A nonequilibrium temperature and fluctuation theorem for soft-mode turbulence

Hidaka, Yoshiki; Hosokawa, Yusaku; Oikawa, Noriko; Tamura, Koyo; Anugraha, Rinto; Kai, Shoichi

doi:10.1016/j.physd.2009.07.003

Cited by 15 publications

(15 citation statements)

References 20 publications

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“…We experimentally found the dual structure of the modal autocorrelation in SMT and have theoretically revealed the mechanisms of the dual structure [29]. It has been reported that the spatiotemporal disorder in SMT generates non-thermal fluctuations [12,30] by which a nonMarkovian (i.e., memory) effect is expected to play a significant role in the relaxation dynamics.…”

Section: Introductionmentioning

confidence: 76%

Compressed exponential relaxation as superposition of dual structure in pattern dynamics of nematic liquid crystals

Narumi

Nugroho

Yoshitani

et al. 2013

AIP Conference Proceedings

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Soft-mode turbulence (SMT) is the spatiotemporal chaos observed in homeotropically aligned nematic liquid crystals, where non-thermal fluctuations are induced by nonlinear coupling between the NambuGoldstone and convective modes. The net and modal relaxations of the disorder pattern dynamics in SMT have been studied to construct the statistical physics of nonlinear nonequilibrium systems. The net relaxation dynamics is well-described by a compressed exponential function and the modal one satisfies a dual structure, dynamic crossover accompanied by a breaking of time-reversal invariance. Because the net relaxation is described by a weighted mean of the modal ones with respect to the wave number, the compressed-exponential behavior emerges as a superposition of the dual structure. Here, we present experimental results of the power spectra to discuss the compressed-exponential behavior and the dual structure from a viewpoint of the harmonic analysis. We also derive a relationship of the power spectra from the evolution equation of the modal autocorrelation function. The formula will be helpful to study non-thermal fluctuations in experiments such as the scattering methods.

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Section: Introductionmentioning

confidence: 76%

Compressed exponential relaxation as superposition of dual structure in pattern dynamics of nematic liquid crystals

Narumi

Nugroho

Yoshitani

et al. 2013

AIP Conference Proceedings

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“…In preceding articles, we discussed how to describe the motion of a particle in SMT using a generalized version of the Langevin equation [4,6]. Thermal Brownian motion is accurately described by the Langevin equation,…”

Section: Summary and Discussionmentioning

confidence: 99%

“…The random motion driven by nonthermal fluctuations or chaotic flows [1][2][3][4][5][6] has been investigated in the context of nonlinear physics and statistical mechanics far from equilibrium. Among these phenomena, motion dynamics driven by soft-mode turbulence (SMT) in the electroconvection of a nematic liquid crystal is interesting because of the existence of hierarchical structures such as locally aligned convective rolls and a globally disordered structure [7,8].…”

Section: Introductionmentioning

confidence: 99%

“…Among these phenomena, motion dynamics driven by soft-mode turbulence (SMT) in the electroconvection of a nematic liquid crystal is interesting because of the existence of hierarchical structures such as locally aligned convective rolls and a globally disordered structure [7,8]. Previous studies discussed the statistical-mechanical properties of the Brownianlike motion in SMT, such as anomalous behavior in the short time regime [4], the non-Gaussian distribution of velocity [5], and the application of the fluctuation theorem (FT) [6]. In these articles, although the asymptotic behavior of the finite-time diffusion coefficient was qualitatively associated with the local structure of SMT, the quantitative relation is still ambiguous.…”

Section: Introductionmentioning

confidence: 99%

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Duality of diffusion dynamics in particle motion in soft-mode turbulence

et al. 2013

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Nonthermal Brownian motion is investigated experimentally by injecting a particle into soft-mode turbulence (SMT), in the electroconvection of a nematic liquid crystal. It is clarified that the particle motion can be classified into two phases: fast motion, where particles move with the local convective flow, and slow motion, where they are carried by global slow pattern dynamics. We propose a simplified model to clarify the mechanism of the short-time and asymptotic behavior of diffusion. In our model, the correlation time is estimated as a function of a control parameter ɛ. The scaling of the SMT pattern correlation time, τ(d)∼ɛ(-1), is estimated from the particle dynamics, which is consistent with a previous report observed from the Eulerian viewpoint. The origin of the non-Gaussian distribution of the displacement in the short-time regime is also discussed and an analytical curve is introduced that quantitatively agrees with the experimental data. Our results clearly illustrate the characteristics of diffusive motion in SMT, which are considerably different from the conventional Brownian motion.

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“…It is therefore natural to approach the turbulence problem from the perspective of nonequilibrium statistical mechanics [12,13,14,15,16]. The statistical properties of turbulence in connection with the deviation from equilibrium has been investigated from the angles of fluctuation-dissipation theorem (FDT) [17,18,19], fluctuation theorem [20,21,22,23], large deviation theory [24,25,26], and time asymmetry in Lagrangian statistics [27,28,29,30,31] among others.…”

Section: Introductionmentioning

confidence: 99%

Potential landscape and flux field theory for turbulence and nonequilibrium fluid systems

Zhang

Wang

2018

Annals of Physics

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Turbulence is a paradigm for far-from-equilibrium systems without time reversal symmetry. To capture the nonequilibrium irreversible nature of turbulence and investigate its implications, we develop a potential landscape and flux field theory for turbulent flow and more general nonequilibrium fluid systems governed by stochastic Navier-Stokes equations. We find that equilibrium fluid systems with time reversibility are characterized by a detailed balance constraint that quantifies the detailed balance condition. In nonequilibrium fluid systems with nonequilibrium steady states, detailed balance breaking leads directly to a pair of interconnected consequences, namely, the non-Gaussian potential landscape and the irreversible probability flux, forming a 'nonequilibrium trinity'. The nonequilibrium trinity characterizes the nonequilibrium irreversible essence of fluid systems with intrinsic time irreversibility and is manifested in various aspects of these systems. The nonequilibrium stochastic dynamics of fluid systems including turbulence with detailed balance breaking is shown to be driven by both the nonGaussian potential landscape gradient and the irreversible probability flux, together with the reversible convective force and the stochastic stirring force. We reveal an underlying connection of the energy flux essential for turbulence energy cascade to the irreversible probability flux and the non-Gaussian potential landscape generated by detailed balance breaking. Using the energy flux as a center of connection, we demonstrate that the four-fifths law in fully developed turbulence is a consequence and reflection of the nonequilibrium trinity. We also show how the nonequilibrium trinity can affect the scaling laws in turbulence.

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A nonequilibrium temperature and fluctuation theorem for soft-mode turbulence

Cited by 15 publications

References 20 publications

Compressed exponential relaxation as superposition of dual structure in pattern dynamics of nematic liquid crystals

Compressed exponential relaxation as superposition of dual structure in pattern dynamics of nematic liquid crystals

Duality of diffusion dynamics in particle motion in soft-mode turbulence

Potential landscape and flux field theory for turbulence and nonequilibrium fluid systems

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