On Sunday, September 15, 2019 at 12:13:27 AM UTC-5, 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 >
There is the classical definition S = ∂E/∂T for isobaric systems. Yet in general entropy is a rather subjective and slippery concept. With the Boltzmann formula S = k log(Ω) for Ω the volume of phase space any uncertainty in Ω results in tiny errors because of the logarithm. LC -- 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/90f1b9a3-652c-498d-a6ef-3f30dabc1973%40googlegroups.com.
