On the energetic analysis of autonomous quantum systems

TL;DR

This thesis introduces a comprehensive formalism for analyzing energy exchanges in autonomous quantum systems, avoiding common approximations and providing a rigorous thermodynamic framework for quantum regimes.

Contribution

It presents a novel, exact formalism based on Schmidt decomposition for local energy characterization without relying on traditional approximations.

Findings

Effective Hamiltonians accurately represent local energies.

Method treats subsystems equally without approximations.

Establishes a new route for quantum thermodynamic quantities.

Abstract

In this thesis, we focus on the energetic analysis within autonomous quantum systems. To this aim, we propose a novel and general formalism for a dynamic description of the energy exchanges between interacting subsystems. From the Schmidt decomposition approach, we identify effective Hamiltonians as the representative operators for characterizing the local internal energies, whose expectation values satisfy the usual thermodynamic notion of energy additivity. In contrast to the currently used methodologies, such procedure treats the subsystems with equal footing and do not rely on any sort of approximations and additional hypotheses, e.g., semi-classical description, weak-coupling regime, strict energy conservation and Markovian dynamics. In short, our proposal contributes to the development of QT by providing a new formalism that does not suffer from the usual restrictive shortcomings and establishes a new and exact route for defining other general thermodynamic quantities to the quantum regime.