Quantum Thermodynamics with Nonequilibrium Steady States

Abstract

This thesis investigates the thermodynamics of quantum systems far from equilibrium, with particular emphasis on nonequilibrium steady states (NESS). Its central contributions are twofold: a methodological development of the mesoscopic leads technique for modeling open quantum systems, and a geometric framework for understanding entropy production in slow transitions between NESS.

The first part of the thesis refines the mesoscopic leads approach, providing a consistent thermodynamic description within this formalism. By treating each lead as a finite quantum system weakly coupled to an external Markovian reservoir, the method enables a Markovian embedding of the extended system, even when the central system itself exhibits non-Markovian dynamics. Within this framework, we derive expressions for heat currents and entropy production, recovering the Landauer-Büttiker formula in the limit of large leads. As an application, the method is used to study thermal rectification in a periodically driven double quantum dot.

The second part focuses on entropy production in slow, quasistatic transitions between nonequilibrium steady states. Using the Hatano-Sasa decomposition, we separate the total entropy production into adiabatic and non-adiabatic contributions, where the latter quantifies deviations from instantaneous steady states. In the slow-driving limit, this non-adiabatic entropy production is shown to be governed by a Riemannian metric on the space of control parameters, allowing the use of geometric techniques to derive thermodynamic bounds.

In addition to these original results, the thesis offers pedagogical reviews of foundational topics in quantum thermodynamics, including a comprehensive introduction to Gaussian fermionic systems without pairing terms and a modern exposition of the Hatano-Sasa framework for both classical Markov chains and Lindblad master equations.