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Gonzalez-Ayala, J., Cordero, R. and Angulo-Brown, F. (2015) Is the (3 + 1) − d Nature of the Universe a Thermodynamic Necessity? EPL (Europhysics Letters), arXiv:1502.01843v2.

has been cited by the following article:

• TITLE: Proof That Spatial Transitions Release/Absorb Energy That Compactification Necessarily Leads to Changes in Volume, Energy and Entropy

  AUTHORS: Christopher Pilot

  KEYWORDS: Spatial Transitions, Box Quantization, Compactification

  JOURNAL NAME: Journal of High Energy Physics, Gravitation and Cosmology, Vol.5 No.2, February 15, 2019

  ABSTRACT: Using simple box quantization, we demonstrate explicitly that a spatial transition will release or absorb energy, and that compactification releases latent heat with an attendant change in volume and entropy. Increasing spatial dimension for a given number of particles costs energy while decreasing dimensions supplies energy, which can be quantified, using a generalized version of the Clausius-Clapyeron relation. We show this explicitly for massive particles trapped in a box. Compactification from N -dimensional space to (N - 1) spatial dimensions is also simply demonstrated and the correct limit to achieve a lower energy result is to take the limit, Lw → 0, where Lw is the compactification length parameter. Higher dimensional space has more energy and more entropy, all other things being equal, for a given cutoff in energy.