Information theoretic approach to fluctuations and electron flows between molecular fragments

The elements of the information theoretic approach to instantaneous electron distributions between molecular subsystems are developed by following the thermodynamic theory of fluctuations and irreversible processes. The distribution function and information theoretic basis of the stockholder partitioning, defining the equilibrium distributions of electrons among subsystems, are briefly summarized. The nonequilibrium (instantaneous) local entropy deficiency and the state parameters and their associated intensive conjugates in the entropy deficiency representation are introduced using the promolecule-referenced local measures of the information distance (entropy deficiency) of Kullback and Leibler between the instantaneous subsystem electron densities, conserving the overall molecular density and the free or Hirshfeld subsystem electron densities, respectively. Within a local description, the Gaussian distribution function of Einstein's theory is introduced, predicting a local dispersion of the subsystem density to be proportional to the molecular density and the square root of the free subsystem share in the promolecule density. The key concepts of the local irreversible thermodynamics of molecular subsystems are introduced for alternative information theoretic entropy-deficiency representations. They include the corresponding affinities (forces) and the conjugate fluxes (response quantities), which together determine the local entropy deficiency source. The Onsager reciprocity relations are derived and justified through fluctuations.