Quantum Physics


Entropy Rate of Thermal Diffusion

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 = 2kBT/ℎ (in natural units of information per second). The rate is calculated using a Gaussian process with a variance of (Δx0 + Δp⋅t/m)2. One would be keen to notice that the solution to the quantum mechanical diffusion of a free particle is (Δx0)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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