Classical field theory and stochastic properties of hyperbolic equations of dissipative processes

Márkus, Ferenc; Gambár, Katalin; Vázquez, F.; Río, J. A. del

doi:10.1016/s0378-4371(99)00054-0

Cited by 10 publications

(5 citation statements)

References 46 publications

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“…As a consequence of this, it can be shown that the Chapman-Kolgomorov equation is fulfilled, the Onsager's regression hypothesis is valid and the system fluctuations can be handled [21].…”

Section: Elaboration Of Formalism and The Directions Of Applicationsmentioning

confidence: 76%

Application of Potentials in the Description of Transport Processes

2016

APH

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“…As a consequence of this, it can be shown that the Chapman-Kolgomorov equation is fulfilled, the Onsager's regression hypothesis is valid and the system fluctuations can be handled [21].…”

Section: Elaboration Of Formalism and The Directions Of Applicationsmentioning

confidence: 76%

Application of Potentials in the Description of Transport Processes

2016

APH

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“…[14] is the mass term, and the lack of first time derivative. If we set m ϕ = 0, then this is the special case of that, with α = 0.…”

Section: Appendix a Summary Of The Preliminariesmentioning

confidence: 99%

Searching the laws of thermodynamics in the Lorentz-invariant thermal energy propagation equation

Szőllősi

Márkus

2015

Physics Letters A

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“…The developed theory of nonequilibrium thermodynamics includes the Hamiltonian formulation of those dissipative processes [15] which can be given linear parabolic and hyperbolic differential equations (e.g., Fourier heat conduction and telegrapher equation) [16,17]. The completed Poissonbracket formalism is worked out for these processes; moreover, successful steps were taken towards the description of behavior of quantum [18,19] and stochastic phenomena [20] within dissipative systems.…”

Section: ͑10͒mentioning

confidence: 99%

Generalized Hamilton-Jacobi equation for simple dissipative processes

Márkus

Gambár

2004

Phys. Rev. E

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Following the method of classical mechanics, we calculate the action for Fourier heat conduction from the classical Hamilton-Jacobi equation. We can write a Schrödinger-type equation and we obtain its solution, the kernel by which we may introduce a kind of wave function. Mathematically, we follow Bohm's method introduced to quantum mechanics. The generalized Hamilton-Jacobi equation-which may be handled as a quantum-thermodynamical form-can be calculated. Irreversibility and dissipation are included in a natural way in the field theory of nonequilibrium thermodynamics, so in this way we obtain a quantum-thermodynamical approach of simple dissipative processes.

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Classical field theory and stochastic properties of hyperbolic equations of dissipative processes

Cited by 10 publications

References 46 publications

Application of Potentials in the Description of Transport Processes

Application of Potentials in the Description of Transport Processes

Searching the laws of thermodynamics in the Lorentz-invariant thermal energy propagation equation

Generalized Hamilton-Jacobi equation for simple dissipative processes

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