Recent years have seen tremendous progress in the theoretical understanding of quantum systems driven dissipatively by coupling to different baths at their edges. This was possible because of concurrent advances in the models used to represent these systems, the methods employed, and the analysis of the emerging phenomenology. A comprehensive review of these three integrated research directions is given. First provided is an overarching view of the models of boundary-driven open quantum systems, in both the weak- and strong-coupling regimes. This is followed by a review of state-of-the-art analytical and numerical methods that are exact, perturbative, and approximate. Finally, the transport properties of some paradigmatic one-dimensional chains are discussed, with an emphasis on disordered and quasiperiodic systems, the emergence of rectification and negative differential conductance, and the role of phase transitions, and an outlook on further research options is given.

Thermodynamic uncertainty relations (TURs) place strict bounds on the fluctuations of thermodynamic quantities in terms of the associated entropy production. In this Letter, we identify the tightest (and saturable) matrix-valued TUR that can be derived from the exchange fluctuation theorems describing the statistics of heat and particle flow between multiple systems of arbitrary dimensions. Our result holds for both quantum and classical systems, undergoing general finite-time nonstationary processes. Moreover, it provides bounds not only for the variances, but also for the correlations between thermodynamic quantities. To demonstrate the relevance of TURs to the design of nanoscale machines, we consider the operation of a 2-qubit swap engine undergoing an Otto cycle and show how our results can be used to place strict bounds on the correlations between heat and work.

Autonomous engines operating at the nanoscale can be prone to deleterious fluctuations in the heat and particle currents. Thermodynamic uncertainty relations (TURs) express a fundamental lower bound which translates a trade-off relation between precision and entropy production. Importantly, recent studies have shown that they can be violated in the quantum regime, thus motivating the search for analogous quantum counterparts. In this paper, we show that the geometry of quantum nonequilibrium steady states alone directly implies the existence of TUR, but with a looser bound, which is not violated by the above recent findings. The geometrical nature of this result makes it extremely general, establishing a fundamental limit for the thermodynamics of precision. Our proof is based on the McLennan-Zubarev ensemble, which provides an exact description of nonequilibrium steady states. We first prove that the entropy production of this ensemble can be expressed as a quantum relative entropy. The TURs are then shown to be a direct consequence of the Cramer-Rao bound, a fundamental result from parameter estimation theory. By combining techniques from many-body physics and information sciences, our approach also helps to shed light on the delicate relationship between quantum effects and current fluctuations in autonomous machines, where new general bound on the power output are found and discussed.

Thermodynamic irreversibility is well characterized by the entropy production arising from non-equilibrium quantum processes. We show that the entropy production of a quantum system undergoing open-system dynamics can be formally split into a term that only depends on population unbalances, and one that is underpinned by quantum coherences. This allows us to identify a genuine quantum contribution to the entropy production in non-equilibrium quantum processes. We discuss how these features emerge both in Lindblad-Davies differential maps and finite maps subject to the constraints of thermal operations. We also show how this separation naturally leads to two independent entropic conservation laws for the global system-environment dynamics, one referring to the redistribution of populations between system and environment and the other describing how the coherence initially present in the system is distributed into local coherences in the environment and non-local coherences in the system-environment state. Finally, we discuss how the processing of quantum coherences and the incompatibility of non-commuting measurements leads to fundamental limitations in the description of quantum trajectories and fluctuation theorems.

Continuously measured quantum systems are characterized by an output current, in the form of a stochastic and correlated time series, which conveys crucial information about the underlying quantum system. The many tools used to describe current fluctuations are scattered across different communities: quantum opticians often use stochastic master equations, while a prevalent approach in condensed-matter physics is provided by full counting statistics. These, however, are simply different sides of the same coin. Our goal with this tutorial is to provide a unified toolkit for describing current fluctuations. This not only provides novel insights, by bringing together different fields in physics, but also yields various analytical and numerical tools for computing quantities of interest. We illustrate our results with various pedagogical examples and connect them with topical fields of research, such as waiting-time statistics, quantum metrology, thermodynamic uncertainty relations, quantum point contacts, and Maxwell’s demons. Published by the American Physical Society 2024

We introduce the idea of weakly coherent collisional models, where the elements of an environment interacting with a system of interest are prepared in states that are approximately thermal but have an amount of coherence proportional to a short system-environment interaction time in a scenario akin to well-known collisional models. We show that, in the continuous-time limit, the model allows for a clear formulation of the first and second laws of thermodynamics, which are modified to include a nontrivial contribution related to quantum coherence. Remarkably, we derive a bound showing that the degree of such coherence in the state of the elements of the environment represents a resource, which can be consumed to convert heat into an ordered (unitarylike) energy term in the system, even though no work is performed in the global dynamics. Our results therefore represent an instance where thermodynamics can be extended beyond thermal systems, opening the way for combining classical and quantum resources.