scholarly journals Non-equilibrium steady state formation in 3+1 dimensions

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Christian Ecker ◽  
Johanna Erdmenger ◽  
Wilke van der Schee
Keyword(s):  
Steady State ◽  
Energy Density ◽  
Rarefaction Wave ◽  
Riemann Problem ◽  
State Formation ◽  
Numerical Solutions ◽  
Entanglement Entropy ◽  
Rarefaction Waves ◽  
Combined System ◽  
Non Equilibrium

We present the first holographic simulations of non-equilibrium steady state formation in strongly coupled \mathcal{N}=4𝒩=4 SYM theory in 3+1 dimensions. We initially join together two thermal baths at different temperatures and chemical potentials and compare the subsequent evolution of the combined system to analytical solutions of the corresponding Riemann problem and to numerical solutions of ideal and viscous hydrodynamics. The time evolution of the energy density that we obtain holographically is consistent with the combination of a shock and a rarefaction wave: A shock wave moves towards the cold bath, and a smooth broadening wave towards the hot bath. Between the two waves emerges a steady state with constant temperature and flow velocity, both of which are accurately described by a shock+rarefaction wave solution of the Riemann problem. In the steady state region, a smooth crossover develops between two regions of different charge density. This is reminiscent of a contact discontinuity in the Riemann problem. We also obtain results for the entanglement entropy of regions crossed by shock and rarefaction waves and find both of them to closely follow the evolution of the energy density.

scholarly journals Uniqueness of rarefaction waves in multidimensional compressible Euler system

2015 ◽  
Vol 12 (03) ◽  
pp. 489-499 ◽  
Author(s):  
Eduard Feireisl ◽  
Ondřej Kreml
Keyword(s):  
Shock Wave ◽  
Rarefaction Wave ◽  
Riemann Problem ◽  
Euler System ◽  
Entropy Solutions ◽  
Infinitely Many Solutions ◽  
Rarefaction Waves ◽  
Convex Integration ◽  
Wave Solutions ◽  
Compressible Euler

We show that 1D rarefaction wave solutions are unique in the class of bounded entropy solutions to the multidimensional compressible Euler system. Such a result may be viewed as a counterpart of the recent examples of non-uniqueness of the shock wave solutions to the Riemann problem, where infinitely many solutions are constructed by the method of convex integration.

Supradegeneracy and the Second Law of Thermodynamics

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.

scholarly journals Modules or Mean-Fields?

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 552 ◽  
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.

scholarly journals Lifshitz hydrodynamics at generic z from a moving black brane

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Aruna Rajagopal ◽  
Larus Thorlacius
Keyword(s):  
Field Theory ◽  
Steady State ◽  
Critical Exponent ◽  
Stress Tensor ◽  
Perfect Fluid ◽  
Scale Invariance ◽  
Linear Momentum ◽  
Black Brane ◽  
Dilaton Gravity ◽  
Non Equilibrium

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.

Thermal Diffusivity of the Mott Insulator Ca2RuO4 in a Non-equilibrium Steady State

2021 ◽  
Vol 90 (6) ◽  
pp. 063601
Author(s):  
Shuji Kawasaki ◽  
Akitoshi Nakano ◽  
Hiroki Taniguchi ◽  
Hai Jun Cho ◽  
Hiromichi Ohta ◽  
...  
Keyword(s):  
Steady State ◽  
Thermal Diffusivity ◽  
Mott Insulator ◽  
Non Equilibrium

A steady-state non-equilibrium molecular dynamics approach for the study of evaporation processes

2013 ◽  
Vol 139 (13) ◽  
pp. 134701 ◽  
Author(s):  
Jianguo Zhang ◽  
Florian Müller-Plathe ◽  
Méziane Yahia-Ouahmed ◽  
Frédéric Leroy
Keyword(s):  
Molecular Dynamics ◽  
Steady State ◽  
Non Equilibrium Molecular Dynamics ◽  
Non Equilibrium

Verification of Finite Volume Computations on Steady-State Fluid Flow and Heat Transfer

2001 ◽  
Vol 124 (1) ◽  
pp. 11-21 ◽  
Author(s):  
J. Cadafalch ◽  
C. D. Pe´rez-Segarra ◽  
R. Co`nsul ◽  
A. Oliva
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Steady State ◽  
Finite Volume ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Independent Solution ◽  
Post Processing ◽  
Square Duct ◽  
Flow And Heat Transfer

This work presents a post-processing tool for the verification of steady-state fluid flow and heat transfer finite volume computations. It is based both on the generalized Richardson extrapolation and the Grid Convergence Index GCI. The observed order of accuracy and a error band where the grid independent solution is expected to be contained are estimated. The results corresponding to the following two and three-dimensional steady-state simulations are post-processed: a flow inside a cavity with moving top wall, an axisymmetric turbulent flow through a compressor valve, a premixed methane/air laminar flat flame on a perforated burner, and the heat transfer from an isothermal cylinder enclosed by a square duct. Discussion is carried out about the certainty of the estimators obtained with the post-processing procedure. They have been shown to be useful parameters in order to assess credibility and quality to the reported numerical solutions.

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