Cell Language Theory, The: Connecting Mind And Matter

The Universality of the Planckian Distribution Equation 369

“6x9” b2861 The Cell Language Theory: Connecting Mind and Matter

If Statement (8.18) turns out to be true, the following two corollaries

may follow:

The Planckian distribution equation is to the Planck radiation equation

what the Shannon equation is to the Boltzmann–Gibbs equation. (8.19)

The Shannon equation measures DISORDER; the Planckian distribution

equation measures ORDER. (8.20)

Table 8.5 A possible relation among entropy, quanta, and information. PRE = Planck

Radiation Equation; PDE = Planckian Distribution Equation

1 Concept Entropy (1) Quanta (2) Information (3)

2 Field of study Thermodynamics Quantum

mechanics

Informatics

3 Experiment/

measurement

S = DQ/T Blackbody

radiation spectra

Selecting m out of n

possibilities or

choices

4 Statistical

mechanical

formulation

S = - kSpi log pi

Boltzmann–Gibbs

entropy (1866)a

U(λ,T ) = (2πhc^2 /λ^5 )/

(ehc/λkT –1) PRE

(1900)

IP = log 2 (AUC(P)/

AUC(G)), where

IP = Planckian

information,

AUC = area under

curve; P = PDE,

and G = Gaussian-

like equation, i.e.,

y = A e–(x–μ)^2/(2σ^2)

(2014)

5 Mathematical

formulation

H = - kSpi log pi

Shannon entropy

(1948)

y = (A/(x + B)^5 )/

(eC/(x + B) – 1) PDE

(2008)

I = log 2 (n/m)

A unified theory of

the amount of

information

6 Emergent concept Tendency toward

disorganization

Tendency toward

organization

A measure of the

order

7 Functors [370,

371] connecting

rows 4 and 5

Mathematical form Mathematical form

Wave–particle

duality

Energy quantization

Mathematical form

a Reduces to S = k ln W when all pi values are equal, W stands for the number of the microstates con-

sistent with the macrostate of the system, and k is the Boltzmann constant.

b2861_Ch-08.indd 369 17-10-2017 12:09:19 PM