Effect of Tear Size and Location on Supraspinatus Tendon Strain During Activities of Daily Living and Physiotherapy.

The supraspinatus tendon plays a crucial role in shoulder abduction, making it one of the common structures affected by injury. Clinically, crescent-shaped tears are the most commonly seen tear shape. By developing six specimen-specific, three-dimensional, supraspinatus-infraspinatus finite element model with heterogeneous material properties, this study aimed to examine the changes in tissue deformation (maximum principal strain) of the supraspinatus tendon due to specimen-specific material properties and rotator cuff tear size. FE models with small- and medium-sized full-thickness crescent-shaped tears were subjected to loads seen during activities of daily living and physiotherapy. Six fresh-frozen cadaveric shoulders were dissected to mechanically test the supraspinatus tendon and develop and validate FE models that can be used to assess changes in strain due to small (< 1 cm, equivalent to 20-30% of the tendon width) and medium-sized (1-3 cm, equivalent to 40-50% of the tendon width) tears that are located in the middle and posterior regions of the supraspinatus tendon. FE predictions of maximum principal strain at the tear tips were examined to determine whether failure strain was reached during activities of daily living (drinking and brushing teeth) and physiotherapy exercises (prone abduction and external rotation at 90° abduction). No significant differences were observed between the middle and posterior tear failure loads for small- and medium-sized tears. For prone abduction, there was a potential risk for tear progression (exceeded failure strain) for medium-sized tears in the supraspinatus tendon's middle and posterior regions. For external rotation at 90° abduction, one model with a middle tear and two with posterior tears experienced failure. For all daily activity loads, the strain never exceeded the failure strain. Our three-dimensional supraspinatus-infraspinatus FE model shows that small tears appear unlikely to progress based on the regional strain response; however, medium-sized tears are at higher risk during more strenuous physiotherapy exercises. Furthermore, differences in patient-specific tendon material properties are important in determining whether the tear will progress. Therefore, patient-specific management plans based on tear size may be beneficial to improve clinical outcomes.

Nontrivial effect of dephasing: Enhancement of rectification of spin current in graded XX chains.

In order to reveal mechanisms to control and manipulate spin currents, we perform a detailed investigation of the dephasing effects in the open XX model with a Lindblad dynamics involving global dissipators and thermal baths. Specifically, we consider dephasing noise modeled by current-preserving Lindblad dissipators acting on graded versions of these spin systems, that is, systems in which the magnetic field and/or the spin interaction are growing (decreasing) along the chain. In our analysis, we study the nonequilibrium steady state via the covariance matrix using the Jordan-Wigner approach to compute the spin currents. We find that the interplay between dephasing and graded systems gives rise to a nontrivial behavior: When we have homogeneous magnetic field and graded interactions we have rectification enhancement mechanisms, and when we have fully graded systems we can control the spin current in order to keep the direction of the particle and/or spin flow even with inverted baths. We describe our result in detailed numerical analysis and we see that rectification in this simple model indicates that the phenomenon may generally occur in quantum spin systems.

Battery Charging in Collision Models with Bayesian Risk Strategies.

We constructed a collision model where measurements in the system, together with a Bayesian decision rule, are used to classify the incoming ancillas as having either high or low ergotropy (maximum extractable work). The former are allowed to leave, while the latter are redirected for further processing, aimed at increasing their ergotropy further. The ancillas play the role of a quantum battery, and the collision model, therefore, implements a Maxwell demon. To make the process autonomous and with a well-defined limit cycle, the information collected by the demon is reset after each collision by means of a cold heat bath.

Experimental Validation of Fully Quantum Fluctuation Theorems Using Dynamic Bayesian Networks.

Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small systems. Their general validity arbitrarily far from equilibrium makes them invaluable in nonequilibrium physics. So far, experimental studies of quantum fluctuation relations do not account for quantum correlations and quantum coherence, two essential quantum properties. We here apply a novel dynamic Bayesian network approach to experimentally test detailed and integral fully quantum fluctuation theorems for heat exchange between two quantum-correlated thermal spins-1/2 in a nuclear magnetic resonance setup. We concretely verify individual integral fluctuation relations for quantum correlations and quantum coherence, as well as for the sum of all quantum contributions. We further investigate the thermodynamic cost of creating correlations and coherence.

Rectification induced by geometry in two-dimensional quantum spin lattices.

We address the role of geometrical asymmetry in the occurrence of spin rectification in two-dimensional quantum spin chains subject to two reservoirs at the boundaries, modeled by quantum master equations. We discuss the differences in the rectification for some one-dimensional cases, and present numerical results of the rectification coefficient R for different values of the anisotropy parameter of the XXZ model, and different configurations of boundary drives, including both local and nonlocal dissipators. Our results also show that geometrical asymmetry, along with inhomogeneous magnetic fields, can induce spin current rectification even in the XX model, indicating that the phenomenon of rectification due to geometry may be of general occurrence in quantum spin systems.

Current fluctuations in nonequilibrium discontinuous phase transitions.

Discontinuous phase transitions out of equilibrium can be characterized by the behavior of macroscopic stochastic currents. But while much is known about the average current, the situation is much less understood for higher statistics. In this paper, we address the consequences of the diverging metastability lifetime-a hallmark of discontinuous transitions-in the fluctuations of arbitrary thermodynamic currents, including the entropy production. In particular, we center our discussion on the conditional statistics, given which phase the system is in. We highlight the interplay between integration window and metastability lifetime, which is not manifested in the average current, but strongly influences the fluctuations. We introduce conditional currents and find, among other predictions, their connection to average and scaled variance through a finite-time version of large deviation theory and a minimal model. Our results are then further verified in two paradigmatic models of discontinuous transitions: Schlögl's model of chemical reactions, and a 12-state Potts model subject to two baths at different temperatures.

Joint Fluctuation Theorems for Sequential Heat Exchange.

We study the statistics of heat exchange of a quantum system that collides sequentially with an arbitrary number of ancillas. This can describe, for instance, an accelerated particle going through a bubble chamber. Unlike other approaches in the literature, our focus is on the joint probability distribution that heat Q 1 is exchanged with ancilla 1, heat Q 2 is exchanged with ancilla 2, and so on. This allows us to address questions concerning the correlations between the collisional events. For instance, if in a given realization a large amount of heat is exchanged with the first ancilla, then there is a natural tendency for the second exchange to be smaller. The joint distribution is found to satisfy a Fluctuation theorem of the Jarzynski-Wójcik type. Rather surprisingly, this fluctuation theorem links the statistics of multiple collisions with that of independent single collisions, even though the heat exchanges are statistically correlated.

Experimental Assessment of Entropy Production in a Continuously Measured Mechanical Resonator.

The information on a quantum process acquired through measurements plays a crucial role in the determination of its nonequilibrium thermodynamic properties. We report on the experimental inference of the stochastic entropy production rate for a continuously monitored mesoscopic quantum system. We consider an optomechanical system subjected to continuous displacement Gaussian measurements and characterize the entropy production rate of the individual trajectories followed by the system in its stochastic dynamics, employing a phase-space description in terms of the Wigner entropy. Owing to the specific regime of our experiment, we are able to single out the informational contribution to the entropy production arising from conditioning the state on the measurement outcomes. Our experiment embodies a significant step towards the demonstration of full-scale control of fundamental thermodynamic processes at the mesoscopic quantum scale.

Landauer's Principle at Zero Temperature.

Landauer's bound relates changes in the entropy of a system with the inevitable dissipation of heat to the environment. The bound, however, becomes trivial in the limit of zero temperature. Here we show that it is possible to derive a tighter bound which remains nontrivial even as T→0. As in the original case, the only assumption we make is that the environment is in a thermal state. Nothing is said about the state of the system or the kind of system-environment interaction. Our bound is valid for all temperatures and is always tighter than the original one, tending to it in the limit of high temperatures.

Quantum Fluctuation Theorems beyond Two-Point Measurements.

We derive detailed and integral quantum fluctuation theorems for heat exchange in a quantum correlated bipartite thermal system using the framework of dynamic Bayesian networks. Contrary to the usual two-projective-measurement scheme that is known to destroy quantum features, these fluctuation relations fully capture quantum correlations and quantum coherence at arbitrary times. We further obtain individual integral fluctuation theorems for classical and quantum correlations, as well as for local and global quantum coherences.

Heat rectification on the XX chain.

In order to better understand the minimal ingredients for thermal rectification, we perform a detailed investigation of a simple spin chain, namely, the open XX model with a Lindblad dynamics involving global dissipators. We use a Jordan-Wigner transformation to derive a mathematical formalism to compute the heat currents and other properties of the steady state. We have rigorous results to prove the occurrence of thermal rectification even for slightly asymmetrical chains. Interestingly, we describe cases where the rectification does not decay to zero as we increase the system size, that is, the rectification remains finite in the thermodynamic limit. We also describe some numerical results for more asymmetrical chains. The presence of thermal rectification in this simple model indicates that the phenomenon is of general occurrence in quantum spin systems.

Collisional Quantum Thermometry.

We introduce a general framework for thermometry based on collisional models, where ancillas probe the temperature of the environment through an intermediary system. This allows for the generation of correlated ancillas even if they are initially independent. Using tools from parameter estimation theory, we show through a minimal qubit model that individual ancillas can already outperform the thermal Cramer-Rao bound. In addition, due to the steady-state nature of our model, when measured collectively the ancillas always exhibit superlinear scalings of the Fisher information. This means that even collective measurements on pairs of ancillas will already lead to an advantage. As we find in our qubit model, such a feature may be particularly valuable for weak system-ancilla interactions. Our approach sets forth the notion of metrology in a sequential interactions setting, and may inspire further advances in quantum thermometry.

Thermodynamics of Weakly Coherent Collisional Models.

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.

Thermodynamic Uncertainty Relations from Exchange Fluctuation Theorems.

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.

Reversing the direction of heat flow using quantum correlations.

Heat spontaneously flows from hot to cold in standard thermodynamics. However, the latter theory presupposes the absence of initial correlations between interacting systems. We here experimentally demonstrate the reversal of heat flow for two quantum correlated spins-1/2, initially prepared in local thermal states at different effective temperatures, employing a Nuclear Magnetic Resonance setup. We observe a spontaneous energy flow from the cold to the hot system. This process is enabled by a trade off between correlations and entropy that we quantify with information-theoretical quantities. These results highlight the subtle interplay of quantum mechanics, thermodynamics and information theory. They further provide a mechanism to control heat on the microscale.

Wigner Entropy Production Rate.

The characterization of irreversibility in general quantum processes is an open problem of increasing technological relevance. Yet, the tools currently available to this aim are mostly limited to the assessment of dynamics induced by equilibrium environments, a situation that often does not match the reality of experiments at the microscopic and mesoscopic scale. We propose a theory of irreversible entropy production that is suited for quantum systems exposed to general, nonequilibrium reservoirs. We illustrate our framework by addressing a set of physically relevant situations that clarify both the features and the potential of our proposal.

Thermal conductance of a two-level atom coupled to two quantum harmonic oscillators.

We have determined the thermal conductance of a system consisting of a two-level atom coupled to two quantum harmonic oscillators in contact with heat reservoirs at distinct temperatures. The calculation of the heat flux as well as the atomic population and the rate of entropy production are obtained by the use of a quantum Fokker-Planck-Kramers equation and by a Lindblad master equation. The calculations are performed for small values of the coupling constant. The results coming from both approaches show that the conductance is proportional to the coupling constant squared and that, at high temperatures, it is proportional to the inverse of temperature.

Energy rectification in quantum graded spin chains: Analysis of the XXZ model.

In this work, with focus on the energy-transport properties in quantum, low-dimensional, graded materials, we address the investigation of the energy (and spin) current in XXZ open chains with graded inner structures and driven out of equilibrium by magnetization pumping applied at the ends. We study several types of graded structures in different situations in order to show a ubiquitous occurrence of energy rectification, even for the system under a homogeneous magnetic field. Due to technical difficulties, we carry out the computation for small chains, but we present arguments that indicate the extension of some results to larger systems. Recalling the generic existence of energy rectification in classical, graded materials, which are described by anharmonic chains of oscillators, and recalling also the anharmonicity of these XXZ models, which involve quartic terms in more transparent representation in terms of fermionic creation and annihilation operators, we may say that our results extend the ubiquity of energy rectification occurrence in classical graded materials to the case of quantum systems.

Nonequilibrium quantum chains under multisite Lindblad baths.

We study a quantum XX chain coupled to two heat reservoirs that act on multiple sites and are kept at different temperatures and chemical potentials. The baths are described by Lindblad dissipators, which are constructed by direct coupling to the fermionic normal modes of the chain. Using a perturbative method, we are able to find analytical formulas for all steady-state properties of the system. We compute both the particle or magnetization current and the energy current, both of which are found to have the structure of Landauer's formula. We also obtain exact formulas for the Onsager coefficients. All properties are found to differ substantially from those of a single-site bath. In particular, we find a strong dependence on the intensity of the bath couplings. In the weak-coupling regime, we show that the Onsager reciprocal relations are satisfied.

Fluctuations of the heat exchanged between two quantum spin chains.

The statistics of the heat exchanged between two quantum XX spin chains prepared at different temperatures is studied within the assumption of weak coupling. This provides simple formulas for the average heat and its corresponding characteristic function, from which the probability distribution may be computed numerically. These formulas are valid for arbitrary sizes and therefore allow us to analyze the role of the thermodynamic limit in this nonequilibrium setting. It is found that all thermodynamic quantities are extremely sensitive to the quantum phase transition of the XX chain.