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arXiv · 1010.1148

Thermodynamics of photons on fractals

Eric Akkermans·Gerald V. Dunne·Alexander Teplyaev
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Abstract

A thermodynamical treatment of a massless scalar field (a "photon") confined to a fractal spatial manifold leads to an equation of state relating pressure to internal energy, $P V_s=U/d_s$, where $d_s$ is the spectral dimension and $V_s$ defines the "spectral volume". For regular manifolds, $V_s$ coincides with the usual geometric spatial volume, but on a fractal this is not necessarily the case. This is further evidence that on a fractal, momentum space can have a different dimension than position space. Our analysis also provides a natural definition of the vacuum (Casimir) energy of a fractal. We suggest ways that these unusual properties might be probed experimentally.

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Eric Akkermans, Gerald V. Dunne, Alexander Teplyaev. 2010-12-02. Thermodynamics of photons on fractals. https://doi.org/10.1103/physrevlett.105.230407

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