[Fis] other entropies?

Dear FISers,

Let me add a couple of new aspects to the many interesting topics around
(apologies for further diverting out):

First about Tsallis' Entropy. As the defenders of this relatively new
approach to entropy claim (late 80's), the classical entropy around
Clausius-Boltzmann, assumes ergodicity of the state space, vicinity to
equilibrium, and extensivity. But what happens when your state space is
severely limited by multiple 'accidents' that do not let the system move
ergodically, or when the system is far from equilibrium, or nonextensivity
is the rule? Then the new entropy modifies with a power law the classical
one (it contains a "q" factor describing the emerging fractality of the
state space; if q equals 1, then Boltzmann entropy follows). This new
approach has been explored in a variety of fields, and it looks very
intriguing in order to follow the "cascades" and discontinuities of the
energy flow in biology (life is but the paradise of 'bonds' which link
together, 'glue in' the vagaries of component entities: molecularly,
cellularly, individuals, socially...). Seemingly the inspiration for this
new entropy comes from comments by Einstein in 1910. See at the Web:
tsallis.cat.cbpf.br

Second, 'multiscale entropy'. It is a fact that physiological time series
often exhibit novel features at different scales (e.g., heart beat
intervals) and their entropy could vary according to the timescale at which
it is measured. By re-sampling the original time series at various scales
(creating sub-samples) a collection of data possesing different
coarse-graining may be obtained ---I am awfully summarizing from Chiavo,
2002. The resulting quantity termed 'multiscale entropy' appears as a
function of time, and surprisingly it is almost constant for healthy
individuals, while it ostensibly increases or decreases for heart
pathologies (congestion, fibrillation)... The underlying wisdom is that the
biological organism looks for a 'constancy of surprise' in its inner
arrangements and evaluations. It is quite a profound theme, that the author
(Chiavo) relates to our operations on other perceptual items (eg., sound,
music itself), and that I cannot help but relate to the 'value' theme both
in biology (fitness) and in our social-economic practices (myopic,
'congestive' unsustainable approaches to economic value--this might be an
interesting theoretical question for the environmental economics debate).

I was willing to say something on 'order' too. Shouldn't the 'criteria' be
antecedent, rather than otherwise (looking for the criteria)? I mean, items
get 'ordered' or 'disordered' with respect to some previous criteria held
by the observer --change the criteria, the evaluation result will change.
The same (half-neat) room is highly disordered for the toddler, who will
playingly act so to get it completely 'ordered' for his
perception---appearing then in complete randomness for the adult. The same
'action/perception' cycle underlies the child and the adult, but from a
very different memory-rule guidance (criteria); and also in the case of the
scientific observer...finally science is based on conventions and covenants
to socially build and expand a repertoire of knowledge that stems out from
the motor-based cognition of the individual.

best

Pedro

PS. While writing this message I have seen Werner's posting: it is a big
pleasure that he is again in the fis arena!

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Received on Tue Jun 8 13:43:04 2004