Abstract
Microscopic formula to describe the entropy of biomolecular solutions are derived based on the Gibbs formula of entropy, and the generalized Langevin theory combined with the RISM/3D-RISM theory. Two formula are derived: one is concerned with the conformational fluctuation of a biomolecule, and the other with the density fluctuation of solvent around a solute. The formula derived for the entropy associated with the conformational fluctuation is Sconf=12kBlog2π3NA+3N2kBwhere N is the number of atoms in the solute, and A is the determinant of the inverse of the variance–covariance matrix of conformational fluctuation.The formula for the entropy of solvent at a pair of positions around a solute is also derived to be, ssolv(r,r′)=12kBlog2πnB+3n2kBwhere n is the number of atoms in a solvent molecule, and B is essentially the determinant of the matrix of the density-pair-correlation functions. The entropy at a local position r may be obtained by integrating the expression by r′ over the entire volume of the system.The feasibility of the calculation to find the entropies is discussed.
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