A possible cosmological application of some thermodynamic properties of the black body radiation in $n-$dimensional Euclidean spaces

TL;DR

This paper extends thermodynamic properties of black body radiation to n-dimensional Euclidean spaces, exploring their behavior at high temperatures and low dimensions, with potential implications for cosmology and the universe's dimensionality.

Contribution

It generalizes thermodynamic properties of black body radiation to n-dimensional spaces and analyzes their behavior, including thermodynamic potentials and efficiency, revealing features relevant to cosmology.

Findings

Maxima and minima in thermodynamic potentials at high temperatures and low dimensions.

Potential application of results to cosmological models.

Proposed link between 3D universe and thermodynamic optimality.

Abstract

In this work we present the generalization of some thermodynamic properties of the black body radiation (BBR) towards an $n-$dimensional Euclidean space. For this case the Planck function and the Stefan-Boltzmann law have already been given by Landsberg and de Vos and some adjustments by Menon and Agrawal. However, since then no much more has been done on this subject and we believe there are some relevant aspects yet to explore. In addition to the results previously found we calculate the thermodynamic potentials, the efficiency of the Carnot engine, the law for adiabatic processes and the heat capacity at constant volume. There is a region at which an interesting behavior of the thermodynamic potentials arise, maxima and minima appear for the $n-d$ BBR system at very high temperatures and low dimensionality, suggesting a possible application to cosmology. Finally we propose that an optimality criterion in a thermodynamic framework could have to do with the $3-d$ nature of the universe.