**Diversity and Entropy**

**Shu-Kun Lin**

Molecular Diversity Preservation International (MDPI), Saengergasse
25, CH-4054 Basel, Switzerland.

(New address: Matthaeusstrasse
11, CH-4057 Basel, Switzerland -- added on 28 October 2007)

Tel. +41 79 322 3379; Fax +41 61 302 8918. E-mail: lin@mdpi.org, http://www.mdpi.org/lin/

*Received: 28 January 1999 / Accepted: 5 February 1999 /
Published: 11 February 1999*

*Entropy*
has been launched as a scientific journal to provide an advanced forum
for the community of entropy and information researchers.

There are many types of entropy reported in the scientific
literature [1]. The great diversity in the concept and definition may
cause
tremendous problems. My own humble suggestion is the following
regarding
the main two kinds of entropy: 1. Any information-theoretic entropy
(Shannon's
entropy [2],
*H*) should be defined in a way that its relation with
information is clear. 2. Any theories regarding thermodynamic entropy
(classical
entropy, *S*, or the entropy of Clausius, Gibbs and Boltzmann and
Plank) should conform with the second law of thermodynamics.

For information-theoretic entropy, if one uses entropy and information interchangeably, which has often happened even among some physicists [3], for any well defined system and processes, we cannot make meaningful intellectual discussion [3].

A famous thermodynamic entropy theory is Dr. Ilya Prigogine's dissipative structure theory. It has been presented by most of my respected teachers as unbelievably important, beautiful and useful. Therefore, 20 years ago as a young student of chemistry, I wanted to understand Prigogine's theory and I studied all kinds of related mathematics and physics, including several graduate courses in physics, to prepare myself. Now, after more than 20 years, first 10 years of theoretical investigation, then, several years of diverse experimental practice in chemistry laboratories, I have a clear opinion regarding this entropy theory. Its main problem is that it does not conform with the second law of thermodynamics [4]. Therefore, it is not a surprise that an honest chemist (among any other educated chemists, physicists, biologists, etc.) will tell you that he has never found an application of this entropy theory in chemistry (or in biology, physics, engineering, ...) [5].

However, the messy and confusing situation regarding
entropy-related studies has provided opportunities for us: clearly
there
are still many very interesting studies to pursue. For instance, one
immediate
task is to investigate whether the information-theoretic entropy and
the
thermodynamic entropy are compatible or not compatible, i.e., whether
both
need to satisfy a definition of "information is related to entropy
loss",
what relation the information-theoretic entropy has to the second law
of
thermodynamics and whether there is any correlation between
information-theoretic
entropy and thermodynamic entropy. To make the life of the students of
younger generations easier, entropy related concepts need to be
clarified
and well defined. The relation of entropy with many other concepts need
to be studied. These reasons alone would justify our launching of this
new journal *Entropy*.

Nevertheless, diversity is good in another sense:
the very diverse areas involved in the adaption and the application of
the entropy concept and of those various good theories of entropy will
definitely generate a very active scientific forum. Our journal *Entropy*
will strongly support this forum, publishing high quality papers from
areas
as diverse as physics, chemistry, biology, economy and philosophy.

*Acknowledgments: *I am very grateful to Dr. Georgi P.
Gladyshev
(url http://endeav.org email academy@endeav.org)
for his numerous useful comments. The author also would like to thank
Dr. Thomas D. Schneider
(url http://www-lecb.ncifcrf.gov/~toms/
email toms@ncifcrf.gov)
for English corrections.

**References and Notes**

1. (a) Hillman, C. Entropy
on the world wide web
(http://www.mdpi.org/entropy/entropyweb/).

(b) Denbigh, K. G. Note on entropy, disorder and
disorganization. *Brit. J. Phil. Sci. ***1989 **, *40*,
323-332.
(http://www.endeav.org/evolut/text/denbig1/denbig1e.htm).

(c) Lowe, J.P. Entropy: conceptual disorder.
*J. Chem. Educ. ***1988**, *65 *, 403-406.

(d) Lambert, F. L. The second law
of thermodynamics
(http://www.secondlaw.com/index.html).

2. (a) Shannon, C. E. A mathematical theory of communication.
*Bell Sys. Tech. J.* **1948**, *27*, 323-332; 379-423.

(b) Claude E. Shannon's classic 1948 paper [2a]
is now available electronically: Shannon, C. E. A Mathematical Theory
of Communication
(http://cm.bell-labs.com/cm/ms/what/shannonday/paper.html).

3. (a) Lin, S. -K. Understanding structural stability
and process spontaneity based on the rejection of the Gibbs paradox of
entropy of mixing. *J. Mol. Struc. (Theorochem)* **1997**, *398*,
145-153.
(This paper in pdf format can be downloaded at http://www.mdpi.org/lin/lin-rpu.htm).

(b) Lin, S. -K. Gibbs paradox of entropy of mixing:
Experimental facts, its rejection, and the theoretical consequences.
*J. Theoret. Chem.* **1996**, *1*, 135-150.
(This paper in pdf format can be downloaded at http://www.mdpi.org/lin/lin-rpu.htm).

(c) Lin, S. -K. Molecular diversity assessment:
Logarithmic relations of information and species diversity and
logarithmic
relations of entropy and indistinguishability after rejection of Gibbs
paradox of entropy of mixing. *Molecules* **1996**, *1*,
57-67.
(This paper in pdf format can be downloaded at http://www.mdpi.org/lin/lin-rpu.htm).

(d) Lin, S. -K. Correlation of entropy with similarity
and symmetry. *J. Chem. Inf. Comp. Sci.* **1996**, *36*,
367-376.
(This paper in pdf format can be downloaded at http://www.mdpi.org/lin/lin-rpu.htm).

4. (a) Based on his observation of the so-called
"order out of chaos" examples, Pregogine himself also questioned the
validity
of the second law of thermodynamics; see Prigogine's comments in the
paragraph
regarding the second law of thermodynamics in his Nobel lecture [4b].

(b) Prigogine, I. Time, structure, and fluctuations.
*Science***1978**, *201*, 777-785.

(c) For an early critique, see: Lin, S. -K. Time
symmetry and thermodynamics. *Comp. Math. Applic. Int'l. J.* **1991**,
*22 *(12), 67-76.

5. However, all contributions on Prigogine's dissipative structure theory are still welcomed based on our editorial policy.

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