Time parametrization and stationary distributions in a relativistic gas

Ghodrat, Malihe; Montakhab, Afshin

doi:10.1103/physreve.82.011110

Cited by 16 publications

(20 citation statements)

References 31 publications

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“…This relativistic relation for temperature is not a true relation, and in fact, the temperature’s relation depends on the thermocouple apparatus used. A true thermocouple rejects this definition of temperature (For example, see [8], [10], [11]). Thus, to obtain a true relation between temperature and acceleration, we use concepts of BIon:…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Model for the Signal of Death and Emergence of Mind Out of Brain in Izhikevich Neuron Model

Fioranelli¹,

Sepehri²,

Roccia³

et al. 2019

Open Access Maced J Med Sci

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AIM:In this paper, using a mathematical model, we will show that for special exchanged photons, the Hamiltonian of a collection of neurons tends to a constant number and all activities is stopped. These photons could be called as the dead photons. To this aim, we use concepts of Bio-BIon in Izhikevich Neuron model.METHODS:In a neuron, there is a page of Dendrite, a page of axon’s terminals and a tube of Schwann cells, axon and Myelin Sheath that connects them. These two pages and tube form a Bio-Bion. In a Bio-Bion, exchanging photons and some charged particles between terminals of dendrite and terminals of axon leads to the oscillation of neurons and transferring information. This Bion produces the Hamiltonian, wave equation and action potential of Izhikevich Neuron model. Also, this Bion determines the type of dependency of parameters of Izhikevich model on temperature and frequency and obtains the exact shape of membrane capacitance, resting membrane potential and instantaneous threshold potential.RESULTS:Under some conditions, waves of neurons in this BIon join to each other and potential shrinks to a delta function. Consequently, total Hamiltonian of the system tends to a constant number and system of neuron act like a dead system. Finally, this model indicates that all neurons have the ability to produce similar waves and signals like waves of the mind.CONCLUSION:Generalizing this to biology, we can claim that neurons out of the brain can produce signals of minding and imaging and thus mind isn’t confined to the brain.

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Section: Introductionmentioning

confidence: 99%

A Mathematical Model for the Signal of Death and Emergence of Mind Out of Brain in Izhikevich Neuron Model

Fioranelli¹,

Sepehri²,

Roccia³

et al. 2019

Open Access Maced J Med Sci

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“…We therefore simply build such a generalized thermodynamic function using the Jüttner distribution and use it to calculate various thermodynamic relations. The Jüttner distribution is given by [9,10]:…”

Section: Resultsmentioning

confidence: 99%

Thermodynamics of a morphological transition in a relativistic gas

Montakhab¹,

Shahsavar²,

Ghodrat³

2014

Physica A: Statistical Mechanics and its Applications

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Recently, a morphological transition in the velocity distribution of a relativistic gas has been pointed out which shows hallmarks of a critical phenomenon. Here, we provide a general framework which allows for a thermodynamic approach to such a critical phenomenon. We therefore construct a thermodynamic potential which upon expansion leads to Landau-like (mean-field) theory of phase transition. We are therefore able to calculate critical exponents and explain the spontaneous emergence of order parameter as a result of relativistic constraints. Numerical solutions which confirm our thermodynamic approach are also provided. Our approach provides a general understanding of such a transition as well as leading to some new results. Finally, we briefly discuss some possible physical consequences of our results as well as considering the case of quantum relativistic gases.Comment: 5 pages, 5 figures. To appear in Physica

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“…instead of MB distribution ( f MB ) [56][57][58][59][60][61]. Jüttner distribution is indeed the relativistic extension of generalized isotropic MB distribution when E(p) = mγ(p)c 2 .…”

Section: Relativistic Gasmentioning

confidence: 99%

A Note on Effects of Generalized and Extended Uncertainty Principles on Jüttner Gas

2021

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In recent years, the implications of the generalized (GUP) and extended (EUP) uncertainty principles on Maxwell–Boltzmann distribution have been widely investigated. However, at high energy regimes, the validity of Maxwell–Boltzmann statistics is under debate and instead, the Jüttner distribution is proposed as the distribution function in relativistic limit. Motivated by these considerations, in the present work, our aim is to study the effects of GUP and EUP on a system that obeys the Jüttner distribution. To achieve this goal, we address a method to get the distribution function by starting from the partition function and its relation with thermal energy which finally helps us in finding the corresponding energy density states.

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Time parametrization and stationary distributions in a relativistic gas

Cited by 16 publications

References 31 publications

A Mathematical Model for the Signal of Death and Emergence of Mind Out of Brain in Izhikevich Neuron Model

A Mathematical Model for the Signal of Death and Emergence of Mind Out of Brain in Izhikevich Neuron Model

Thermodynamics of a morphological transition in a relativistic gas

A Note on Effects of Generalized and Extended Uncertainty Principles on Jüttner Gas

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