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Recent progress in nanoscale materials science has pushed the basic research on physical effects while going to such length scales. Particularly, the study of size effects on heat conductivity has attracted much theoretical and experimental interest. In this work we explore the possibilities to study such kinds of phenomena through the quantization of the… (More)

- Ferenc Márkus, Katalin Gambár
- Physical review. E, Statistical, nonlinear, and…
- 2005

We introduce an abstract scalar field and a covariant field equation, by which we make an attempt to connect the Fourier heat conduction and wave-like heat propagation. This field can be the generalization of the usual temperature from a dynamical point of view. It is shown that a kind of effective mass of this thermal process can be calculated. Finally, we… (More)

- Ferenc Márkus, Katalin Gambár
- Physical review. E, Statistical, nonlinear, and…
- 2003

In the present paper we discuss the possible form and meaning of Fisher, bound, and physical information in some special cases. It seems to us that an unusual choice of bound information may describe the behavior of dissipative processes.

- Katalin Gambár, Ferenc Márkus
- Open Syst. Inform. Dynam.
- 2001

We have shown in our previous works how to introduce the quantization procedure into the theory of heat conduction. In the present paper we point out where and why we need to complete the previous results to obtain the Hamiltonian by which we can bring 'zero point' energy into the theory of thermal field. We calculate the energy and the quasi-particle… (More)

- Katalin Gambár, Ferenc Márkus
- Open Syst. Inform. Dynam.
- 2005

We calculate the Lagrangian for certain type of differential equations of nonlinear heat conduction, applying potential function method introduced previously. On the other hand, we point out that these kind of nonlinear parabolic differential equations describe Markovian processes in a new phase space.

- Ferenc Márkus, Katalin Gambár
- Physical review. E, Statistical, nonlinear, and…
- 2004

In the present Rapid Communication we calculate the density matrix of heat conduction based on the field theory of nonequilibrium thermodynamics, which was worked out in the last 10 years. Applying these results we can discuss the existence of the maximal temperature and a possible upper limit for its value. We point out, proposing relevant physical… (More)

- Ferenc Márkus, Katalin Gambár
- Physical review. E, Statistical, nonlinear, and…
- 2004

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… (More)

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