On Monday, September 16, 2019 at 1:23:09 AM UTC-6, Russell Standish wrote: > > 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. >
How could the second term be negligible for large values of h? AG > > 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 hpc...@hpcoders.com.au > <javascript:> > 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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/0a314df1-ffa8-4369-8045-e395c2e8d8db%40googlegroups.com.
