# Positive curvature can mimic a quantum

## TL;DR

This paper explores how positive Ricci curvature in the space of quantum states supports the idea that quantum mechanics emerges from a deterministic theory, using Ricci flow to model dissipation and information loss.

## Contribution

It introduces a novel application of Ricci flow to model the emergence of quantum mechanics from an underlying deterministic framework, emphasizing the role of positive Ricci curvature.

## Key findings

- Positive Ricci curvature characterizes the space of quantum states.
- Ricci flow models dissipation and information loss in emergent quantum systems.
- Thermodynamical analogy supports the emergent quantum mechanics hypothesis.

## Abstract

We elaborate on the existing idea that quantum mechanics is an emergent phenomenon, in the form of a coarse-grained description of some underlying deterministic theory. We apply the Ricci flow as a technical tool to implement dissipation, or information loss, in the passage from an underlying deterministic theory to its emergent quantum counterpart. A key ingedient in this construction is the fact that the space of physically inequivalent quantum states (either pure or mixed) has positive Ricci curvature. This leads us to an interesting thermodynamical analogy of emergent quantum mechanics.