Intensive nature of fluctuations:reconceptualizing Kirkwood-Buff theory via elementary algebra

Quantifying the role of solvation in soft matter and complex solutions has been made challenging by the fluctuational nature of solvation, as well as by the tedious calculus associated with it in converting thermodynamic variables. A new algebraic approach to fluctuation proposed here eliminates the tedious calculus, demonstrated by a simple rederivation of the Kirkwood-Buff theory of solutions, as well as by the calculation of higher-order fluctuations in inhomogeneous solutions. This new approach is based on a new physical insight into fluctuation in solution; concentration fluctuation, since it is independent of system size, is an invariant under transformation between ensembles, with different expressions depending on the choice of extensive variables. This is because a full set of intensive thermodynamic quantities can be represented in multiple yet equivalent ways.