Entropy production in 2D theory in the Kadanoff–Baym approach

Nishiyama, Akihiro

doi:10.1016/j.nuclphysa.2009.10.081

Cited by 17 publications

(19 citation statements)

References 40 publications

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“…As long as we know, this is the first work to calculate the time dependence of entropy in non-integrable field theory except for the kinetic entropy shown in Ref. [41].…”

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confidence: 95%

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Entropy production from chaoticity in Yang-Mills field theory with use of the Husimi function

et al. 2016

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We investigate possible entropy production in Yang-Mills (YM) field theory by using a quantum distribution function called Husimi function fH(A, E, t) for YM field, which is given by a coarse graining of Wigner function and non-negative. We calculate the Husimi-Wehrl (HW) entropy SHW(t) = −TrfH log fH defined as an integral over the phase-space, for which two adaptations of the test-particle method are used combined with Monte-Carlo method. We utilize the semiclassical approximation to obtain the time evolution of the distribution functions of the YM field, which is known to show a chaotic behavior in the classical limit. We also make a simplification of the multi-dimensional phase-space integrals by making a product ansatz for the Husimi function, which is found to give a 10-20 per cent over estimate of the HW entropy for a quantum system with a few degrees of freedom. We show that the quantum YM theory does exhibit the entropy production, and that the entropy production rate agrees with the sum of positive Lyapunov exponents or the Kolmogorov-Sinai entropy, suggesting that the chaoticity of the classical YM field causes the entropy production in the quantum YM theory.

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“…As long as we know, this is the first work to calculate the time dependence of entropy in non-integrable field theory except for the kinetic entropy shown in Ref. [41].…”

mentioning

confidence: 95%

“…This is a first work to calculate the time evolution of entropy in a non-integrable field theory except for the kinetic entropy shown in Ref. [41] as long as we know. We have shown that the HW entropy is produced and the growth rates roughly agree with Lyapunov exponents.…”

mentioning

confidence: 98%

Entropy production from chaoticity in Yang-Mills field theory with use of the Husimi function

et al. 2016

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“…In this section, we derive a kinetic entropy current from the Kadanoff-Baym equations with first order approximation of the gradient expansion and show the H-theorem for the leading-order approximations in the coupling expansion based on [56][57][58]. The analysis in this section is similar to that in open systems (the central region connected to the left and the right region) [59].…”

Section: Kinetic Entropy Current In the Kadanoff-baym Equations And Tmentioning

confidence: 99%

Non-Equilibrium Quantum Brain Dynamics: Super-Radiance and Equilibration in 2 + 1 Dimensions

Nishiyama

Tanaka

Tuszyński

2019

Entropy

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We derive time evolution equations, namely the Schrödinger-like equations and the Klein–Gordon equations for coherent fields and the Kadanoff–Baym (KB) equations for quantum fluctuations, in quantum electrodynamics (QED) with electric dipoles in 2 + 1 dimensions. Next we introduce a kinetic entropy current based on the KB equations in the first order of the gradient expansion. We show the H-theorem for the leading-order self-energy in the coupling expansion (the Hartree–Fock approximation). We show conserved energy in the spatially homogeneous systems in the time evolution. We derive aspects of the super-radiance and the equilibration in our single Lagrangian. Our analysis can be applied to quantum brain dynamics, that is QED, with water electric dipoles. The total energy consumption to maintain super-radiant states in microtubules seems to be within the energy consumption to maintain the ordered systems in a brain.

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“…In this section, we introduce the kinetic entropy current in the first order of the gradient expansion [63][64][65], and give a proof of the H-theorem in the Next-to-Leading Order approximation of the coupling expansion and in the Leading-Order approximation in the tunneling coupling expansion. The variable of Green functions and self-energy is (X, p) with the center-of-mass coordinate X x y 2 º + and momentum p by the use of the Fourier transformation of the relative space-time x−y of (x, y) in this section.…”

Section: Kinetic Entropy Current and The H-theoremmentioning

confidence: 99%

Non-Equilibrium ϕ⁴ theory for networks: towards memory formations with quantum brain dynamics

Nishiyama

Tuszyński

2019

J. Phys. Commun.

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We investigate the time evolution of quantum fields in neutral scalar f 4 theory for open systems with the central region and the multiple reservoirs (networks) as a toy model of quantum field theory of the brain. First we investigate the Klein-Gordon (KG) equations and the Kadanoff-Baym (KB) equations in open systems in d+1 dimensions. Next, we introduce the kinetic entropy current and provide the proof of the H-theorem for networks. Finally, we solve the KG and the KB equations numerically in spatially homogeneous systems in 1+1 dimensions. We find that decoherence, entropy saturation and chemical equilibration all occur during the time evolution in the networks. We also show how coherent field transfer takes place in the networks.where water molecules' electric dipoles surrounding neurons become aligned in the same direction with the direction of the spontaneous breakdown of the rotational symmetry leading to a macroscopic ordered state. It has also been hypothesized that these coherent states might be specifically formed in the axonal and dendritic microtubule bundles which pack neuronal interiors in the brain [28]. Consequently, Nambu-Goldstone quanta emerging in the SSB effect, called polaritons, are absorbed into longitudinal modes of photons, and massive photons are created (via a Higgs mechanism). When photons acquire mass, they can stay in the coherent regions in the brain. In such situations they are called evanescent photons. The order parameters associated with this phenomenon are the coherent photon fields and the coherent charged Bose fields, which correspond to the mass of photons and the square root of the number of aligned dipoles. QBD describes several characteristic physical properties of memory, namely its diversity, long-term imperfect stability and nonlocality [6,7] and it does so by adopting unitarily inequivalent vacua in QFT. Vacua in QFT are different from those in quantum mechanics. Diverse unitarily inequivalent vacua in QFT appear due to the presence of an infinite number of the degrees of freedom of quantum fields [35]. Here, the term 'nonlocality' in QFT is distinguished from quantum nonlocality with entanglement. The dynamical order in the QFT system is maintained by massless quanta propagating in the whole coherent region, in which the propagation speed is consistent with the special theory of relativity. The size of each coherent region is on the order of 50 μm. Each memory is subdivided by coherent states distributed in several regions of the brain. In QBD, there are at least two types of quantum mechanisms of information transfer and integration among coherent regions. The first one is related to microtubules which connect two coherent regions [28]. Pulse propagation from one side (connected with one coherent state) to the other side (connected with the other) of microtubules can occur due to the self-induced transparency without the thermal loss of coherence since the time-scale of propagation is less than that of thermal interactions. What is required for this to occur i...

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Entropy production in 2D theory in the Kadanoff–Baym approach

Cited by 17 publications

References 40 publications

Entropy production from chaoticity in Yang-Mills field theory with use of the Husimi function

Entropy production from chaoticity in Yang-Mills field theory with use of the Husimi function

Non-Equilibrium Quantum Brain Dynamics: Super-Radiance and Equilibration in 2 + 1 Dimensions

Non-Equilibrium ϕ⁴ theory for networks: towards memory formations with quantum brain dynamics

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Entropy production in 2D theory in the Kadanoff–Baym approach

Cited by 17 publications

References 40 publications

Entropy production from chaoticity in Yang-Mills field theory with use of the Husimi function

Entropy production from chaoticity in Yang-Mills field theory with use of the Husimi function

Non-Equilibrium Quantum Brain Dynamics: Super-Radiance and Equilibration in 2 + 1 Dimensions

Non-Equilibrium ϕ4 theory for networks: towards memory formations with quantum brain dynamics

Contact Info

Product

Resources

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Non-Equilibrium ϕ⁴ theory for networks: towards memory formations with quantum brain dynamics