Argument: Had the entropy of the Universe been an actual observable, these erroneous estimates for total entropy would have been ruled out by observation alone.
Instead, each of the values Srelativistic and SBH were revised
when they were discovered to be subdominant in light of new theoretical knowledge
on the composition and the nature of interactions present in the Universe.
Proof: A good example of how entropy is not a measurable quantity can be found in the cosmologists’ evolving understanding of the Universe’s entropy, in recent decades
The first estimates of the (observable) Universe’s entropy date from around 1980
and stemmed from thermodynamics, attributing the bulk of the Universe’s entropy to
the blackbody radiation of the cosmic microwave background, Srelativistic ∼1090, expressed in natural units, G = c = ~ = kB = 1. Some years later the realisation that the
entropy of gravity could not be overlooked in the overall budget led to this value being
revised by Frautschi, and later firmed up by Penrose.
The conclusion is that the formation of supermassive black holes has led the gravitational contribution to today dominate over that from the microwave background by around 15 orders of magnitude, SBH ∼ 10104
More recently this estimate has had to be revised yet again to account for the fact
that the vacuum energy Λ dominates the Universe’s energy density today, so that the
corresponding entropy that Λ generates at the cosmic horizon has to be considered. It
turns out our previous estimate of the Universe’s entropy due to gravity is wrong yet
again, and altogether negligible when compared to the entropy of the vacuum which
dominates over the gravity value by a further twenty or so orders of magnitude, SΛ ∼
10124
The point here is, with the example of the evolving understanding of the
Universe’s entropy, illustrates the premise that the estimated entropy for a system is a function of the observer’s knowledge of the system.
References (proof & premise):
1. Biocosmology: Biology from a cosmological
perspective, Marina Cortˆes,1,2 Stuart A. Kauffman
In order to talk about the entropy of the universe, one has to extend thermodynamics to include gravity.
Hello,
I think, that entropy is a very complex term. There are so many different entropies. But as you quoted, entropy measures the knowledge of the given system. Thus maximal knowledge is just the ground state. Entropy proves that the future is only probabilistically determined. Moreover the systems are prepared to be in thermal equilibrium, which is the fate of the Universe. However, complexity is an alternative. Developed by Leonard Susskind an others. His book "Three Lectures on Complexity and Black Holes" explains complexity. Complexity shows that the Universe will be or is just infinite.
Take care
Kay zum Felde
Kay Zum Felde Yes, unfortunately the term entropy from classical thermodynamics was overtaken by other sciences. Still, there is single thermodynamic entropy with clear meaning that has nothing to do with knowledge or information. It is experimentally measured physical value similar to other thermodynamic properties. See, for example, JANAF Thermochemical Tables https://janaf.nist.gov/
Hello Evgenyi,
knowledge or information are terms in order to find a meaning, a physical meaning. Shannon introduced the term information. Usual the idea "disorder" is popular. With knowledge I mean, the ground state has maximal "order" and thus we know this state. Then the system is evolving, driven by some perturbation, like temperature and is evolving until its thermodynamic equilibrium if the system is closed, of course. There're many different entropy theories, Boltzmann, Shannon, Renyi, Kullback-Leibler difference, and there is complexity, which is not really entropy, but very interesting, since complexity is not moving towards thermodynamic equilibrium, but always increasing patterns. It is related to chaos theory, and importantly it is a theory of finite Hamiltonians.
Take care Kay
Hello Kay ( Kay Zum Felde ),
Could you please open JANAF Tables, take the substance of your choice and tell me the difference between different thermodynamic properties from the viewpoint of Shannon information? What is the difference, for example, between entropy and enthalpy values in that table?
Evgenii
Hello Evgeni,
Well, the thermodynamic potential all will repeat the measurements. They are used, in case of the measurement of f.e., temperature or entropy. You use F in the first case and U in the second case. But this is simple. Interesting are cases of von Neumann entropy and information entropy. They are different.
Take care Kay
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