Formulations of Quantum Thermodynamics and Applications in Open Systems

TL;DR

This paper explores quantum thermodynamics in open systems, focusing on entropy and ergotropy approaches to quantify non-Markovianity, analyze energy dynamics, and propose a new thermodynamic formulation based on ergotropy.

Contribution

It introduces an ergotropy-based thermodynamic framework and compares it with entropy-based methods, providing new tools to measure non-Markovianity and energy flow in quantum systems.

Findings

Ergotropy dynamics show freezing and sudden death phenomena.

Ergotropy-based heat flow more accurately detects non-Markovianity.

Passive state changes relate directly to the first law in quantum thermodynamics.

Abstract

Quantum thermodynamics has emerged as a central field for understanding how energy conversion processes occur in microscopic systems. In these systems, effects such as coherence, entanglement, and non-Markovianity play key roles. In this thesis, we explore different ways to describe quantum thermodynamics, using two main approaches: one based on entropy and the other on ergotropy. First, we introduce a generalized approach to quantify non-Markovianity through the breakdown of monotonicity in thermodynamic functions. In this context, the entropy-based heat flow serves as a practical tool to witness and measure quantum memory in unital maps that do not reverse the sign of the internal energy. Next, we analyze the dynamics of ergotropy in open qubits under both Markovian and non-Markovian evolutions. We identify phenomena such as freezing and sudden death of ergotropy, and we establish an analytical relation between the change in ergotropy and the environment-induced work . This provides a clear physical interpretation for the additional term in the first law in the entropy-based formulation. Finally, we propose an ergotropy-based thermodynamic formulation, in which heat is reinterpreted in terms of the change of the passive state associated with the density operator governing the quantum dynamics. This approach allows one to measure non-Markovianity of unital maps more generally and accurately than the entropy-based heat flow. This advantage comes from the direct link between heat and von Neumann entropy, a property ensured by invariance under passive transformations. Moreover, the out-of-equilibrium temperature naturally remains non-negative, similarly to equilibrium thermodynamics.