Note: what follows is an abbreviated text taken from the presentation.
The whole file, too big for our list, can be found at fis web pages:
http://fis.sciforum.net/wp-content/uploads/sites/2/2014/11/Planckian_information.pdf
A very recent article developing similar ideas:
http://www.mdpi.com/2078-2489/8/1/24
Greetings to all--Pedro
---
*What is the Planckian information ?*
*S**UNGCHUL JI*
/Department of Pharmacology and Toxicology
Ernest Mario School of Pharmacy
Rutgers University/
/s...@pharmacy.rutgers.edu/
*
*
The Planckian information (I_P) is defined as the information produced
(or used) by the so-called Planckian processes which are in turn defined
as any physicochemical or formal processes that generate long-tailed
histograms fitting the Planckian Distribution Equation (PDE),
y = (A/(x + B^5)/(Exp(C/(x + B)) – 1)(1)
where A, B and C are free parameters, x is the class or the bin to
whichobjects or entities belong, and y is the frequency [1, 1a].The PDE
was derived in 2008 [2] from the blackbody radiation equation discovered
by M. Planck (1858-1947) in 1900, by replacing the universal constants
and temperature with free parameters, A, B and C.PDE has been found to
fit not only the blackbody radiation spectra (as it should) but also
numerous other long-tailed histograms [3, 4] (see Figure 1).
One possible explanation for the universality of PDE is that many
long-tailed histograms are generated by some selection mechanisms acting
on randomly/thermally accessible processes [3]. Since random processes
obey the Gaussian distribution, the ratio of the area under the curve
(AUC) of PDE to that of Gaussian-like symmetric curves can be used as a
measure of non-randomness or the order generated by the Planckian processes.
As can be seen in *Figs. 1 (g), (i), (k), (o), (r) *and*(t), *the curves
labeled ‘Gaussian’ or ‘Gaussian-like’ overlap with the rising phase of
the PDE curves.The ‘Gaussian-like’ curves were generated by Eq. (2),
which was derived from the Gaussian equation by replacing its
pre-exponential factor with free parameter A:
y = Ae^– (x – ^μ ^)^2/(2 ^σ ^^2) (2)
The degree of mis-match between the area under the curve (AUC) of PDE,
Eq. (1), and that of GLE, Eq. (2), is postulated to be a measure of
/non-randomness/ (and hence /order/).GLE is associated with random
processes, since it is symmetric with respect to the sign reversal of in
its exponential term, (x - µ).This /measure of order/ is referred to as
the Planckian Information (I_P ) defined quantitatively as shown in Eq.
(3) or Eq. (4):
I_P = log_2 (AUC(PDE)/AUC(GLE))bits(3)
or
I_P= log_2 [∫P(x)dx/∫G(x)dx]bits(4)
where P(x) and G(x) are the Plackian Distribution Equation and the
Gaussian-Like Equation, respectively.
It is generally accepted that there are at least three basic aspects to
information – /amount/, /meaning, /and /value. //Planckian information/
is primarily concerned with the /amount/ (and hence the /quantitative/
aspect) of information.There are numerous ways that have been suggested
in the literature for /quantifying information/ bedside the well-known
Hartley information, Shannon entropy, algorithmic information, etc
[5].The Planckian information, given by Equation (3), is a new measure
of information that applies to the /Planckian process/ generally defined
as in (5):
“Planckian processes are the physicochemical, neurophysiological, (5)
biomedical, mental, linguistic, socioeconomic, cosmological, or any
other processes that generate long-tailed histograms obeying the
Planckian distribution equation (PDE).”
The Planckian information represents the degree of organization of
physical (or nonphysical) systems in contrast to the Boltzmann or the
Boltzmann-Gibbs entropy which represents the disorder/disorganization of
a physical system, whether the system involved is atoms, enzymes, cells,
brains, human societies, or the Universe.I_P is related to the
“organized complexity” and S is realted to “disorganized complexity” of
Weaver [6].The organization represented by I_P results from
/symmetry-breaking selection/ /processes /applied to some randomly
accessible (and hence symmetrically distributed) processes, whether the
system involved is atoms, enzymes, cells, brains, languages, human
societies, or the Universe [3, 4], as schematically depicted in *Figure 2*.
There is a great confusion in science and philosophy concerning the
relation between the concepts of /information/ and /entropy/ as pointed
out by Wicken [7].A large part of this confusion may be traced back to
the suggestions made by Schrödinger in 1944 [8] and others subsequently
(e.g., von Neumann, Brillouin, etc.) that /order/ can be measured as the
/inverse of/ /disorder/ (D) and hence that information can be measured
as negative entropy (see the second column in *Table 1*).
