Entropy, topological theories and emergent quantum mechanics

TL;DR

This paper explores a duality between classical thermostatics and a quantum-mechanical theory with a finite-dimensional Hilbert space, linking entropy, topological field theory, and emergent quantum mechanics.

Contribution

It introduces a novel duality connecting classical thermostatics to a finite-dimensional quantum theory and discusses the role of entropy in emergent quantum frameworks.

Findings

Thermostatic processes have a quantum dual with a finite-dimensional Hilbert space.

The kernel of a Hamiltonian operator corresponds to quasistatic quantum states.

Connections between thermostatics, topological field theory, and emergent quantum mechanics are established.

Abstract

The classical thermostatics of equilibrium processes is shown to possess a quantum-mechanical dual theory with a finite-dimensional Hilbert space of quantum states. Specifically, the kernel of a certain Hamiltonian operator becomes the Hilbert space of quasistatic quantum mechanics. The relation of thermostatics to topological field theory is also discussed in the context of the emergent approach to quantum theory, where the concept of entropy plays a key role.