On entropy/information continuity in molecular electronic states^*

* This article is dedicated to Prof. Andreas Savin on the occasion of his 65th birthday.

^†

^†Throughout the article x denotes a scalar quantity, x stands for the row- or column-vector, and x represents a square or rectangular matrix. The natural logarithm log = ln used in the Shannon entropy expresses the amount of information in nats (natural units): 1 nat = 1.44 bits.

ABSTRACT

In the information-theoretic (IT) description of electronic states in molecules, the current and source concepts of the continuity relations for densities of quantum descriptors of the state resultant entropic content combining the probability and current/phase contributions are examined and interpreted. The resultant Shannon- and Fisher-type functionals, isomorphic in the position and momentum representations of quantum mechanics, are explored and the corresponding information sources are established. All these thermodynamic-like expressions in terms of the relevant IT intensities, affinities, fluxes and probability sources predict the vanishing entropy source for the zero intensities associated with the state modulus (probability) and phase (current) degrees of freedom.

GRAPHICAL ABSTRACT

KEYWORDS:

• Current/phase entropy/information measures
• information continuity
• information theory
• quantum Shannon/Fisher entropy/information
• position/momentum representations
• resultant entropy sources

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

* This article is dedicated to Prof. Andreas Savin on the occasion of his 65th birthday.

^† Throughout the article x denotes a scalar quantity, x stands for the row- or column-vector, and x represents a square or rectangular matrix. The natural logarithm log = ln used in the Shannon entropy expresses the amount of information in nats (natural units): 1 nat = 1.44 bits.