

Vol 22 (5) ◽

pp. 552 ◽

Cited By ~ 2

Author(s):

Thomas Parr ◽

Noor Sajid ◽

Karl J. Friston

Keyword(s):

Steady State ◽

Message Passing ◽

Mean Field Theory ◽

Functional Anatomy ◽

Mean Field ◽

State Density ◽

Stochastic Dynamical Systems ◽

Conditional Independency ◽

The Brain ◽

Non Equilibrium

The segregation of neural processing into distinct streams has been interpreted by some as evidence in favour of a modular view of brain function. This implies a set of specialised ‘modules’, each of which performs a specific kind of computation in isolation of other brain systems, before sharing the result of this operation with other modules. In light of a modern understanding of stochastic non-equilibrium systems, like the brain, a simpler and more parsimonious explanation presents itself. Formulating the evolution of a non-equilibrium steady state system in terms of its density dynamics reveals that such systems appear on average to perform a gradient ascent on their steady state density. If this steady state implies a sufficiently sparse conditional independency structure, this endorses a mean-field dynamical formulation. This decomposes the density over all states in a system into the product of marginal probabilities for those states. This factorisation lends the system a modular appearance, in the sense that we can interpret the dynamics of each factor independently. However, the argument here is that it is factorisation, as opposed to modularisation, that gives rise to the functional anatomy of the brain or, indeed, any sentient system. In the following, we briefly overview mean-field theory and its applications to stochastic dynamical systems. We then unpack the consequences of this factorisation through simple numerical simulations and highlight the implications for neuronal message passing and the computational architecture of sentience.

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Review of the holographic Lifshitz theory

International Journal of Modern Physics A ◽

10.1142/s0217751x1430049x ◽

2014 ◽

Vol 29 (24) ◽

pp. 1430049 ◽

Cited By ~ 6

Author(s):

Chanyong Park

Keyword(s):

Field Theory ◽

Finite Temperature ◽

Quasinormal Mode ◽

Thermodynamic Quantities ◽

Black Brane ◽

Zero Temperature ◽

Hydrodynamic Properties ◽

Relativistic Field ◽

Thermal Entropy ◽

Lifshitz Theory

We review interesting results achieved in recent studies on the holographic Lifshitz field theory. The holographic Lifshitz field theory at finite temperature is described by a Lifshitz black brane geometry. The holographic renormalization together with the regularity of the background metric allows to reproduce thermodynamic quantities of the dual Lifshitz field theory where the Bekenstein–Hawking entropy appears as the renormalized thermal entropy. All results satisfy the desired black brane thermodynamics. In addition, hydrodynamic properties are further reviewed in which the holographic retarded Green functions of the current and momentum operators are studied. In a nonrelativistic Lifshitz field theory, intriguingly, there exists a massive quasinormal mode at finite temperature whose effective mass is linearly proportional to temperature. Even at zero temperature and in the nonzero momentum limit, a quasinormal mode still remains unlike the dual relativistic field theory. Finally, we account for how adding impurity modifies the electric property of the nonrelativistic Lifshitz theory.

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