Hi,
As I began to discuss on April 18 on these lists, there may be an
irreducibly triadic relation among THERMODYNAMICS, QUANTUM MECHANICS, and
INFORMATICS, thus forming a mathematical category (the TQI category ?).
This idea is represented diagrammatically in Figure 1. There are two main
points that I would like to emphasize in Figure 1:
(1) Boltzmann's entropy equation played a major role in deriving the
blackbody radiation equation by M. Planck in 1900 [5, 6], which in turn led
to the derivation of the "Planckian information equation" (PIE) in 2015
[1, 2]. PIE is shown in Row 4 and Column 3 in Table 1 and the related
equation, Planckian distribution equation (PDE) [3], is shown in Row 5 and
Column 2.
(2) Thermodynamics, quantum mechanics, and informatics constitute an
irreducible triad of communication (also called semiosis by Peircean
scholars). That is, it is impossible to communicate, at all scales from
microscopic to macroscopic to cosmological, without energy dissipation
(thermodynamics), discrete objects to choose from (quantum mechanics), and
selection mechanism of one or more objects from the message source
(informatics).
f
g
Boltzmann's entropy equation --------> Planck radiation
equation ---------> Planckian information equation
(1872-5)
(1900) (2015) [1, 2]
(Thermodynamics) (Quantum
mechanics) (Informatics)
|
^
|
|
|____________________________________________________________|
h
Figure 1. The hypothesis that the TQI (Thermodynamics, Quantum mechanics,
and Informatics) category is essential for communication or semiosis.
f = quantization or organization; g = selection; h =
grounding, or realization. Naming of these arrows are of secondary
importance, since there are more
than one ways of naming them depending on the context of
discourse. The commutative condition is thought to be satisfied: f x g = h.
The rest of Table 1 is explained in my 4/18 post.
Table 1. A possible relation among entropy, quanta, and information
1. Concept
*Entropy* (1)
*Quanta *(2)
*Information *(3)
2. Field of inquiry
Thermodynamics
Quantum mechanics
Informatics
3. Experiment/
Measurement
S = ΔQ/T
Blackbody radiation spectra
Selecting m out of n possibilities*
4. Statistical mechanical
formulation
S = k log W
Boltzmann entropy
(1872-5)
S = - k∑Pi log Pi
*Boltzmann-Gibbs entropy *
(1866)
U(λ, T) =
(2πhc2/λ5)/(ehc/λkT – 1)
*Planck radiation equation*
(PRE) (1900) [5,6]
IP = log2(AUC(P)/AUC(G))
where IP = Planckian information [1, 2], AUC = area under the curve, P =
PDE, and G = *Gaussian-like equation* [2],
y = Ae–(x - µ)^2/2*σ^2
5. Mathematical formulation
H = - K∑Pi log Pi
*Shannon entropy*(1948)
y =
(a/(Ax+B)5)/(eb/(Ax + B)– 1)
*Planckian distribution equation* (PDE) (2008) [3]
I = A log2 (n/m)
*a unified theory of the amount of information*(UTAI) (2015) [4]
6. Emerging Concept
A measure of *DISORDER*
Quantization of action needed for *ORGANIZATION*
A measure of the *ORDER *of an organized system
*Assumed to be of equal probabilities for simplicity.
If you have any questions, suggestions, or criticisms, please let me know.
All the best.
Sung
--
Sungchul Ji, Ph.D.
Associate Professor of Pharmacology and Toxicology
Department of Pharmacology and Toxicology
Ernest Mario School of Pharmacy
Rutgers University
Piscataway, N.J. 08855
732-445-4701
www.conformon.net
References:
[1] Ji, S. (2015). Planckian distributions in molecular machines, living
cell, and brains: The wave-particle duality in biomedical sciences.
In: *Proceedings
of the International Conference on Biology and Biomedical Engineering*.
Vienna, March 15-17, 2015. Pp. 115-137. Uploaded to ResearchGate in
March, 2015.
[2] Ji, S. (2015). Planckian information (IP): A new measure of order
in atoms, enzymes, cells, brains, human societies and the cosmos. In: *Unified
Field Mechanics: Natural Science Beyond the Veil of Spacetime* (R. L.
Amoroso, P. Rowlands & L. H. Kauffman, eds.), World Scientific, New Jersey
(to appear). Manuscript available upon request.
[3] Ji, S. (2012). Molecular Theory of the Living Cell: Concepts,
Molecular Mechanisms, and Biomedical Applications. Springer, New York.
Chapters 11 and 12. PDF available athttp://www.conformon.net under
Publications > Book Chapters.
[4] Ji, S. (2015). A unified theory of the AMOUNT of information (UTAI)
carried by a sign. Biosemiotics and PEIRCE-L lists, April 12, 2015.
[5] Vlasak, W. Plancks' theory and thermodynamics.
http://pubs.acs.org/subscribe/archive/ci/31/102/html/02learning.html
[6] Fowler, M. Plancks' Route to the Black Body Radiation Formula and
Quantization. http://galileo.phys.virginia.edu/classes/252/PlanckStory.htm
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