[Fis] Fwd: Entropy, the Second Law, and Life

Loet Leydesdorff loet at leydesdorff.net
Sat Jan 9 09:14:12 CET 2021

Dear colleagues,

>>>What are erroneous about the following assertions:
>>>“If entropy was dimensionless, it would not be related to chemical 
>>>“If entropy was dimensionless, thermodynamics would not be related to 
>>>general law of mass action which connects chemical transformations 
>>>(equations) to dynamics.”
>It seems important to distinguish between thermodynamic and 
>probabilistic entropy.  Probabilistic entropy = Shannon's H is yet 
>S = k(B) * H with the dimensionality Watt/Kelvin inherited from k(B), 
>the Boltzmann constant.
As a statistic H is less constrained than S as a chemo-physical.

For example, in case of a ideal collision between billiard balls, no 
entropy is generated, but the Kullback-Leibler (1951) divergence 
(derived from Shannon's H as a dynamic elaboration (Theil, 1972)) will 
be maximal.

Similarly, the mutual information in three dimensions can be negative in 
the statistical domain, but not in the chemo-physical one. The 
thermodynamic entropy is the special case (which was historically first) 
in which the system of reference is composed of positions and momenta.  
Probabilistic entropy is generated by any redistribution of 
probabilities. For example, in  a system of transactions.

As more often, the order in the morphogenesis (S before H) is 
analytically changed from the perspective of hindsight. H allows us to 
move to the specification of anticipation (Rosen). Feedback loops may 
lead to the generation of negative (probabilistic !) entropy. See also: 
Krippendorff, 2009; Ulanowicz, 1997.

Krippendorff, K. (2009). Information of Interactions in Complex Systems. 
International Journal of General Systems, 38(6), 669-680.

Kullback, S., & Leibler, R. A. (1951). On Information and Sufficiency. 
The Annals of Mathematical Statistics, 22(1), 79-86.

Theil, H. (1972). Statistical Decomposition Analysis. Amsterdam/ London: 

Ulanowicz, R. E. (1997). Ecology, The Ascendent Perspective. New York: 
Columbia University Press.


Loet Leydesdorff


Professor emeritus, University of Amsterdam
Amsterdam School of Communication Research (ASCoR)

loet en leydesdorff.net <mailto:loet en leydesdorff.net>; 


ORCID: http://orcid.org/0000-0002-7835-3098;

"The Evolutionary Dynamics of Discursive Knowledge" at

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