Entropy Rate of Thermal Diffusion

ABSTRACT

The thermal diffusion of a free particle is a random process and generates entropy at a rate equal to twice the particle’s temperature, (in natural units of information per second). The rate is calculated using a Gaussian process with a variance of which is a combination of quantum and classical diffusion. The solution to the quantum diffusion of a free particle is derived from the equation for kinetic energy and its associated imaginary diffusion constant; a real diffusion constant (representing classical diffusion) is shown to be . We find the entropy of the initial state is one natural unit, which is the same amount of entropy the process generates after the de-coherence time, .

Cite this paper

J. Haller Jr., "Entropy Rate of Thermal Diffusion,"*Journal of Modern Physics*, Vol. 4 No. 10, 2013, pp. 1393-1399. doi: 10.4236/jmp.2013.410167.

J. Haller Jr., "Entropy Rate of Thermal Diffusion,"

References

[1] J. Haller Jr., Journal of Modern Physics, Vol. 4 2013, pp. 85-95. http://dx.doi.org/10.4236/jmp.2013.47A1010

[2] Yamamoto and Imamoglu, “Mesoscopic Quantum Optics,” John Wiley & Sons, New York, 1999.

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http://www.worldcat.org/title/fundamentals-of-plasma-physics/oclc/32880244?referer=di&ht=edition

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http://dx.doi.org/10.2307/2372390

[1] J. Haller Jr., Journal of Modern Physics, Vol. 4 2013, pp. 85-95. http://dx.doi.org/10.4236/jmp.2013.47A1010

[2] Yamamoto and Imamoglu, “Mesoscopic Quantum Optics,” John Wiley & Sons, New York, 1999.

[3] Cover and Thomas, “Elements of Information Theory,” John Wiley & Sons, New York, 1991.

[4] Bracewell, “The Fourier Transform and Its Applications,” 2nd Edition, McGraw Hill, New York, 1986.

[5] C. W. Gardiner and P. Zoller, “Quantum Noise,” Springer, Berlin, 2004.

[6] Shankar, “Principles of Quantum Mechanics,” Plenum Press, New York, 1994.

[7] Feynman, “Lectures on Physics,” Addison-Wesley Publishing, Reading, 1965.

[8] Bohm, “Quantum Theory,” Dover Publications, Mineola, 1989.

[9] Shankar, “Principles of Quantum Mechanics,” Plenum Press, New York, 1994.

[10] Bittencourt, “Fundamentals of Plasma Physics,” 2nd Edition, Sao Jose dos Campos, 1995.

http://www.worldcat.org/title/fundamentals-of-plasma-physics/oclc/32880244?referer=di&ht=edition

[11] Einstein, “Investigation on the Theory of, the Brownian Movement,” Translated by Cowper, Dover, 1956.

[12] Einstein, “The Meaning of Relativity,” 5th Edition, Princeton University Press, Princeton, 1956.

[13] I. I. Hirshman, American Journal of Mathematics, Vol. 79, 1957, p. 152.

http://dx.doi.org/10.2307/2372390