On Sat, Sep 14, 2019 at 10:13:27PM -0700, Alan Grayson wrote: > > > On Saturday, September 14, 2019 at 7:12:34 AM UTC-6, Alan Grayson wrote: > > If the early universe, say before the emergence of the CMBR, consisted of > a > random collection of electrons and photons, wouldn't this correspond to a > high, not low entropy? Wouldn't it be analogous to gas with many possible > states? Yet cosmologists seem hard pressed to explain an initial or early > state assuming the entropy is low. AG > > > When I was an undergraduate I took a course in Classical Thermodynamics and > recall being satisfied that entropy was well-defined. I never took a course in > Classical Statistical Mechanics, but I've seen Boltzmann's equation for S and > wonder how N, the number of possible states is defined. If we have a gas > enclosed in a container, we can divide it into occupation cells of fixed > volume > to calcuate S. But why can't we double the number of cells by reducing their > volume by half? How then is S well defined in the case of Classical > Statistical > Mechanics? TIA, AG
It actually isn't. The point bothered me too. The number of states is basically V/h, where V is the volume of phase space occupied by the system, and h a cell size. Therefore, entropy is klog V - klog h For a large range of values of h, the second term is just a negligible constant offset to the total entropy. However, as h→0, entropy blows up. And that what classical statistical mechanics tells you. Enter quantum mechanics. Heisenberg's uncertainty relation tells us that ΔxΔp ≥ ℏ, so in the above entropy formula, h is constrained to be larger than ℏ³. Quantum mechanics saves classical statistical physics' bacon. Nothing blows up. -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow [email protected] Economics, Kingston University http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/20190916072249.GC5030%40zen.
