Gravity, entropy, and cosmology in search of clarity.pdfVIP

Gravity, entropy, and cosmology: in search of clarity David Wallace June 2009 Abstract I discuss the statistical mechanics of gravitating systems and in par- ticular its cosmological implications, and argue that many conventional views on this subject in the foundations of statistical mechanics embody significant confusion; I attempt to provide a clearer and more accurate account. In particular, I observe that (i) the role of gravity in entropy calculations must be distinguished from the entropy of gravity, that (ii) although gravitational collapse is entropy-increasing, this is not usually because the collapsing matter itself increases in entropy, and that (iii) the Second Law of Thermodynamics does not owe its validity to the statistical mechanics of gravitational collapse. 1 Introduction On pain of a crisis in physics, the entropy of the early Universe had better be lower than its present entropy. This is sometimes presented as some deep requirement at the core of statistical mechanics, but there are more straight- forward reasons why it had better be true: namely, the Second Law of ther- modynamics says that the entropy of a closed system never decreases (and has increased in a great many processes which have occurred in the past and con- tinue to occur today); the early Universe is in the past; therefore if its entropy is higher than the present Universe’s entropy, the Second Law has been violated. And in fact, it is not merely necessary that the entropy of the early Universe was lower than at present: it must have been lower in such a way as to facilitate the existence