Particle-exchange machines utilize electronic transport to continuously transfer heat between fermionic reservoirs. Here, we introduce a model coupling a quantum mechanical resonator to a particle-exchange machine hosted in a quantum dot (QD) and let the system run autonomously. This way, part of the energy exchanged between the reservoirs can be stored in the resonator in the form of self-oscillations. Our analysis goes well beyond previous works by exploring the slow transport regime and accessing arbitrarily strong dot-resonator coupling. First, we introduce a faithful measure of self-oscillations, and use it to certify that they can occur in the slow-transport regime. We furthermore show that the electrical current through the dot can be used to witness self-oscillations. Finally, we establish that, under realistic conditions, self-oscillations occur only when the machine operates as a heater. We define an experimentally measurable performance metric characterizing the efficiency of current-to-self-oscillations conversion. It reveals that, counterintuitively, strong dot-resonator coupling is detrimental to the conversion performance. The framework developed here can be readily implemented in a variety of nanoscale devices, such as a suspended carbon nanotube with an embedded QD.

The accurate prediction of temperature-dependent magnetization dynamics is a fundamental challenge in computational magnetism. While atomistic spin dynamics simulations have emerged as a powerful tool for studying magnetic phenomena, their classical nature leads to significant deviations from experimental observations, particularly at low temperatures. Here we present a comprehensive implementation of quantum-corrected atomistic spin dynamics into the VAMPIRE software package, based on the open-system Landau-Lifshitz-Gilbert equation with a quantum thermostat. Our implementation incorporates memory effects along with colored noise derived from quantum-mechanical considerations that improve the description of the equilibrium magnetization. We demonstrate excellent quantitative agreement with experimental magnetization curves for nickel and gadolinium across the full temperature range. Our results establish that incorporating quantum environmental effects and colored noise substantially enhances the predictive capabilities of atomistic spin dynamics simulations, providing a robust framework for modeling temperature-dependent magnetic phenomena in localized moment magnetic systems.

The last two decades has seen quantum thermodynamics become a well established field of research in its own right. In that time, it has demonstrated a remarkably broad applicability, ranging from providing foundational advances in the understanding of how thermodynamic principles apply at the nano-scale and in the presence of quantum coherence, to providing a guiding framework for the development of efficient quantum devices. Exquisite levels of control have allowed state-of-the-art experimental platforms to explore energetics and thermodynamics at the smallest scales which has in turn helped to drive theoretical advances. This Roadmap provides an overview of the recent developments across many of the field's sub-disciplines, assessing the key challenges and future prospects, providing a guide for its near term progress.

Engineering the properties of a reservoir and its coupling to a quantum system is a powerful tool for simulating quantum thermodynamic processes and for generating otherwise inaccessible steady states. Yet tailoring both the reservoir and its coupling within a single platform remains challenging. Here we introduce a platform, in which an ancilla qubit mediates the coupling of a target system to a reservoir, providing independent control over the interaction form, coupling strength, and effective reservoir temperature. Our implementation uses the electron spin of a single nitrogen-vacancy center in diamond as the ancilla and a proximal ^13C nuclear spin as the target. By alternating engineered unitary interactions with dissipative ancilla resets, we realize dynamics naturally described by a collision model, enabling straight-forward tracking of the work, heat, coherence, and entropy generated at every collision. We experimentally demonstrate conventional thermalization and also realize anti-thermalization: the stabilization of the target system in a temperature opposite to that of its reservoir. Finally, harnessing this steady-state engineering, we utilize the nuclear spin as a quantum battery, achieving a steady-state ergotropy exceeding 70% of the theoretical maximum.

High precision measurements are essential to solve major scientific and technological challenges, from gravitational wave detection to healthcare diagnostics. Quantum sensing delivers greater precision, but an in-depth optimization of measurement procedures has been overlooked. Here, we present a systematic strategy for parameter estimation in the low-data limit that integrates experimental control parameters and natural symmetries. The method is guided by a Bayesian quantifier of precision gain, enabling adaptive optimization tailored to the experiment. We provide general expressions for optimal estimators for any parameter. The strategy's power is demonstrated in a quantum technology experiment, in which ultracold caesium atoms are confined in a micromachined hole in an optical fiber. We find a fivefold reduction in the fractional variance of the estimated parameter, compared to the standard measurement procedure. Equivalently, our strategy achieves a target precision with a third of the data points previously required. Such enhanced device performance and accelerated data collection will be essential for applications in quantum computing, communication, metrology, and the wider quantum technology sector.

Nanoelectromechanical resonators provide an ideal platform for investigating the interplay between electron transport and nonlinear mechanical motion. Externally driven suspended carbon nanotubes, containing an electrostatically defined quantum dot, are especially promising. These devices possess two main sources of nonlinearity: the electromechanical coupling and the intrinsic contributions of the resonator that induce a Duffing-like nonlinear behavior. In this work, we observe the interplay between the two sources across different driving regimes. The main nonlinear feature we observe is the emergence of archlike resonances in the electronic transport when the resonator is strongly driven. We show that our model is in good agreement with our experimental electron transport measurements on a suspended carbon nanotube. This characterization paves the way for the exploration of nonlinear phenomena using mesoscopic electromechanical resonators.

The canonically consistent quantum master equation (CCQME) method to treat system-bath dynamics is used to describe intramolecular proton transfer in the thioacetylacetone molecule (TAA, C5H8OS), modeled as an N-level quantum system coupled to a solvent. The solvent is represented as a harmonic bath (a continuum of oscillators) characterized by Ohmic-Drude spectral density. We benchmark the secularized population dynamics and steady-state populations predicted by CCQME against numerically exact hierarchical equations of motion (HEOM) theory and compare it to the corresponding secularized Redfield results. Our results reveal that Redfield dynamics deviates increasingly from the HEOM reference as the system-bath coupling strength grows. In contrast, for not too strong couplings, the secularized CCQME population dynamics remains consistent with HEOM over an extended system-bath coupling range and approaches the second-order mean force Gibbs state. A complementary non-secular calculation shows that retaining population-coherence coupling reveals limitations of the second-order treatment for coherence-sensitive observables.

Magnetization dynamics is commonly described by the stochastic Landau-Lifshitz-Gilbert (LLG) equation. However, on picosecond timescales, inertial and open-system extensions of the LLG equation are necessary to interpret recent experiments. While it has been anticipated that these extensions make the magnetization dynamics non-Markovian, to date, the question of the extent of non-Markovianity has remained unanswered. Here, we provide a systematic quantification of the degree of non-Markovianity in these magnetization models using established measures. We find that, while the standard LLG equation exhibits strictly positive entropy production rates, inertial and open-system LLG dynamics display temporarily negative entropy production rates, which signal non-Markovian dynamics, as we demonstrate both analytically and numerically. Our numerical calculations show that experiments requiring the open-system LLG equation are more non-Markovian than those described by classical or inertial LLG equations. Non-Markovianity in magnetization dynamics on picosecond timescales has recently been identified experimentally and can be described by extensions to the Landau-Lifshitz-Gilbert equation. The authors introduce a systematic quantification of the experimentally observed non-Markovianity based on the negativity of entropy production rates.

Memory effects arise in many complex systems, from protein folding, to the spreading of epidemics and financial decisions. While so-called non-Markovian dynamics is common in larger systems with interacting components, observations in fundamental physical systems have been confined to specifically engineered cases. Here, we report the experimental observation of non-Markovian dynamics in an elemental material, crystalline cobalt. By driving this material with an intense terahertz electromagnetic field, we bring its magnetisation into a non-equilibrium state and follow its evolution. We measure the sample's low temperature magnetic response in the time domain which leads to an unexpectedly rich multi-peaked spectrum in the Fourier domain, that cannot be explained by established models. We use open quantum system theory, which predicts a non-Markovian memory kernel in the dynamical equations to capture the fundamental interaction between the spin system and the phonon bath. Simulations based on this theory produce a multi-peaked spectrum, which matches the measured one. Our non-Markovian approach is also able to reproduce the modification of the spectrum at higher temperatures. Our findings demonstrate that non-Markovian effects are observable at a much more fundamental level than previously thought, opening the door to their exploration and control in a broad range of condensed matter systems.

The ability to couple a solitary spin to high-frequency motion is a crucial advancement for a range of applications, including quantum sensing, intermediate and long-distance spin-spin coupling, and quantum information processing. Although proposed theoretically over a decade ago, experimental demonstrations have remained elusive. Here we report the observation of spin-mechanical coupling in a carbon nanotube device. We demonstrate this coupling in two configurations: off-resonant, with spin and mechanics excited by separate tones, and resonant, driven by a single tone. The coupling manifests as a shift and broadening of the electric dipole spin resonance (EDSR), respectively. Our theoretical model, which accounts for the tensor character of the coupling and mechanical non-linearity, reproduces the data with very good agreement. Our results demonstrate a previously unobserved spin-mechanical coupling, offering versatile tools for exploring macroscopic quantum phenomena, quantum thermodynamics, and quantum simulation.

We show how work can be extracted from number-state coherence in a two-mode Bose-Einstein condensate. With careful tuning of parameters, a sequence of thermodynamically reversible steps transforms a Glauber coherent state into a thermal state with the same energy probability distribution. The work extracted during this process arises entirely from the removal of quantum coherence. More generally, we characterise quantum (from coherence) and classical (remaining) contributions to work output, and find that in this system the quantum contribution can be dominant over a broad range of parameters. The proportion of quantum work output can be further enhanced by squeezing the initial state. Due to the many-body nature of the system, the work from coherence can equivalently be understood as work from entanglement.

Thermalization of isolated and open quantum systems has been studied extensively. However, being the subject of investigation by different scientific communities and being analysed using different mathematical tools, the connection between the isolated (IQS) and open (OQS) approaches to thermalization has remained opaque. Here we demonstrate that the fundamental difference between the two paradigms is the order in which the long time and the thermodynamic limits are taken. This difference implies that they describe physics on widely different time and length scales. Our analysis is carried out numerically for the case of a double quantum dot (DQD) coupled to a fermionic lead, also known as the interacting resonant level model in quantum impurity physics. We show how both OQS and IQS thermalization can be explored in this model on equal footing, allowing a fair comparison between the two. We find that while the quadratically coupled (free) DQD experiences no isolated thermalization, it of course does experience open thermalization. For the non-linearly interacting DQD coupled to a fermionic lead, the many-body interaction in the DQD breaks the integrability of the whole system. We find that this system shows strong evidence of both OQS and IQS thermalization in the same dynamics, but at widely different time scales, consistent with reversing the order of the long time and the thermodynamic limits.

Nanoelectromechanical resonators provide an ideal platform for investigating the interplay between electron transport and nonlinear mechanical motion. Externally driven suspended carbon nanotubes, containing an electrostatically defined quantum dot are especially promising. These devices possess two main sources of nonlinearity: the electromechanical coupling and the intrinsic contributions of the resonator that induce a Duffing-like nonlinear behavior. In this work, we observe the interplay between the two sources across different driving regimes. The main nonlinear feature we observe is the emergence of arch-like resonances in the electronic transport when the resonator is strongly driven. We show that our model is in good agreement with our experimental electron transport measurements on a suspended carbon nanotube. This characterization paves the way for the exploration of nonlinear phenomena using mesoscopic electromechanical resonators.

The energy cost of erasing a bit of information was fundamentally lower bounded by Landauer, in terms of the temperature of its environment, W kBT ln 2. Energy consumption and heat generation in computers is now a pressing issue, but real electronic devices operate out of equilibrium and are subject to other noise sources besides temperature. Considering a quantum dot charge bit as a concrete model, we here derive a tighter bound, rigorously quantifying the dissipative impact of lifetime broadening and potential difference, in terms of a few experimentally measurable parameters. In practical contexts, these additional contributions may significantly outweigh the cost due to temperature alone. The results shed light not only on theoretical limits of erasure but also on constraints in realistic devices.

Coupling the vibrations of an oscillator to electronic transport is a key building block for nanoelectromechanical systems. They describe many nanoscale electrical components such as molecular junctions. Inspired by recent experimental developments, we derive a quantum master equation that describes nanoelectromechanical systems in a generally overlooked situation: when the electronic transport is slower than the natural frequency of the oscillator. Here, a semi-classical model is no longer valid and we develop the missing fully quantum approach. Moreover, we go beyond the wide-band limit and study the consequence of maintaining energy dependent tunneling rates, which are required to describe effects found in real devices. To benchmark our results, we compare with numerically exact results obtained with the hierarchical equations of motion method, and find overall good agreements in the experimentally accessible steady state regime. Furthermore, we derive from the microscopic model a ready to use particle current expression that replicates features already observed experimentally.

There are many exotic thermodynamic processes that are hard to study in nature. Here, we synthesize a structured environment to explore the extremes of thermodynamics. We present an engine running at extreme temperatures of above ten Mega-Kelvin. Our underdamped engine is realised by electrically levitating and controlling a charged microparticle in vacuum. Giant fluctuations are observed in the engine's heat exchange with the environment, while its efficiency shows stochastic events where more work is performed by the engine than heat consumed. Moreover, the non-uniformity of the synthetic environment leads to the particle experiencing position dependent diffusion, a critical phenomenon in microscale biological processes. We theoretically account for the effects of multiplicative noise and find excellent agreement with the observed behavior.

"A battery powers a device" can be read as "work stored in the battery is being transported to the device." In quantum batteries, the total amount of stored work can be measured by ergotropy, which is the maximal work extractable by unitary operations. Transporting ergotropy is fundamentally different from transporting energy, and here we find that ergotropy can be gained even when the transmission channel is strictly energy conserving. We show that, generically, ergotropy transport is lossy whenever the two systems start uncorrelated. In contrast, for a large class of correlated initial states, transport can be gainful. Furthermore, a single correlated state can be used multiple times, allowing to transport without losses an order of magnitude more work than the battery capacity. Correlations are thus a useful resource for ergotropy transport, and we quantify how this resource is consumed during gainful transport.

Ergotropy – the maximal amount of unitarily extractable work – measures the “charge level” of quantum batteries. We prove that in large many-body batteries ergotropy exhibits a concentration of measure phenomenon. Namely, the ergotropy of such systems is almost constant for almost all states sampled from the Hilbert–Schmidt measure. We establish this by first proving that ergotropy, as a function of the state, is Lipschitz-continuous with respect to the Bures distance, and then applying Levy's measure concentration lemma. In parallel, we showcase the analogous properties of von Neumann entropy, compiling and adapting known results about its continuity and concentration properties. Furthermore, we consider the situation with the least amount of prior information about the state. This corresponds to the quantum version of the Jeffreys prior distribution – the Bures measure. In this case, there exist no analytical bounds guaranteeing exponential concentration of measure. Nonetheless, we provide numerical evidence that ergotropy, as well as von Neumann entropy, concentrate also in this case.

The equilibrium properties of nanoscale systems can deviate significantly from standard thermodynamics due to their coupling to an environment. We investigate this here for the θ -angled spin–boson model, where we first derive a compact and general form of the classical equilibrium state including environmental corrections to all orders. Secondly, for the quantum spin–boson model we prove, by carefully taking a large spin limit, that Bohr’s quantum–classical correspondence persists at all coupling strengths. This shows, for the first time, the validity of the quantum–classical correspondence for an open system and gives insight into the regimes where the quantum system is well-approximated by a classical one. Finally, we provide the first classification of the coupling parameter regimes for the spin–boson model, from weak to ultrastrong, both for the quantum case and the classical setting. Our results shed light on the interplay of quantum and mean force corrections in equilibrium states of the spin–boson model, and will help draw the quantum to classical boundary in a range of fields, such as magnetism and exciton dynamics.

The spin-boson model usually considers a spin coupled to a single bosonic bath. However, some physical situations require coupling of the spin to multiple environments. For example, spins interacting with phonons in three-dimensional magnetic materials. Here, we consider a spin coupled isotropically to three independent baths. We show that coupling to multiple baths can significantly increase entanglement between the spin and its environment at zero temperature. The effect of this is to reduce the spin's expectation values in the mean force equilibrium state. In contrast, the classical three-bath spin equilibrium state turns out to be entirely independent of the environmental coupling. These results reveal purely quantum effects that can arise from multi-bath couplings, with potential applications in a wide range of settings, such as magnetic materials.