# Entropy driven transformations of statistical hypersurfaces

## TL;DR

This paper investigates how entropy-driven deformations affect the geometry of statistical hypersurfaces, exploring their structure, special cases, and connections with replicator dynamics in both ideal and super-ideal scenarios.

## Contribution

It introduces a differential framework for understanding entropy-driven deformations of statistical hypersurfaces and links these to replicator dynamics, expanding geometric and dynamic insights.

## Key findings

- Differential relations characterize hypersurface deformations
- Connections established with replicator dynamics
- Analysis of ideal and super-ideal cases

## Abstract

Deformations of geometric characteristics of statistical hypersurfaces governed by the law of growth of entropy are studied. Both general and special cases of deformations are considered. The basic structure of the statistical hypersurface is explored through a differential relation for the variables, and connections with the replicator dynamics for Gibbs' weights are highlighted. Ideal and super-ideal cases are analysed, also considering their integral characteristics.