Thermodynamics of photons on fractals

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.

arXiv comment5 pages, 2 figs; v2 refs added, to appear in PRL

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• Multifractional theories: an unconventional review
• Asymptotic Safety, Fractals, and Cosmology
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• Laplace Operators on Fractals and Related Functional Equations
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• Multifractional theories: an updated review
• How Barrow Entropy Modifies Gravity: With Comments on Tsallis Entropy
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• Spectra of Perfect State Transfer Hamiltonians on Fractal-Like Graphs
• Symmetries and propagator in multifractional scalar field theory
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• Spectral dimensions and dimension spectra of quantum spacetimes
• Walk dimension for light in complex disordered media
• Decoherence and thermalization of Unruh-DeWitt detector in arbitrary dimensions
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• How not to establish the non-renormalizability of gravity
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• Regularized Laplacian determinants of self-similar fractals
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• Quantum Vacuum Energy of Self-Similar Configurations
• Entangling Fractals
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• The Casimir Effect on Laakso Sapces