标题： 宇宙的 $(3+1)-d$ 性质是否是热力学上的必然？ 显示英文标题

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

摘要： 众所周知，在辐射与物质达到平衡很久之前，宇宙在早期可以用一个空间平坦且仅有辐射的模型很好地描述。在这封信中，我们将整个原初宇宙视为一个黑体辐射（BBR）系统，存在于$n-$维欧几里得空间中。我们提出，宇宙的$(3+1)-d$特性可能是源于热力学第二定律的一种热力学选择原理。针对三个空间维度，我们认为它们是通过最小化超体积单位上的亥姆霍兹自由能来选定的，而时间维度，众所周知，是封闭系统熵增原理的结果；即所谓的“时间箭头”。 显示英文摘要

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