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It is well established that at early times, long before the time ofradiation-matter equality, the universe could have been well described by aspatially flat, radiation only model. In this letter we consider the wholeprimeval universe as a black body radiation (BBR) system in an $n-$dimensionalEuclidean space. We propose that the $(3+1)-d$ nature of the universe could bethe result of a kind of thermodynamic selection principle stemming from thesecond law of thermodynamics. In regard the three spatial dimensions we suggestthat they were chosen by means of the minimization of the Helmholtz free energyper hypervolume unit, while the time dimension, as it is well known was theresult of the principle of increment of entropy for closed systems; that is,the so-called arrow of time.

Is the $(3+1)-d$ nature of the universe a thermodynamic necessity?