{"title":"The importance of imagery in quantum mechanics","authors":"Arthur I. Miller","doi":"10.1038/s42254-026-00972-3","DOIUrl":"10.1038/s42254-026-00972-3","url":null,"abstract":"100 years on from Werner Heisenberg and Erwin Schrödinger’s dispute on how to conceptualize quantum mechanics, Arthur I. Miller reflects on the subtleties of visualization in physics.","PeriodicalId":19024,"journal":{"name":"Nature Reviews Physics","volume":"8 8","pages":"474-475"},"PeriodicalIF":46.6,"publicationDate":"2026-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148667607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The importance of imagery in quantum mechanics","authors":"Arthur I. Miller","doi":"10.1038/s42254-026-00972-3","DOIUrl":"10.1038/s42254-026-00972-3","url":null,"abstract":"100 years on from Werner Heisenberg and Erwin Schrödinger’s dispute on how to conceptualize quantum mechanics, Arthur I. Miller reflects on the subtleties of visualization in physics.","PeriodicalId":19024,"journal":{"name":"Nature Reviews Physics","volume":"8 8","pages":"474-475"},"PeriodicalIF":46.6,"publicationDate":"2026-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148667589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Was Schrödinger ever a determinist?","authors":"Flavio Del Santo, Nicolas Gisin","doi":"10.1038/s42254-026-00968-z","DOIUrl":"10.1038/s42254-026-00968-z","url":null,"abstract":"Erwin Schrödinger is often portrayed as a reactionary who resisted the indeterminism introduced by quantum mechanics, but on closer inspection his views on determinism prove to be more complex and more radical.","PeriodicalId":19024,"journal":{"name":"Nature Reviews Physics","volume":"8 8","pages":"472-473"},"PeriodicalIF":46.6,"publicationDate":"2026-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148667588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Universal bounds on entropy production from fluctuating coarse-grained trajectories","authors":"Udo Seifert","doi":"10.1038/s42254-026-00954-5","DOIUrl":"10.1038/s42254-026-00954-5","url":null,"abstract":"Entropy production is arguably the most universally applicable measure of non-equilibrium behaviour, particularly for systems coupled to a heat bath. This setting encompasses driven soft matter as well as biomolecular, biochemical and biophysical systems. Despite the central role of entropy production, direct measurements of it remain challenging, especially in small systems dominated by fluctuations. The main difficulty arises because not all degrees of freedom that contribute to entropy production are experimentally accessible. A key question, therefore, is how to infer entropy production from coarse-grained observations, such as time series of experimentally measurable variables. Over the past decade, stochastic thermodynamics has provided several inequalities that yield model-free lower bounds on entropy production from such coarse-grained data. The major approaches rely on observations of coarse-grained states, fluctuating currents or ticks, correlation functions of coarse-grained observables, and waiting-time distributions between ‘Markovian’ events, which correspond to transitions between mesoscopic states. Here, I systematically review these techniques valid under the sole assumption of a Markovian (that is, memoryless) dynamics on an underlying, not necessarily observable, network of states or following a possibly high-dimensional Langevin equation. I discuss in detail the large class of non-equilibrium steady states and highlight extensions of these methods to time-dependent and relaxing systems. Although our focus is on mean entropy production, I also summarize recent progress in quantifying entropy production along individual coarse-grained trajectories. Entropy production quantifies non-equilibrium behaviour but is hard to measure in fluctuating, partially observed systems. This Review discusses stochastic thermodynamics approaches that infer model-free lower bounds from coarse-grained observables, including states, currents, correlations and waiting times, across steady and time-dependent regimes, and highlights progress in trajectory-level estimation.","PeriodicalId":19024,"journal":{"name":"Nature Reviews Physics","volume":"8 8","pages":"493-507"},"PeriodicalIF":46.6,"publicationDate":"2026-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148667606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Universal bounds on entropy production from fluctuating coarse-grained trajectories","authors":"Udo Seifert","doi":"10.1038/s42254-026-00954-5","DOIUrl":"10.1038/s42254-026-00954-5","url":null,"abstract":"Entropy production is arguably the most universally applicable measure of non-equilibrium behaviour, particularly for systems coupled to a heat bath. This setting encompasses driven soft matter as well as biomolecular, biochemical and biophysical systems. Despite the central role of entropy production, direct measurements of it remain challenging, especially in small systems dominated by fluctuations. The main difficulty arises because not all degrees of freedom that contribute to entropy production are experimentally accessible. A key question, therefore, is how to infer entropy production from coarse-grained observations, such as time series of experimentally measurable variables. Over the past decade, stochastic thermodynamics has provided several inequalities that yield model-free lower bounds on entropy production from such coarse-grained data. The major approaches rely on observations of coarse-grained states, fluctuating currents or ticks, correlation functions of coarse-grained observables, and waiting-time distributions between ‘Markovian’ events, which correspond to transitions between mesoscopic states. Here, I systematically review these techniques valid under the sole assumption of a Markovian (that is, memoryless) dynamics on an underlying, not necessarily observable, network of states or following a possibly high-dimensional Langevin equation. I discuss in detail the large class of non-equilibrium steady states and highlight extensions of these methods to time-dependent and relaxing systems. Although our focus is on mean entropy production, I also summarize recent progress in quantifying entropy production along individual coarse-grained trajectories. Entropy production quantifies non-equilibrium behaviour but is hard to measure in fluctuating, partially observed systems. This Review discusses stochastic thermodynamics approaches that infer model-free lower bounds from coarse-grained observables, including states, currents, correlations and waiting times, across steady and time-dependent regimes, and highlights progress in trajectory-level estimation.","PeriodicalId":19024,"journal":{"name":"Nature Reviews Physics","volume":"8 8","pages":"493-507"},"PeriodicalIF":46.6,"publicationDate":"2026-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148667571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Was Schrödinger ever a determinist?","authors":"Flavio Del Santo, Nicolas Gisin","doi":"10.1038/s42254-026-00968-z","DOIUrl":"10.1038/s42254-026-00968-z","url":null,"abstract":"Erwin Schrödinger is often portrayed as a reactionary who resisted the indeterminism introduced by quantum mechanics, but on closer inspection his views on determinism prove to be more complex and more radical.","PeriodicalId":19024,"journal":{"name":"Nature Reviews Physics","volume":"8 8","pages":"472-473"},"PeriodicalIF":46.6,"publicationDate":"2026-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148667605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Emergence of Fermi-liquid and BCS physics in overdoped cuprates","authors":"B. J. Ramshaw, Steven A. Kivelson","doi":"10.1038/s42254-026-00960-7","DOIUrl":"10.1038/s42254-026-00960-7","url":null,"abstract":"Cuprates are the paradigmatic ‘unconventional’ superconductors: their critical temperature is much higher than can be expected from phonon-mediated pairing, the superconducting gap has d-wave symmetry, and the normal-metallic state appears to be far from a conventional Fermi liquid. These and numerous other experimental facts have led to a consensus that the conventional theory — the Fermi-liquid-based Bardeen–Cooper–Schrieffer (BCS) theory — is the wrong starting point for understanding superconductivity in the cuprates. In this Perspective, we propose that, although underdoped cuprates do indeed require a different theoretical framework, there is a crossover with increasing doping to an overdoped regime in which a BCS-like approach is warranted (at energy scales of the order of the superconducting gap and below), provided that the various forms of disorder are accounted for. We summarize key experimental studies of the low-energy properties of overdoped cuprates, identify properties that are and are not compatible with this proposal, and argue that features that are inconsistent with this approach can in fact be attributed to the expected effects of material disorder. Finally, we provide falsifiable predictions for the behaviour of an ‘ideal’ (disorder-free) overdoped cuprate through which our approach can be tested. Various observed behaviours of overdoped cuprates are inconsistent with a weak-coupling, Fermi-liquid-based Bardeen–Cooper–Schrieffer description. This Perspective argues that these behaviours are consequences of substitutional disorder in a d-wave superconductor with a short-correlation length, and that a weak-coupling approach is possible in the disorder-free limit.","PeriodicalId":19024,"journal":{"name":"Nature Reviews Physics","volume":"8 9","pages":"597-608"},"PeriodicalIF":46.6,"publicationDate":"2026-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148872225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alex Krasnok, Arif Sarwat, William Anderson Jr., Andres Gil
{"title":"Universities need transparent quantum hardware","authors":"Alex Krasnok, Arif Sarwat, William Anderson Jr., Andres Gil","doi":"10.1038/s42254-026-00963-4","DOIUrl":"10.1038/s42254-026-00963-4","url":null,"abstract":"Students need to experience quantum hardware beyond cloud access to learn how an ideal circuit becomes a physical measurement. Universities should therefore procure teachable systems, not showroom machines.","PeriodicalId":19024,"journal":{"name":"Nature Reviews Physics","volume":"8 9","pages":"532-533"},"PeriodicalIF":46.6,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148872226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Graphene FET microfluidic platform for electrochemical molecular fingerprinting","authors":"Roanne Deanne Aves","doi":"10.1038/s42254-026-00973-2","DOIUrl":"10.1038/s42254-026-00973-2","url":null,"abstract":"Roanne Aves describes a platform to integrate graphene-FET based microfluidic modules into one experimental workflow.","PeriodicalId":19024,"journal":{"name":"Nature Reviews Physics","volume":"8 9","pages":"539-539"},"PeriodicalIF":46.6,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148872218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Complexity from minimal state spreading","authors":"Rathindra Nath Das","doi":"10.1038/s42254-026-00967-0","DOIUrl":"10.1038/s42254-026-00967-0","url":null,"abstract":"Rathindra Nath Das recounts how a simple framework to assess complexity published in 2022 shaped his own approach to physics.","PeriodicalId":19024,"journal":{"name":"Nature Reviews Physics","volume":"8 8","pages":"476-476"},"PeriodicalIF":46.6,"publicationDate":"2026-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148667590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}