A possible dynamical phase transition between the dissipative and the non-dissipative solutions of a thermal process

Gambár, Katalin; Márkus, Ferenc

doi:10.1016/j.physleta.2006.09.050

Cited by 12 publications

(16 citation statements)

References 9 publications

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“…the wave-like or ballistic propagation turns into diffusive, then, this transition can be correctly discussed. This may yield remarkable progress, mainly in the interpretation of complex processes [14,28].…”

Section: Elaboration Of Formalism and The Directions Of Applicationsmentioning

confidence: 99%

Application of Potentials in the Description of Transport Processes

2016

APH

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Section: Elaboration Of Formalism and The Directions Of Applicationsmentioning

confidence: 99%

Application of Potentials in the Description of Transport Processes

2016

APH

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“…The long scientific experience on this topic showed that the theories are comparable and connectable on thisLagrangian-Hamiltonian -level, thus in the further development of the theory it is useful to apply this idea and scheme. In order to generate a dynamic temperature and the related covariant Klein-Gordon type field equation, to describe the heat propagation with finite speed -less than the speed of light -of action an abstract scalar potential field has been introduced (Gambár & Márkus, 2007). In this case the thermal energy propagation has wave-like modes.…”

Section: Lorentz Invariant Thermal Energy Propagationmentioning

confidence: 99%

“…Finally, it is important to mention and emphasize that the participating particles of the above treated thermal energy propagation cannot be observable directly as Bollini's and Rocca's detailed studies (Bollini & Rocca, 1997a;b;Bollini et al, 1999) show. This is a consequence of the fact that the tachyons do not move as free particles, thus they can be considered as the mediators of the dynamic phase transition (Gambár & Márkus, 2007;Márkus & Gambár, 2010).…”

Section: Calculation Of the Wheeler Propagatormentioning

confidence: 99%

Can a Lorentz Invariant Equation Describe Thermal Energy Propagation Problems?

Márkus¹

2011

Heat Conduction - Basic Research

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“…The applied mathematical model is based on the Hamiltonian formulation that can include the description of both the classical heat conduction (Fourier's heat conduction) [33] and the Lorentz invariant heat propagation [34,35] insuring a finite speed propagation of thermal signal (i.e., less than the speed of light). In the second treatment the main point is that it involves the classical heat conduction as a limit, thus we need to deal with this description in general.…”

Section: Introductionmentioning

confidence: 99%

“…(The effect of spinodal instability is very important and often found in the modern field theories [36,37].) Moreover, the study of thermal energy propagation from the slow heat conduction to the fast heat propagation clearly shows the existence of a dynamical phase transition [34,38].…”

Section: Introductionmentioning

confidence: 99%

Wheeler Propagator of the Lorentz Invariant Thermal Energy Propagation

Márkus

Gambár

2010

Int J Theor Phys

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Two decades ago it was made the first steps to establish a really Hamiltonian description of field theory of dissipative transport processes in order to apply all of the tools of modern field theories for these kind of processes. The great breakthrough was to introduce such scalar potential fields for the measurable quantities-temperature, pressure, etc.-, by which the complete Lagrangian-Hamiltonian formalism could be developed. Later it has been managed to create the differential equation for the relativistic invariant heat propagation by the help of the scalar field, which field can generate a dynamical temperature immediately. In the present paper it is focused on a farther step in the Lorentz invariant thermal energy propagation. Now, the temperature field satisfies a covariant field equation of a (wave-like) thermal energy propagation with finite speed-less than the speed of light. In our previous works the connection has been clarified between this scalar field and the usual local equilibrium temperature including the classical Fourier's heat conduction. The existence of a dynamical phase transition between the two kinds of propagation, between a wave and a non-wave, i.e., a dynamical phase transition between a non-dissipative and a dissipative thermal process is also found. Presently, it is pointed out that the so-called Wheeler propagator can be obtained without any difficulty for this process inspite of the existence of the dynamical phase transition and it can be seen that the causality condition is completed at the same time.

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A possible dynamical phase transition between the dissipative and the non-dissipative solutions of a thermal process

Cited by 12 publications

References 9 publications

Application of Potentials in the Description of Transport Processes

Application of Potentials in the Description of Transport Processes

Can a Lorentz Invariant Equation Describe Thermal Energy Propagation Problems?

Wheeler Propagator of the Lorentz Invariant Thermal Energy Propagation

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