Correlation between Clinical Outcome and Radiologic Features After Open Reduction and Internal Fixation of Calcaneal Fractures.

BACKGROUND: We aimed to find probable correlation between postoperative radiologic variables and clinical outcomes of surgically treated calcaneal fractures. METHODS: In a retrospective study, 70 unilateral displaced intraarticular calcaneal fractures in adults with follow-up more than 1 year were asked to have a visit. Weightbearing radiographs of both ankles were taken and radiologic parameters, including the differences in values in Böhler and Gissane angles in comparison with the uninjured side, and calcaneocuboid and subtalar joint arthritis based on the Kellgren-Lawrence grading scale, were evaluated. They were considered to find any correlation with clinical outcomes assessed by American Orthopaedic Foot and Ankle Society Ankle-Hindfoot scale, visual analogue scale, Foot Function Index, and Tegner Activity Scale. RESULTS: A total of 61 men (87.1%) and nine women (12.9%) with a mean age of 38.9 ± 12.7 years (range, 18-67 years) were included. Mean follow-up visit for the patients was 25.1 ± 12.7 months. Mean scores of American Orthopaedic Foot and Ankle Society Ankle-Hindfoot scale, visual analogue scale, Foot Function Index, and Tegner Activity Scale were 86.7 ± 12.9, 21.3 ± 22.2, 13.1 ± 15.4, and 5.2 ± 1.1, respectively. The mean Gissane angle and Böhler angle differences were -0.2 ± 8.6 and -3.7 ± 7.2, respectively. Regarding the calcaneocuboid arthritis, 50 (71.4%), 14 (20.0%), and six patients (8.6%) were categorized in grades 0, 1, and 2, respectively. Also, subtalar arthritis was seen in 15 (21.4%), 24 (34.3%), 20 (28.6%), and 11 patients (15.7%), categorized as grades 0, 1, 2, and 3, respectively. No statistical correlation was found between any of the radiologic variables and clinical scores. CONCLUSIONS: There was no significant correlation between Böhler and Gissane angles and the clinical outcomes in surgically treated calcaneal fractures. Also, functional outcomes do not change considerably among different grades of arthritis in calcaneocuboid and subtalar joints, at least during short- to mid-term follow-up periods. Radiologic findings after open reduction and internal fixation of calcaneal fractures are not predictors of function of the patients.

Critical Quantum Metrology Assisted by Real-Time Feedback Control.

We investigate critical quantum metrology, that is, the estimation of parameters in many-body systems close to a quantum critical point, through the lens of Bayesian inference theory. We first derive a no-go result stating that any nonadaptive strategy will fail to exploit quantum critical enhancement (i.e., precision beyond the shot-noise limit) for a sufficiently large number of particles N whenever our prior knowledge is limited. We then consider different adaptive strategies that can overcome this no-go result and illustrate their performance in the estimation of (i) a magnetic field using a probe of 1D spin Ising chain and (ii) the coupling strength in a Bose-Hubbard square lattice. Our results show that adaptive strategies with real-time feedback control can achieve sub-shot-noise scaling even with few measurements and substantial prior uncertainty.

Fundamental Limits in Bayesian Thermometry and Attainability via Adaptive Strategies.

We investigate the limits of thermometry using quantum probes at thermal equilibrium within the Bayesian approach. We consider the possibility of engineering interactions between the probes in order to enhance their sensitivity, as well as feedback during the measurement process, i.e., adaptive protocols. On the one hand, we obtain an ultimate bound on thermometry precision in the Bayesian setting, valid for arbitrary interactions and measurement schemes, which lower bounds the error with a quadratic (Heisenberg-like) scaling with the number of probes. We develop a simple adaptive strategy that can saturate this limit. On the other hand, we derive a no-go theorem for nonadaptive protocols that does not allow for better than linear (shot-noise-like) scaling even if one has unlimited control over the probes, namely, access to arbitrary many-body interactions.

Bath-Induced Correlations Enhance Thermometry Precision at Low Temperatures.

We study the role of bath-induced correlations in temperature estimation of cold bosonic baths. Our protocol includes multiple probes, that are not interacting, nor are they initially correlated to each other. They interact with a bosonic sample and reach a nonthermal steady state, which is measured to estimate the temperature of the sample. It is well known that in the steady state such noninteracting probes may get correlated to each other and even entangled. Nonetheless, the impact of these correlations in metrology has not been deeply investigated yet. Here, we examine their role for thermometry of cold bosonic gases and show that, although being classical, bath-induced correlations can lead to significant enhancement of precision for thermometry. The improvement is especially important at low temperatures, where attaining high precision thermometry is particularly demanding. The proposed thermometry scheme does not require any precise dynamical control of the probes and tuning the parameters and is robust to noise in initial preparation, as it is built upon the steady state generated by the natural dissipative dynamics of the system. Therefore, our results put forward new possibilities in thermometry at low temperatures, of relevance, for instance, in cold gases and Bose-Einstein condensates.

Geometry of Work Fluctuations versus Efficiency in Microscopic Thermal Machines.

When engineering microscopic machines, increasing efficiency can often come at a price of reduced reliability due to the impact of stochastic fluctuations. Here we develop a general method for performing multiobjective optimization of efficiency and work fluctuations in thermal machines operating close to equilibrium in either the classical or quantum regime. Our method utilizes techniques from thermodynamic geometry, whereby we match optimal solutions to protocols parametrized by their thermodynamic length. We characterize the optimal protocols for continuous-variable Gaussian machines, which form a crucial class in the study of thermodynamics for microscopic systems.

Dynamically induced heat rectification in quantum systems.

Heat rectifiers are systems that conduct heat asymmetrically for forward and reversed temperature gradients. We present an analytical study of heat rectification in linear quantum systems. We demonstrate that asymmetric heat currents can be induced in a linear system only if it is dynamically driven. This asymmetry emerges when the driving frequency favors the nonsymmetric heat exchange processes at the expense of the symmetric ones. Finally, we demonstrate the feasibility of such driven harmonic network to work as a thermal transistor, quantifying its efficiency through the dynamical amplification factor.

Using Polarons for sub-nK Quantum Nondemolition Thermometry in a Bose-Einstein Condensate.

We introduce a novel minimally disturbing method for sub-nK thermometry in a Bose-Einstein condensate (BEC). Our technique is based on the Bose polaron model; namely, an impurity embedded in the BEC acts as the thermometer. We propose to detect temperature fluctuations from measurements of the position and momentum of the impurity. Crucially, these cause minimal backaction on the BEC and hence, realize a nondemolition temperature measurement. Following the paradigm of the emerging field of quantum thermometry, we combine tools from quantum parameter estimation and the theory of open quantum systems to solve the problem in full generality. We thus avoid any simplification, such as demanding thermalization of the impurity atoms, or imposing weak dissipative interactions with the BEC. Our method is illustrated with realistic experimental parameters common in many labs, thus showing that it can compete with state-of-the-art destructive techniques, even when the estimates are built from the outcomes of accessible (suboptimal) quadrature measurements.

Individual Quantum Probes for Optimal Thermometry.

The unknown temperature of a sample can be estimated with minimal disturbance by putting it in thermal contact with an individual quantum probe. If the interaction time is sufficiently long so that the probe thermalizes, the temperature can be read-out directly from its steady state. Here we prove that the optimal quantum probe, acting as a thermometer with maximal thermal sensitivity, is an effective two-level atom with a maximally degenerate excited state. When the total interaction time is insufficient to produce full thermalization, we optimize the estimation protocol by breaking it down into sequential stages of probe preparation, thermal contact, and measurement. We observe that frequently interrogated probes initialized in the ground state achieve the best performance. For both fully and partly thermalized thermometers, the sensitivity grows significantly with the number of levels, though optimization over their energy spectrum remains always crucial.