On Sat, Sep 14, 2019, 10:07 AM Alan Grayson <[email protected]> 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 >> > > Here's an easier question: when Boltzmann defined entropy as S = k * log > N, why the log; why not just k*N? AG > I don't know the relationship between heat and information, I think it is relevant to the Bekenstein bound and black hole information, and also the Landauer limit, but there's another definition of entropy in information theory: https://en.m.wikipedia.org/wiki/Entropy_(information_theory) The information theoretical definition of entropy is measured in bits (binary digits). The reason for the logarithm is it takes Log2(N) bits to represent N states. There's nothing special about the base you can also say it takes Log10(N) decimal digits to encode a number N. Jason -- 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/CA%2BBCJUhJqXqgxxK-wPKGXacXUBarUxdTHWed0_nq8RLiKJ_A-w%40mail.gmail.com.
