Nonequilibrium quantum electrodynamics: Entropy production during equilibration

Nishiyama, Akihiro; Tuszyński, Jack A.

doi:10.1142/s021797921850265x

Cited by 5 publications

(15 citation statements)

References 51 publications

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“…This condition simplifies numerical simulations in the Kadanoff-Baym equations since we need not estimate the momentum shift p → p ± α∂ζ in the finite-size lattice for the momentum space. As a result, the simulations for Kadanoff-Baym equations for dipoles and photons will be similar to those in QED with charged bosons in [72].…”

Section: Discussionmentioning

confidence: 58%

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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Section: Discussionmentioning

confidence: 58%

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

Nishiyama

Tanaka

Tuszyński

2019

Entropy

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Section: Discussionmentioning

confidence: 58%

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

Nishiyama¹,

Tanaka²,

Tuszyński³

2019

Preprint

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We derive time evolution equations, namely the Schrodinger-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 1st 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 a 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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“…Even in m 2 >0, we can show the Higgs mechanism with the nonzero expectation value of charged bosons j by preparing nonzero charge density of fermions as in QED with charged fermions [66]. It is also possible to show the nonzero expectation value of charged bosons j by preparing nonzero charge density of incoherent charged bosons [67]. This is because the potential energy j F[¯] is given by m e A phase ) is equivalent to the chemical potential.…”

Section: Discussionmentioning

confidence: 98%

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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Nonequilibrium quantum electrodynamics: Entropy production during equilibration

Cited by 5 publications

References 51 publications

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

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

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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Nonequilibrium quantum electrodynamics: Entropy production during equilibration

Cited by 5 publications

References 51 publications

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

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

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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Product

Resources

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