The study, published in the International Journal of Data Science and Analytics by Grace Kim of Arizona State University and Dongyung Kim of Benedictine University, introduces a modified metric called Atwood-weighted Normalized Mutual Information, or ANMI. The name points to its inspiration: the Atwood number, a dimensionless quantity from fluid dynamics that describes the instability of a interface between two fluids of different densities when the heavier one is accelerated into the lighter one. First formalized by Geoffrey Taylor in his landmark 1950 analysis of liquid surface instability, the Atwood number determines whether small perturbations at a fluid boundary grow into the dramatic, mushroom-shaped fingers known as Rayleigh-Taylor instabilities. The authors argue that an analogous instability afflicts standard NMI when the information density of a model’s predictions diverges sharply from that of the ground truth.

The core problem the researchers target is over-clustering, a scenario in which a model partitions data into far more groups than actually exist, or otherwise produces clusters whose statistical density differs dramatically from the true class structure. In such cases, standard NMI can yield over-optimistic results, reporting high agreement between predictions and ground truth even when the model has failed to match the intrinsic information content of the dataset. This is not merely a theoretical quibble. Recent work cited in the paper, including a 2025 analysis in Nature Communications by Jerdee, Kirkley, and Newman, demonstrated that normalized mutual information is a biased measure for classification and community detection, lending independent weight to the concern that the field’s favorite yardstick systematically distorts comparisons.

To build their corrective, the authors define what they call an Information Atwood Number, denoted A_I, which is computed from the entropy difference between the ground truth distribution and the predicted distribution of labels. Entropy, in the information-theoretic sense, measures how spread out or uncertain a probability distribution is. A model that lumps nearly all images into a handful of giant clusters has a very different entropy profile from one that spreads predictions evenly across many fine-grained categories, and both may differ from the entropy of the true labels. By taking the difference between these entropy profiles and normalizing it in the manner of the classical Atwood number, the researchers obtain a single value that captures how mismatched the information densities of prediction and reality truly are.

That mismatch value then becomes a penalty term. In the ANMI formulation, the standard normalized mutual information score is weighted by a complexity-aware factor derived from the Information Atwood Number. When a model’s predicted distribution closely matches the entropy profile of the ground truth, the penalty is mild and ANMI behaves much like ordinary NMI. But when the densities diverge sharply, as in over-clustering scenarios where a model fragments the data into many sparsely populated groups, the penalty grows and drags the score down. The result, according to the authors’ experimental results, is a metric that provides a more robust and conservative assessment than standard NMI, particularly penalizing models that fail to match the intrinsic information density of the data they are meant to classify.

The physics analogy is more than a naming flourish, the authors suggest. In Rayleigh-Taylor instability, the Atwood number determines the growth rate of perturbations: when the density contrast is small, the interface remains nearly stable, but when it is large, even tiny ripples amplify explosively. Similarly, the researchers argue, small discrepancies between the entropy of predictions and the entropy of truth are benign and barely affect evaluation, whereas large discrepancies signal a fundamental instability in the model’s representation of the data, one that standard NMI fails to register. By encoding the density contrast directly into the metric, ANMI makes that instability visible in the final score. The approach reflects a broader trend of importing concepts from physical science into machine learning evaluation, where dimensionless ratios and conservation-style arguments can expose pathologies that raw performance numbers conceal.

The development and verification of the metric drew on established information-theoretic foundations. The paper builds on Marina Meilă’s influential 2007 work comparing clusterings with information-based distances, and on Vinh, Epps, and Bailey’s 2010 study of normalization properties and chance correction in clustering comparison measures, both of which established the mathematical ground rules for metrics like NMI. The experimental evaluation was conducted on widely used, publicly available benchmark image datasets, including MNIST, CIFAR-10, and STL-10, the standard proving grounds for classification and clustering algorithms. The authors also reference the Scikit-learn machine learning library, the de facto standard implementation environment for such metrics in the Python ecosystem, suggesting a straightforward path for practitioners who wish to adopt the new measure.

The practical stakes are considerable. Clustering and classification evaluation scores do not merely describe models; they decide which models get funded, deployed, and built upon. If NMI systematically rewards over-clustered representations, then research lines that fragment data excessively may appear more promising than they are, while simpler, better-calibrated models are unfairly disadvantaged. In applications such as biomedical image segmentation, where one of the authors has previously published work on numerical methods for partial differential equations in image segmentation, an inflated agreement score could mask a model’s failure to respect the true informational structure of tissue classes. A conservative metric that refuses to flatter entropy-mismatched predictions could change which algorithms rise to the top of leaderboards.

The paper arrives amid a broader reassessment of how the machine learning community grades itself. The 2025 Nature Communications finding that NMI is a biased measure, together with a 2026 Journal of the American Statistical Association paper on validating internal clustering validation measures, indicates that the problem of evaluation bias is attracting attention from multiple directions. ANMI’s contribution is a concrete, computationally simple weighting scheme that any researcher already computing NMI could extend with an entropy calculation on the label distributions. Because the metric requires no additional data beyond what NMI already uses, its adoption cost is low, though its impact will depend on whether independent groups replicate the authors’ findings that the penalty term improves robustness across diverse datasets and clustering regimes.

For now, the study stands as a reminder that the tools scientists use to measure success are themselves scientific instruments, subject to calibration and correction. The image of two fluids of mismatched density, one collapsing catastrophically into the other, turns out to be an apt metaphor for what happens when a model’s information density and the truth’s information density drift apart: the evaluation interface becomes unstable, and scores that look serene on the surface conceal violent disagreement underneath. Whether ANMI becomes a standard fixture in the clustering toolkit or one correction among several in an evolving debate, its central lesson is already clear. The next generation of machine learning benchmarks may owe as much to the physics of fluids as to the mathematics of information.

Subject of Research: A physics-inspired evaluation metric, Atwood-weighted Normalized Mutual Information, for image classification and clustering assessment

Article Title: Atwood-weighted Normalized Mutual Information (ANMI): a physics-inspired metric for image classification evaluation

Article References: Kim, G., & Kim, D. (2026). Atwood-weighted Normalized Mutual Information (ANMI): a physics-inspired metric for image classification evaluation. International Journal of Data Science and Analytics, 22(1), Article 320. https://doi.org/10.1007/s41060-026-01288-2

Image Credits: AI Generated

DOI: 10.1007/s41060-026-01288-2

Keywords: Normalized Mutual Information, ANMI, Atwood number, image classification, clustering evaluation, information theory, entropy, machine learning, over-clustering, Rayleigh-Taylor instability, fluid dynamics, benchmark datasets

Developed by Weibai Zhou, Rong Li, and Dan Huan of Guangzhou College of Commerce, FedEntGate uses a deceptively simple quantity from information theory as its organizing principle: entropy. Each client computes the information entropy of its local dataset, a compact statistical fingerprint that reflects how diverse or homogeneous the data are. A client with highly varied, information-rich data tends to produce updates that are more valuable to the global model, while a client with redundant or repetitive samples contributes little new information. Rather than treating every participant equally, the framework uses this entropy signal to decide, round by round, which clients should bother uploading their gradients at all.

The first pillar of the system is an entropy-aware dynamic gating strategy. Before transmitting anything, a client compares its entropy-sanitized value against a threshold derived from the historical profile of low-entropy, or data-poor, participants. If the value falls below the gate, the client stays silent and uploads nothing; if it passes, the gradient channel opens. This filtering happens at the source, meaning low-quality or redundant updates never enter the network. The consequence is a dramatic reduction in communication. In experiments, roughly three quarters of the upload overhead was eliminated compared with standard baselines, a figure that matters enormously in settings where thousands of constrained devices, such as smartphones or edge sensors, share limited bandwidth.

The second pillar addresses the privacy-utility tension that has haunted differentially private training for years. Conventional approaches apply a uniform amount of Gaussian noise to every client’s gradient, calibrated to a single privacy budget. The result is that clients with rich, informative data are perturbed just as heavily as clients with trivial updates, and the global model suffers. FedEntGate replaces this blunt instrument with an entropy-guided adaptive noise-injection mechanism that establishes a value-aware mapping between data utility and differential privacy budgets. Clients whose entropy signals indicate higher contribution receive less aggressive perturbation, while noisier or less informative participants absorb more, so the total privacy guarantee remains rigorous but the accuracy penalty is distributed more intelligently.

Crucially, the gating decision and the final aggregation are jointly driven by the same differentially private entropy values, transmitted as lightweight real-time metadata. The gate determines whether gradients are uploaded at all, while the entropy values themselves form the aggregation weights through a Softmax function. This design ensures mathematical consistency between who is heard and how loudly they are counted, and it achieves what the authors describe as rigorous privacy-communication decoupling: the communication savings come from suppression at the source, while the privacy accounting proceeds along separate, formally composed channels.

The privacy argument is not hand-waved. In an appendix, the authors provide a formal proof under Rényi differential privacy, decomposing each client’s randomized mechanism into two channels. The gradient channel applies the Gaussian mechanism to clipped gradients, whose sensitivity under substitution adjacency is bounded at twice the clipping norm, yielding a per-round Rényi cost proportional to the inverse squared noise multiplier. The metadata channel, which reveals the binary gate state and conditionally the sanitized entropy, has its own bounded cost derived from the sensitivity of normalized entropy, capped at one over the natural logarithm of the number of classes. Because both channels draw on the same underlying dataset, the sequential composition theorem combines their costs into a single, provable guarantee for every round.

The empirical evaluation, conducted on CIFAR-10 under strict privacy constraints, delivers some of the framework’s most eye-catching numbers. Against the strongest baseline, a participant-selection method called FedEx, FedEntGate improved test accuracy by 6.6 percent, cut communication overhead by approximately 75 percent, and suppressed backdoor attack success rates to below 9.7 percent. That last figure deserves emphasis. Backdoor attacks are among the most insidious threats in federated learning: a malicious participant embeds hidden triggers in the shared model that cause it to misbehave on attacker-chosen inputs while appearing accurate on ordinary data. By weighting aggregation toward genuinely informative, high-entropy updates and filtering out suspicious or redundant contributors, the framework raises the bar for such poisoning attempts without resorting to heavyweight cryptographic defenses.

The authors frame these combined results as pushing forward the practical Pareto frontier, the boundary of achievable trade-offs among three competing objectives that have usually been pursued in isolation: model accuracy, privacy assurance, and communication efficiency. Previous systems typically optimized one axis while quietly sacrificing another, accepting slower convergence for stronger privacy or leaking a little more information for better accuracy. FedEntGate’s claim is that entropy, measured locally and shared in sanitized form, provides a common currency that lets a single mechanism manage all three at once. Experiments also drew on publicly available medical and financial datasets, including Medical-MNIST and a credit card fraud dataset, underscoring the framework’s targeting of privacy-sensitive domains.

The implications extend well beyond a single benchmark. In healthcare, where patient records are legally protected and siloed across institutions, federated learning could unlock diagnostic models trained on populations no single hospital could assemble, provided that privacy guarantees are mathematically airtight and communication costs are bearable. In finance, where fraud patterns shift across regions and customer bases, selectively aggregating the most informative local updates could accelerate detection while keeping transaction data at home. The release of the implementation code and trained models on the Gitee repository, alongside the public datasets used in the study, lowers the barrier for other teams to stress-test the approach on their own heterogeneous data.

Caveats remain, as they always do in fast-moving research. The headline results were obtained on CIFAR-10 under particular privacy settings, and scaling to very large client populations, adversarial entropy fabrication, or domains with different data structures will demand further validation. An adversary might, in principle, inflate its reported entropy to win attention, though the differential privacy noise on the metadata channel complicates such manipulation. Still, the core idea, that a cheap information-theoretic statistic computed on-device can orchestrate who speaks, how much noise they carry, and how much they count, is an elegant piece of systems design. If entropy truly is the common currency of heterogeneous learning, FedEntGate suggests that spending it wisely can buy accuracy, privacy, and bandwidth at the same time, moving privacy-preserving collaborative intelligence closer to everyday deployment.

Subject of Research: Entropy-aware dynamic gating and adaptive differential privacy for heterogeneous federated learning

Article Title: FedEntGate: synergistic attention optimization of entropy-aware dynamic gating and differential privacy in heterogeneous federated learning

Article References: FedEntGate: synergistic attention optimization of entropy-aware dynamic gating and differential privacy in heterogeneous federated learning. (n.d.). https://doi.org/10.1007/s10586-026-06539-2

Image Credits: AI Generated

DOI: 10.1007/s10586-026-06539-2

Keywords: federated learning, differential privacy, Non-IID data, entropy, dynamic gating, backdoor attack, communication efficiency, attention aggregation, data privacy, machine learning, Rényi differential privacy, cluster computing

The stakes of this question are higher than they might first appear. Entropy and temperature pervade chemistry, engineering, cosmology, and information theory, yet their conceptual foundations remain contested. Philosophers of physics have long debated whether these quantities exist because of an irreversible assumption like the second law, because of facts about which states can be reached from which others by adiabatic processes, or for some entirely different reason. The answer matters for another deep question too: whether entropy is intrinsically tied to the arrow of time. If entropy can be defined without invoking irreversibility, then the common intuition that time’s direction flows from entropy increase loses some of its apparent necessity.

Jauch’s insight, published in this same journal more than five decades ago, was deceptively simple. Consider an engine cycling through its volume states, tracing a closed loop in the space of work variables. During such a cycle, the engine may exchange energy with its environment, so its full trajectory, including energy, forms a downward spiral that projects onto a closed curve in the work plane. Kelvin’s famous principle states that a cyclic process cannot absorb heat and convert it entirely into work, which explains why the spiral can go down but not up. Jauch focused on the special case where there is no heat exchange at all, an adiabatic process. In that case, he argued, work must come from somewhere, and if it comes neither from heat nor from a change in the system’s energy, it cannot be produced at all. His conservation law states: a cyclic process without heat exchange cannot perform work.

This principle, Roberts emphasizes, contains no irreversible ingredient. It is what Jauch called the static form of the second principle, weaker than Kelvin’s statement and restricted to conservative systems, those without internal friction such as hysteresis or electrical resistance. The hope was that this clean assumption would free thermodynamics from what Jauch called the wrong impression that the existence of entropy and temperature are characteristic consequences of irreversibility. There was just one problem: Jauch’s proof did not work. Roberts shows in detail that the argument breaks down because Jauch implicitly assumed that every point in a thermodynamic state space can be reached from any other by an adiabatic path. That assumption is precisely what Carathéodory’s principle denies, and it turns out to be incompatible with the very conclusion Jauch was trying to establish.

Remarkably, however, the theorem itself is true. Roberts proves it using an entirely different strategy, one that reframes thermodynamics in the language of fibre bundles and gauge theory, the same mathematical machinery that underlies the Yang-Mills theories of particle physics. The key move is to distinguish two manifolds: an (n-1)-dimensional space of observable work configurations and an n-dimensional space that adds total internal energy as an extra dimension. These are related by a projection map, forming a fibre bundle with one-dimensional fibres. In this picture, work is any one-form that annihilates vertical vectors, energy is a vertical coordinate, and heat is defined as the difference between the change in total energy and the work done, making heat, in a precise sense, unobservable energy.

The geometric reformulation then reveals something striking about Jauch’s conservation law. An adiabatic process defines what is called an Ehresmann connection on the bundle: the collection of horizontal directions satisfying the condition that the heat one-form vanishes. Just as in gauge theory, closed loops in the base space can be lifted to curves in the total space, and the failure of those lifts to close measures curvature, exactly as a vector transported around a loop on a sphere fails to return to its starting orientation. The engine’s downward spiral in energy-versus-volume space looks suspiciously like a holonomy, the gauge-theoretic signature of curvature. Expressed in this language, Jauch’s conservation law says that the adiabatic connection has only locally trivial holonomies, meaning every lifted loop closes. That is precisely the statement that the connection is flat, with zero curvature.

From flatness, the theorem follows elegantly. Roberts shows that a connection with locally trivial holonomy must be involutive, and by the Frobenius theorem, an involutive connection is integrable. This means the kernel of the heat one-form is tangent to a family of surfaces, and there exists a function S that is constant on each of them. Since the one-forms dS and the heat form have the same kernel, they can differ only by a scalar field T, yielding the celebrated relation heat equals temperature times the change of entropy, written as xi equals T dS. Entropy and temperature thus emerge as a direct consequence of a conservation principle interpreted geometrically, sidestepping Carathéodory’s accessibility argument altogether.

The result also settles a historical curiosity. Jauch once credited his idea to the physicist and mathematician Tatiana Afanassjewa, who argued as early as 1925 that irreversibility has no relevance for the existence of entropy. Roberts, however, could find no trace of Jauch’s theorem in her published work, which instead relies on Carathéodory’s theorem. What he did find is that Jauch’s conservation hypothesis follows from her fundamental Entropy Axiom, and that it is strictly weaker than her principle: Jauch’s law assumes less and reaches the same conclusion, without even requiring the notions of equilibrium states or quasi-static processes. In that sense, the new result is strictly stronger than anything in the Afanassjewa tradition.

The framework also opens concrete avenues for future research. Systems in which heat cannot be written as temperature times entropy change, such as those with internal friction, are precisely those whose adiabatic connections have non-zero curvature. This suggests a clean geometric way to model irreversibility itself, as curvature in the adiabatic connection, and it hints at possible thermodynamic analogues of the Aharonov-Bohm effect and geometric phase, phenomena in which gauge curvature produces observable consequences even in regions where the field vanishes. Roberts develops this broader gauge-theoretic view of heat in a companion manuscript, but the present work stands on its own as a corrected and completed foundation.

What emerges is a picture of thermodynamics as a theory with a hidden geometric skeleton. The essential structures required are minimal: a distinction between work and total energy, and the undirected notion of an adiabatic path. From these, and from the flatness of a naturally defined connection, the existence of entropy and temperature follows as an elegant theorem. The second law, the arrow of time, and the irreversibility of spontaneous processes remain real physical phenomena awaiting explanation, but they no longer bear the burden of underwriting the very existence of entropy. Jauch’s half-century-old conjecture, once thought to be broken, turns out to be a window into the deep geometry of heat.

Subject of Research: A gauge-theoretic reconstruction of Jauch's conservation law as a foundation for entropy and temperature in thermodynamics.

Article Title: A New Origin for Entropy: Jauch’s Conservation Law and the Geometry of Thermodynamics

Article References: Roberts, B. W. (2026). A New Origin for Entropy: Jauch’s Conservation Law and the Geometry of Thermodynamics. Foundations of Physics, 56(5), Article 46. https://doi.org/10.1007/s10701-026-00946-6

Image Credits: AI Generated

DOI: 10.1007/s10701-026-00946-6

Keywords: entropy, temperature, thermodynamics, second law, gauge theory, fibre bundles, Ehresmann connection, Jauch conservation law, Carathéodory, irreversibility, holonomy, Frobenius theorem

The original review had presented entropy as a way to quantify uncertainty in medical reasoning, describing it as offering a concise summary of uncertainty that nonetheless lacks a built-in mechanism for action. That admission, the Singapore authors contend, is precisely where the trouble begins. In clinical practice, uncertainty is not merely a quantity to be measured; it is a condition to be navigated, weighed against risks, benefits, and patient values, and ultimately resolved into a decision: treat, test, observe, or reassure. A framework that summarizes uncertainty without specifying how to act on it, they argue, risks creating what they call an illusion of precision, presenting clinicians with a single descriptive number that feels rigorous but resists translation into a concrete clinical act.

The technical heart of the critique lies in a comparison between entropy and Bayesian inference, the dominant framework for reasoning under uncertainty in medicine and statistics. Bayesian models produce state-specific probabilities: the probability, for instance, that a patient with chest pain is having a myocardial infarction versus a benign cause. These actionable probabilities can then be compared against established decision thresholds, most famously formalized by Pauker and Kassirer in the New England Journal of Medicine in 1980. The threshold approach defines a testing threshold and a treatment threshold; if the probability of disease falls below the former, the clinician forgoes testing, and if it rises above the latter, treatment proceeds without further diagnostic workup. This architecture converts probability directly into action, providing a rational bridge between belief and behavior.

Entropy, by contrast, collapses an entire probability distribution into a single scalar. In information theory, the Shannon entropy of a diagnostic hypothesis set is maximal when all possibilities are equally likely and minimal when one diagnosis dominates. A high-entropy differential diagnosis tells the clinician that the situation is genuinely uncertain, but it does not say which diagnosis is most probable, what test would most efficiently reduce the uncertainty, or whether further investigation is even warranted given the stakes. Two patients could carry identical entropy values while demanding radically different management: one with a high-mortality condition hovering near a treatment threshold, the other with a trivial condition with little actionable consequence. The letter’s authors argue that this loss of state-specific information is not a minor technicality but an ontological mismatch between the descriptive reach of entropy and the prescriptive demands of clinical judgment.

The critique also engages with the literature on value of information, a family of methods for prioritizing research and testing by quantifying how much a new piece of information would be worth in terms of improved outcomes. Value of information analysis, as codified by Jackson and colleagues in Epidemiologic Methods in 2021, builds explicitly on decision-theoretic foundations, linking the acquisition of information to expected gains in health. Bayesian probability combined with threshold logic naturally accommodates these calculations: knowing a probability and the payoff matrix of actions allows one to compute the expected value of perfect or sample information. Entropy alone, stripped of state-specific probabilities and payoff structures, cannot perform this function. A clinician told that a case has an entropy of 1.7 bits has learned little about what to do next, whereas a clinician told that the probability of disease is 45 percent against a testing threshold of 30 percent knows immediately that more information is worth acquiring.

What makes the letter particularly provocative is its pivot from decision theory to pedagogy. The authors acknowledge that the original review rightly locates entropy’s true promise in standardization and scalability, especially for artificial intelligence systems trained on vast clinical datasets. In that context, entropy can serve as a useful computational statistic, a way for machine learning systems to flag cases of high diagnostic ambiguity, route them to specialists, or measure model confidence. But the authors warn that the vision of an “entropy-based medicine” must be weighed against its potential educational consequences. Medicine has long oscillated between the aspiration to quantify everything and the recognition that its core practice remains an interpretive, human activity. If trainees learn that good clinical reasoning means minimizing a calculated uncertainty value, the letter suggests, they may lose sight of a more important competency: the cultivated ability to tolerate uncertainty and still act responsibly.

That argument draws on a growing body of medical education scholarship, most prominently the 2016 New England Journal of Medicine perspective by Simpkin and Schwartzstein titled “Tolerating uncertainty — the next medical revolution?” That piece argued that discomfort with uncertainty drives a range of pathology in modern medicine, from excessive diagnostic testing and defensive medicine to communication failures and burnout. Uncertainty tolerance, far from being a soft skill, is framed as a professional capacity intimately linked to clinical judgment, effective patient communication, and patient safety. The Singapore authors build directly on this framing: an “entropy-minimization” mindset, they caution, could distract trainees from the deeper goal of becoming comfortable living with ambiguity. In a busy clinical environment, the temptation to chase a single number that promises clarity is strong, and a pedagogy built around minimizing entropy could reinforce precisely the reflexive, test-driven behavior that educators have spent years trying to moderate.

The debate also carries implications for how artificial intelligence tools will be explained and governed in medicine. As machine learning systems become embedded in triage, imaging interpretation, and predictive analytics, measures of model uncertainty such as entropy will increasingly be surfaced to clinicians, perhaps as confidence scores or risk flags. The letter’s warning suggests that how these numbers are taught, contextualized, and displayed will matter enormously. A confidence metric presented without a decision threshold or a treatment implication invites either blind deference or reflexive dismissal. Used well, however, uncertainty quantification can prompt exactly the right kind of reflection: a pause before acting on a low-confidence prediction, a request for a second opinion, or a conversation with the patient about the limits of what is known. The difference lies not in the mathematics but in the professional culture that surrounds it.

None of this amounts to a rejection of information theory in medicine. The letter is explicit in crediting the original review with a valuable service: introducing a complex concept to a general medical audience and sparking a necessary dialogue on the nature of clinical uncertainty. Its authors position their critique as a call for deeper conversation rather than a dismissal, insisting that before the profession embraces new quantitative tools, it must clarify their proper place in a practice that remains both a science and an art. The historical parallel is instructive. Bayesian reasoning took decades to move from statistical journals into bedside teaching, and only became genuinely useful to clinicians once it was paired with threshold frameworks, likelihood ratios, and pretest probability estimation. Entropy, if it follows a similar path, will need its own translation layer: ways of connecting a global uncertainty measure to the specific probabilities, stakes, and values that drive individual decisions.

For now, the Singapore letter stands as a compact but pointed intervention in one of the most consequential conversations in contemporary medicine: how a profession built on judgment should metabolize the quantitative machinery of the information age. Its message resonates well beyond internal medicine, touching any field wrestling with the promise of AI-assisted uncertainty quantification, from radiology to public health modeling. The core claim is deceptively simple. Measuring uncertainty is not the same as managing it, and a number that summarizes doubt without pointing toward action may, in the hands of an overburdened clinician or a trainee still forming professional habits, do more to obscure good judgment than to support it. As hospitals and developers race to embed uncertainty metrics in clinical workflows, this letter insists that the decisive questions are not computational but philosophical and pedagogical: what do we want clinicians to learn when we teach them to measure what they do not know?

Subject of Research: The limitations of entropy as a quantitative measure of clinical uncertainty in medical decision-making, judgment, and education.

Article Title: Beyond Entropy: Decision Thresholds, Judgment, and Pedagogy

Article References: Sadasiv, M. S., & Chow, M. (2026). Beyond Entropy: Decision Thresholds, Judgment, and Pedagogy. Journal of General Internal Medicine. https://doi.org/10.1007/s11606-026-10746-3

Image Credits: AI Generated

DOI: 10.1007/s11606-026-10746-3

Keywords: entropy, clinical decision-making, uncertainty, Bayesian inference, decision thresholds, medical education, clinical judgment, artificial intelligence, decision theory, value of information, diagnostic uncertainty, internal medicine