Structure Fluctuation Effects on Canonical-Nonlinear Thermodynamics

When we consider classical discrete systems under constant composition, their stable configuration in thermodynamic equilibrium can be typically obtained through the well-known canonica average phi. In configurational thermodynamics, phi as a map from many-body interatomic interaction to equilibrium configuration generally exhibits complicated nonlinearity, strongly depending on their underlying lattice. The connection between nonlinearity in phi (canonical nonlinearity) and the lattice has recently been amply investigated in terms of configurational geometry, leading to establishing its stochastic-thermodynamic treatment. The present work provides natural extention of the proposed treatment, explicitly including the effect of spatial fluctuation of the equilibrium configuration on thermodynamic property of the nonlinearity. We find that the fluctuation affects the upper-bound for the averaged nonlinearity disparity in multiple configurations, as an explicit and additional contribution from stochastic mutual information between focused coordination and its fluctuation, and an implicit contribution from changes in covariance matrix for density of states due to the fluctuation.