**Authors:** John L. Haller Jr.

The thermal diffusion of a free particle is a random process and generates entropy
at a rate equal to twice the particle's temperature, R = 2k_{B}T/ℎ (in natural units of information per
second). The rate is calculated using a Gaussian process with a variance of (Δx_{0} + Δp⋅t/m)^{2}. One
would be keen to notice that the solution to the quantum mechanical diffusion of a free particle is
(Δx_{0})^{2} + (Δp⋅t/m)^{2}, however we assume that concurrent to quantum diffusion, the center of the
wavepacket is also undergoing classical diffusion which adds an addition variance in the amount of
(ℎ⋅t/m), making up the difference. Derivations of the variance and subsequent entropy rate are given.

**Comments:** 9 pages

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[v1] 7 Oct 2009

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