# Where Nonlinearity in Thermodynamic Average Comes from? Configurational Geometry Revisited

## TL;DR

This paper investigates the origin of nonlinearity in thermodynamic averages for classical discrete systems, revealing it stems from deviations in the configurational density of states from a Gaussian distribution, emphasizing the role of configurational geometry.

## Contribution

It provides a theoretical analysis linking nonlinearity in thermodynamic averages to geometrical features of configurational space, revisiting the role of CDOS deviations.

## Key findings

- Nonlinearity originates from deviations in CDOS from Gaussian distribution.
- Configurational geometry significantly influences thermodynamic stability.
- The study highlights the importance of geometrical analysis in thermodynamics.

## Abstract

For classical discrete system under constant composition, we theoretically examine origin of nonlinearity in thermodynamic (so-called canonical) average w.r.t. many-body interactions, in terms of geometrical information in configuratin space. We clarify that nonlinearity essentially comes from deviation in configurational density of states (CDOS) before applying many-body interactions to the system, from multidimensional gaussian distribution. The present finding strongly suggest the significance to investigate how the deviation in CDOS bridges bidirectional stability relationships between equilibrium structure and potential energy in thermodynamic average.