Re: Conservation of Information?

On 3 Bře, 19:09, John Bailey <john_bai...@xxxxxxxxxxxxxxxx> wrote:
On Fri, 29 Feb 2008 19:21:54 -0800 (PST), John Graeme

In the context of your question, "information" might be taken as
another word for "entropy." By some but possibly not all of the
participants.

There are two entropies, one defined in thermodynamics, one by Shannon
in his theory of communication. Shannon was interested, how many different
messages can be formed from the given set of symbols. These messages
are formed by the permutations of symbols.

Maximum has symmetry group S(n), each symbols appears only once.
If some symbols repeat, say aaabbccde, the polynomial coefficient must
be modified for nonpermutable symbols. Information entropy is defined
as binary logarithm. Than it has an interpretation as binary decision tree..

In thermodynamics, individual molecules can not spread in the whole system,
as symbols in texts. They form particles. But they can change energy, thus
another permutations are possible, say abccddeee. These permutations
are measured by another polynomial coefficient. Its logarithm was proposed by
Boltzmann as base for thermodynamical entropy. It is defined as natural
logarithm.

Both polynomial appear in enumeration of the terms of the product n^m.
Thus both entropies, when applicable, are additive. Anybody can check it.
kunzmilan

.

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