This review presents a thermodynamic perspective on quantum coupled transport processes in nanoscale systems. Our analysis is formulated within the framework of entropy production rate, the central quantity governing non-equilibrium processes and expressed through conjugate force-flux pairs. Although thermodynamic laws are universal across classical and quantum domains, the discussion is developed within a microscopic open quantum system framework, focusing on quantum dots (QDs) coupled to electronic reservoirs. We first examine elementary single transport processes and highlight their strong thermodynamic constraints in the near-equilibrium regime. This motivates the study of coupled transport, where multiple force-flux pairs coexist and interact, leading to richer thermodynamic behaviour. Using entropy production as the guiding principle, we analyse coupled energy and particle transport in a minimal two-terminal single-QD setup and show how conventional thermoelectric phenomena, including Seebeck and Peltier effects as well as thermoelectric heat engines and refrigerators, naturally emerge as thermodynamic cross-effects. We then extend the framework to a three-terminal coupled quantum dot (CQD) geometry, which provides a versatile platform for studying coupled transport and reduces, under suitable constraints, to the well-known Sánchez-Büttiker configuration. Beyond standard cross-effects, we discuss the phenomenon of inverse currents in coupled transport (ICC), where a current flows against mutually parallel thermodynamic forces without violating the second law. We show that ICC requires breaking the symmetry between energy and particle transport and identify the conditions for its realization in coupled quantum-dot systems with attractive interdot interactions.
This review presents a thermodynamic perspective on quantum coupled transport processes in nanoscale systems. Our analysis is formulated within the framework of entropy production rate, the central quantity governing non-equilibrium processes and expressed through conjugate force-flux pairs. Although thermodynamic laws are universal across classical and quantum domains, the discussion is developed within a microscopic open quantum system framework, focusing on quantum dots (QDs) coupled to electronic reservoirs. We first examine elementary single transport processes and highlight their strong thermodynamic constraints in the near-equilibrium regime. This motivates the study of coupled transport, where multiple force-flux pairs coexist and interact, leading to richer thermodynamic behaviour. Using entropy production as the guiding principle, we analyse coupled energy and particle transport in a minimal two-terminal single-QD setup and show how conventional thermoelectric phenomena, including Seebeck and Peltier effects as well as thermoelectric heat engines and refrigerators, naturally emerge as thermodynamic cross-effects. We then extend the framework to a three-terminal coupled quantum dot (CQD) geometry, which provides a versatile platform for studying coupled transport and reduces, under suitable constraints, to the well-known Sánchez-Büttiker configuration. Beyond standard cross-effects, we discuss the phenomenon of inverse currents in coupled transport (ICC), where a current flows against mutually parallel thermodynamic forces without violating the second law. We show that ICC requires breaking the symmetry between energy and particle transport and identify the conditions for its realization in coupled quantum-dot systems with attractive interdot interactions.
Driven quantum systems are systems in which a set of parameters obeys a time-dependent protocol, both periodic and non-periodic. The study of these systems bridges theoretical advances with experimental realizations in a variety of platforms—these range from quantum dot arrays to molecular junctions to trapped ions. The theoretical study is challenging due to the inherent non-equilibrium nature of the problem. These systems offer an interesting playground for quantum thermodynamics. They can be studied as quantum machines, such as refrigerators, heat pumps or engines. This poses the challenge of redefining the laws of thermodynamics in the quantum realm. This effort implies taking into account the presence of coherence, entanglement and strong correlations with the environment. In this conceptual framework, we attempt to shed new light on specific setups with applications in quantum metrology. In the first part of the Thesis, we present novel results on the thermodynamics and transport properties of quantum dots. After thoroughly introducing the main methods, namely non-equilibrium Green's functions and scattering matrix techniques, we apply these tools to adiabatic charge pumping. In this context, quantum dots, subjected to external periodic driving, act as nano-mechanical engines, transferring charge from a source to a drain. We investigate the conditions under which the pumped charge becomes quantized and how thermodynamic quantities behave in this regime. Next, we will focus on the charge shuttle mechanism in movable quantum dots as an example of a quantum clock. This physical model describes transport through a molecular state bound to two leads by van der Waals forces, with an electric field pushing the molecule from the source to the drain. The periodic oscillations arising from the system's dissipative limit cycle solution provide the basis for time measurement. We examine quantum noise primarily associated with the tunnelling process. In the second part, we propose a quantum clock that utilizes the free energy resources generated by coupling to a quantum battery, consisting of an integrable spin chain driven out of equilibrium by a quench in a chosen parameter. The operating conditions of the clock in the manifold of parameters are examined, leading to the requirement of the crossing of the critical point in the battery. The lifetime of the battery's resources is found to be extensive in its size, even when choosing a global coupling observable in the battery.
Thermodynamics is a phenomenological theory describing the energy conversion of work and heat. At its origins thermodynamics was developed in order to understand and improve heat engines. In conventional thermodynamics, however, only such processes are completely describable which are slow enough to keep the system of interest in an equilibrium state with its thermal environment at all times. On the contrary, all real physical processes are accompanied by non-equilibrium phenomena. These are mathematically described with the help of the irreversible entropy production, i.e. the dissipated work divided by the temperature of the bath. The second law of thermodynamics merely states that the irreversible entropy production is on average always positive. The modern trend of miniaturization, however, leads to smaller and smaller devices. On short length scales thermal noise as well as quantum fluctuations become important. Thus, usual thermodynamic quantities as work and heat acquire stochastic nature. Moreover, in the quantum regime a completely new theory had to be invented, since classical notions of work and heat are no longer valid. The present dissertation contributes to this prevailing field by the derivation of analytical expressions for the entropy production in open and closed quantum system far from thermal equilibrium. The theoretical treatment is motivated by an experimental point of view. The obtained results were derived from the reduced dynamics of the quantum mechanical system, which may be coupled to a thermal bath. To this end, it was dealt with methods and approaches of statistical physics, conventional thermodynamics, quantum information theory and the theory of open quantum systems. In this dissertation the most important physical systems are treated. First, an isolated system is considered before later on a heat bath is included. The limit of weak as well as of strong coupling are analyzed in detail. For isolated systems it turns out that a geometric approach is able to capture the thermodynamic properties, completely. To this end, the irreversible entropy production is sharply estimated from below by the angle between the real non-equilibrium state and the corresponding equilibrium one. Further, it is shown that the Heisenberg uncertainty relation for energy and time can be formulated more precisely in terms of that angle. As experimental system cold ion traps are introduced, in which the theoretical predictions can be verified. For weakly coupled systems, then, the irreversible entropy production is identified and a fluctuation theorem is derived by merely thermodynamic arguments. As experimental system we, again, propose the cold ion traps, where the heat bath can be simulated with the help of LASER light. In the limit of strong coupling a semiclassical description of the reduced quantum system is discussed. Again, an analytically exact expression for the entropy production and the corresponding fluctuation theorem is derived. A physical system, in which strong coupling to the environment can be analyzed, is given by Josephson junctions. This dissertation discusses the entropy production for isolated, weakly coupled, and overdamped quantum systems. For these physical regimes analytical relation are derived and experimental systems proposed, with which the predictions can be verified.
Quantum heat transport governs energy exchange processes and statistical laws in non-equilibrium quantum systems, and plays a pivotal role in quantum thermodynamics. We investigate the steady-state thermal transport of a noncommuting coupled spin system. We employ the quantum dressed master equation approach within the framework of open quantum system theory to accurately analyze the non-equilibrium dynamics, ensuring the validity of transport results in the strong coupling regime. Our results demonstrate that noncommuting spin coupling serves as a significant resource for modulating the nonlinearity of the heat current. Specifically, in the weak spin-coupling regime, the system exhibits robust negative differential thermal conductance (NDTC) across various spin numbers. By deriving analytical expressions for the heat current in both the single-spin and large-spin limits, we reveal that this NDTC behavior is governed by microscopic cycle fluxes. Physically, this arises because spin excitation channels induced by the cold reservoir are suppressed under a large temperature bias, thereby blocking energy exchange cycles. Conversely, in the strong spin-coupling and large temperature bias regime, the quantum system demonstrates pronounced thermal rectification. This high rectification efficiency originates from the unidirectional saturation of the heat current, rendering the system a promising candidate for high-performance thermal diodes. Furthermore, we extend the model to a three-terminal configuration to construct a quantum thermal transistor. By manipulating the temperature of the gate reservoir, we achieve efficient modulation and amplification of heat flow between the source and drain. The heat amplification factor is shown to far exceed unity in specific operating regions, confirming significant thermal amplification.
Abstract We derive the basic laws of phenomenological non-equilibrium thermodynamics for small open systems, whose quantum nature can no longer be neglected. Emphasis is put from the beginning on deriving them from an underlying microscopic system on deriving them from an underlying microscopic system–bath picture. Commonly considered approximation schemes (wea k coupling master equations) are reviewed and their thermodynamics is studied. The zeroth law is discussed for small systems and exact identities for the entropy production, valid at strong coupling and in the non non-Markovian regime, are introduced. We discu ss the effect of finite baths even out of equilibrium and use the framework of repeated interactions to study microscopic non-equilibrium resources. The chapter concludes with the study of particle transport and thermoelectric devices, which were realized in experiments. This chapter focuses entirely on the dynamics of a system coupled to a bath without any external interventions.
Deriving the laws of thermodynamics from a microscopic picture is a central quest of statistical mechanics.This tutorial focuses on the derivation of the first and second law for isolated and open quantum systems far from equilibrium, where such foundational questions also become practically relevant for emergent nanotechnologies.The derivation is based on a microscopic definition of five essential quantities: internal energy, thermodynamic entropy, work, heat, and temperature.These definitions are shown to satisfy the phenomenological laws of nonequilibrium thermodynamics for a large class of states and processes.The consistency with previous results is demonstrated.The framework applies to multiple baths including particle transport and accounts for processes with, e.g., a changing temperature of the bath, which is determined microscopically.An integral fluctuation theorem for entropy production is satisfied.In summary, this tutorial introduces a consistent and versatile framework to understand and apply the laws of thermodynamics in the quantum regime and beyond.
A central open question in quantum thermodynamics is the identification of thermodynamic entropy away from equilibrium. Although thermodynamic entropy coincides with the von Neumann entropy for a Gibbs state at equilibrium, the thermodynamic role of quantum coherence generated during nonequilibrium evolution remains unclear. Here, we show that von Neumann entropy does not, in general, represent the thermodynamic entropy governing heat exchange in coherent nonequilibrium quantum systems. By integrating the resource theory of quantum coherence with thermodynamic principles, we develop a general framework for nonequilibrium quantum thermodynamics. We identify thermodynamic entropy with the energy entropy derived from energy-measurement statistics and introduce a dynamical temperature extending the equilibrium concept to nonequilibrium states. Consequently, we obtain an exact entropy-balance relation separating the entropy flux associated with heat exchange from the coherence-loss contribution to entropy production, establishing an operational connection between quantum coherence, heat flow, and total entropy change. Unlike approaches relying on equilibrium reference states or stationary Gibbs ensembles, our framework uses instantaneous dynamical quantities and remains valid throughout transient nonequilibrium evolution. It provides consistent dynamical definitions of temperature, work, heat, and free energy. Applying the formalism to an exactly solvable open quantum system, we show that the first and second laws hold throughout transient evolution and that equilibrium thermodynamics emerges dynamically in the weak-coupling long-time limit. Our results establish a unified framework for coherent nonequilibrium quantum thermodynamics and suggest opportunities for controlling heat dissipation through coherence engineering in quantum thermal technologies.