The Entropy Rate of Thermal Diffusion

Details The Entropy Rate of Thermal Diffusion The Entropy Rate of Thermal Diffusion

2001-06-26

arxiv.org/abs/math/0106215v3

Mathematics

Probability

Nine pages with equations and a figure

Scientific paper

The thermal diffusion of a free particle is a random process and generates entropy at a rate equal to twice the particle's temperature times Boltzmann's constant divided by hbar (in natural units of information per second). The rate is calculated using a Gaussian process with a variance of (delta_x0 + delta_p*t/m)^2. One would be keen to notice that the solution to the quantum mechanical diffusion of a free particle is (delta_x0)^2 + (delta_p*t/m)^2, however we assume that concurrent to quantum diffusion, the center of the wavepacket is also undergoing real classical diffusion which adds an additional variance in the amount of (hbar*t/m). The solution to the quantum diffusion of a free particle is derived from the equation for kinetic energy. Lastly the real diffusion constant of a free particle is shown to be D = hbar/(2m) after apply the Minkowski transformation to the quantum equation.

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