On Mon, Oct 19, 2020 at 3:55 PM Bruce Kellett <[email protected]> wrote:
> On Mon, Oct 19, 2020 at 3:31 PM Jason Resch <[email protected]> wrote: > >> >> > As explained on that page, the bound is not limited to black holes, it >> says something more general which relates entropy bounds to the product of >> spherical radius and mass. >> > > The entropy bound you are talking about is > > S <= 2pi RE. > > This is saturated when the radius and energy are related as for a black > hole: > To add to my earlier comments, I think that this way of writing the Bekenstein bound is seriously misleading. It is not exactly incorrect, but it does give the impression that the radius, R, of the volume is independent of the mass-energy, E. However, the bound does not mean that one can increase the entropy by simply increasing the volume, leaving the mass-energy constant. Entropy is a physical quantity, and it is matter, not empty space, that has entropy. So although the bound above can become arbitrarily large for a fixed anergy by simply increasing the volume, the maximum attainable entropy of any physical system is not thereby increased. The maximum entropy of a physical system (fixed mass-energy) is given when the bound is saturated. In other words, when the radius is that of the corresponding black hole: R = 2E (or 2M in natural units). Likewise, one cannot increase the entropy by an arbitrary increase in the mass-energy for a fixed volume. Once the mass equals half the radius of the spherical volume, M = R/2, a black hole forms, and no more mass can be added without increasing the radius. Bruce > R = 2M, for which S = 4pi M^2. > > Nothing mysterious here. I was talking about maximum possible entropy, > which occurs when the bound is saturated, as for a black hole. > > That is really all that the Bekenstein bound says. It is a bound, after > all, and has information about the entropy only when that bound is > saturated. > > So for a fixed amount of mass, the entropy is maximized when that mass is > in the form of a black hole. Increasing the volume surrounding the BH makes > no difference to the entropy maximum for that mass. > > Bruce > >> -- 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/CAFxXSLRVn-4LW%2BYnbuVi4tFGVbEmWLpaq_9e7ZQ60cevoYDMug%40mail.gmail.com.
