A Possible Cosmological Application of Some Thermodynamic Properties of the Black Body Radiation in n-Dimensional Euclidean Spaces

Entropy

Julian Gonzalez-Ayala¹  Jennifer Perez-Oregon²  Rubén Cordero²  Fernando Angulo-Brown² 

[1] Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, CP 07738, Mexico;

关键词: black body radiation;    n-dimensional Euclidean space;    cosmology;   

DOI  :  10.3390/e17074563

来源: mdpi

【 摘 要 】

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, not 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 arises: maxima and minima appear for the n-dimensional 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 be related to the 3-dimensional nature of the universe.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland