# Generalised Complex Geometry in Thermodynamical Fluctuation Theory

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Geometry and Fluctuations

#### 2.1. Riemannian Geometry

#### 2.2. Symplectic Geometry

**F**.

#### 2.3. Complex Geometry and Kähler Geometry

#### 2.4. Generalized Complex Geometry

## 3. When “Quantum” Becomes “Thermal”

#### 3.1. Inclusion of a Gravitational Field

#### 3.2. The Unruh Effect

#### 3.3. Transformation to an Accelerated Frame as a B-Transformation

#### 3.4. A Nonuniform Gravitational Field

**Hypothesis 1.**Regard classical phase space as a generalized complex manifold. In the presence of a nonstatic and/or nonuniform, but nevertheless weak, gravitational field, the inertial-frame Schroedinger wavefunction ψ remains form-invariant under a transformation to a locally accelerated frame, where its value is ${\psi}^{\prime}$, provided that ψ and ${\psi}^{\prime}$ are related according to the law

## 4. Conclusions

## Author Contributions

## Conflicts of Interest

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Fernández de Córdoba, P.; Isidro, J.M.
Generalised Complex Geometry in Thermodynamical Fluctuation Theory. *Entropy* **2015**, *17*, 5888-5902.
https://doi.org/10.3390/e17085888

**AMA Style**

Fernández de Córdoba P, Isidro JM.
Generalised Complex Geometry in Thermodynamical Fluctuation Theory. *Entropy*. 2015; 17(8):5888-5902.
https://doi.org/10.3390/e17085888

**Chicago/Turabian Style**

Fernández de Córdoba, P., and J. M. Isidro.
2015. "Generalised Complex Geometry in Thermodynamical Fluctuation Theory" *Entropy* 17, no. 8: 5888-5902.
https://doi.org/10.3390/e17085888