Entropy and Dimensions (Following Landau and Lifshitz)

Some time ago I wrote about volumes of spheres in multi-dimensional phase space - as needed in integrals in statistical mechanics. The post was primarily about the curious fact that the 'bulk of the volume' of such spheres is contained in a thin shell beneath their hyperspherical surfaces. The trick to calculate something reasonable is … Continue reading Entropy and Dimensions (Following Landau and Lifshitz)

Spheres in a Space with Trillions of Dimensions

I don't venture into speculative science writing - this is just about classical statistical mechanics; actually about a special mathematical aspect. It was one of the things I found particularly intriguing in my first encounters with statistical mechanics and thermodynamics a long time ago - a curious feature of volumes. I was mulling upon how … Continue reading Spheres in a Space with Trillions of Dimensions