Generalised complex geometry in thermodynamical fluctuation theory

TL;DR

This paper explores how generalised complex geometry, which bridges symplectic and complex geometries, can be applied to analyze thermodynamical fluctuations influenced by gravitational fields, exemplified by a simplified Unruh effect scenario.

Contribution

It introduces the application of generalised complex geometry to thermodynamical fluctuation theory in gravitational contexts, providing a new analytical framework.

Findings

Generalised complex geometry effectively models thermodynamical fluctuations with gravitational effects.

The framework offers insights into the thermalising influence of gravity on quantum states.

Simplified Unruh effect demonstrates the practical utility of the geometric approach.

Abstract

We present a brief overview of some key concepts in the theory of generalised complex manifolds. This new geometry interpolates, so to speak, between symplectic geometry and complex geometry. As such it provides an ideal framework to analyse thermodynamical fluctuation theory in the presence of gravitational fields. To illustrate the usefulness of generalised complex geometry, we examine a simplified version of the Unruh effect: the thermalising effect of gravitational fields on the Schroedinger wavefunction.