Diversity and Entropy

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, Entropy 1999, 1 2 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. …