Pathwise observables—functionals of stochastic trajectories—are at the heart of time-averaged statistical mechanics and are central to thermodynamic inequalities such as uncertainty relations, speed limits, and correlation bounds. They provide a means of thermodynamic inference in the typical situation, when not all dissipative degrees of freedom in a system are experimentally accessible. So far, theories focusing on pathwise observables have been developing in two major directions, diffusion processes and Markov-jump dynamics, in a virtually disjoint manner. Moreover, even the respective results for diffusion and jump dynamics were derived with a patchwork of different approaches that are predominantly indirect. Stochastic calculus was recently shown to provide a direct approach to pathwise observables of diffusion processes, while a corresponding framework for jump dynamics remained elusive. In our work, we develop, in an exact parallelism with continuous-space diffusion, a complete stochastic calculus for pathwise observables of Markov-jump processes. We formulate a “Langevin equation” for jump processes, define general pathwise observables, and establish their covariation structure, whereby we fully account for transients and time-inhomogeneous dynamics. We prove the known kinds of thermodynamic inequalities in their most general form and discuss saturation conditions. We determine the response of pathwise observables to general (including thermal) perturbations and introduce a corresponding response-function formalism. We carry out the continuum limit to achieve the complete unification of diffusion and jump dynamics. In addition, we connect the framework to quantum unraveling and the Belavkin equation for open quantum systems, associating quantum and classical descriptions of thermal systems. Our results open avenues in the direction of discrete-state analogs of generative diffusion models and the learning of stochastic thermodynamics from fluctuating trajectories.

Moiré superlattices in semiconductors exhibit a rich variety of interaction-induced topological states, including quantum anomalous Hall (QAH) effects [1–8]. A recent study hinted that twisted ${\mathrm{WSe}}_2$ homobilayer (${\mathrm{tWSe}}_2$) could host a QAH state but lacked direct evidence of ferromagnetism, a key hallmark of this phase [9]. Here, we report the first direct evidence of QAH states in ${\mathrm{tWSe}}_2$ with spontaneous ferromagnetism. Specifically, we employ polarization-resolved attractive polaron spectroscopy on a dual-gated, 2° ${\mathrm{tWSe}}_2$ and observe direct signatures of spontaneous time-reversal symmetry breaking at hole filling $\nu =1$. Together with a Chern number ($C$) measurement via Streda formula analysis, we identify this magnetized state as a topological state, characterized by $C=1$. Furthermore, we demonstrate that these topological and magnetic properties are tunable via a finite displacement field, between a QAH ferromagnetic state and an antiferromagnetic state. Our findings position ${\mathrm{tWSe}}_2$ as a highly versatile, stable, and optically addressable platform for investigating topological order and strong correlations in two-dimensional landscapes.

The thermal noise of mirror coatings for gravitational-wave detectors critically depends on the elastic properties of the constituent materials. Data analyses and theoretical models typically assume each material is homogeneous and isotropic, but isotropy has never been explicitly verified. Using Brillouin light scattering (BLS), we demonstrate that ion-beam-sputtered ${\mathrm{SiO}}_2$—a material still viable for future mirror coatings—exhibits cylindrical elastic symmetry, with in-plane isotropy but a notable 6% compressive anisotropy along the film normal. This anisotropy remains unchanged after the postdeposition heat treatment currently used in ground-based detectors ($500°\mathrm{C}$, 10 h) but is nearly eliminated at $900°\mathrm{C}$. Infrared reflectivity experiments support these findings by directly revealing heterogeneities in the distribution of bridging and nonbridging oxygen structures along the growth axis. While BLS measures the real part of the elastic constants at gigahertz frequencies, the data reveal negligible contributions from mechanical relaxations in the kilohertz to gigahertz range, making BLS a valid substitute for low-frequency properties obtained from standard anisotropy-insensitive techniques. Our results highlight that restoring isotropy through heat treatment—by softening the material, enabling more than 7% out-of-plane expansion, and smoothing out structural heterogeneities—may play a key role in reducing thermal noise. This proof-of-concept study extends beyond silica, providing critical insights for the design of future coatings.

Despite being governed by the familiar laws of Hookean mechanics, elastic shells patterned with an internal structure (i.e., metashells) exhibit a wealth of unusual mechanical properties with no counterparts in unstructured materials. Here I show that much of this behavior can be captured by a real-valued analog of the inhomogeneous Schrödinger equation, with the lateral pressure experienced by the internal structure in the role of the wave function. In the fine structure limit—i.e., when the length scale associated with the internal structure is much smaller than the local radius of curvature—this approach reveals the existence of localized states, in which elastic deformations are prevented to diffuse away from their origin, thereby allowing the internal structure to smoothly adapt to the intrinsic geometry of the metashell. Leveraging on an analogy with scattering states in nearly free electrons, I further show that periodic metashells, obtained from the repetition of the same structural unit periodically in space, support elastic Bloch waves, corresponding to stationary periodic configurations of the internal structure and characterized by a geometry-dependent band structure. When applied to crystalline monolayers, this approach provides a generalization of the elastic theory of interacting topological defect to compressible systems.

Advanced quantum technologies rely on non-Gaussian states of light, essential for universal quantum computation, fault-tolerant error correction, and quantum sensing. Their practical realization, however, faces hurdles: Simulating large multimode generators is computationally demanding, and benchmarks such as the stellar rank do not capture how effectively photon detections yield useful non-Gaussianity. We address these challenges by introducing the non-Gaussian control parameters $(s_0,{\delta }_0)$, a continuous and operational measure that goes beyond stellar rank. Leveraging these parameters, we develop a universal optimization method that reduces photon-number requirements and greatly enhances success probabilities while preserving state quality. Applied to the Gottesman-Kitaev-Preskill state generation, for example, our method cuts the required photon detections by a factor of 3 and raises the preparation probability by nearly ${10}^8$. Demonstrations across cat states, cubic phase states, Gottesman-Kitaev-Preskill states, and even random states confirm broad gains in experimental feasibility. Our results provide a unifying principle for resource-efficient non-Gaussian state generation, charting a practical route toward scalable optical quantum technologies and fault-tolerant quantum computation.

The fidelity and quantum nondemolition character of the dispersive readout in circuit QED are limited by unwanted transitions to highly excited states at specific photon numbers in the readout resonator. This observation can be explained by multiphoton resonances between computational states and highly excited states in strongly driven nonlinear systems, analogous to multiphoton ionization in atoms and molecules. In this work, we utilize the multilevel nature of high-$E_J/E_C$ transmons to probe the excited-state dynamics induced by strong drives during readout. With up to ten resolvable states, we quantify the critical photon number of ionization, the resulting state after ionization, and the fraction of the population transferred to highly excited states. Moreover, using pulse shaping to control the photon number in the readout resonator in the high-power regime, we tune the adiabaticity of the transition and verify that transmon ionization is a Landau-Zener-type transition. We further extend these methods to a typical transmon with $E_J/E_C\approx 55$ and probe the offset-charge dependence of ionization dynamics in a timed-resolved manner. Our experimental results agree well with the theoretical prediction from a semiclassical driven transmon model and may guide future exploration of strongly driven nonlinear oscillators.

To maintain homeostasis, living cells process information with networks of interacting molecules. Traditional models for cellular information processing have focused on networks of chemical reactions between molecules. Here, we describe how networks of physical interactions could contribute to the processing of information inside cells. In particular, we focus on the impact of biomolecular condensation, a structural phase transition found in cells. Biomolecular condensation has recently been implicated in diverse cellular processes. Some of these are essentially computational, including classification and control tasks. We place these findings in the broader context of embodied computation, an emerging framework for describing how the native dynamics of nonlinear physical systems can be leveraged to perform complex computations. The synthesis of these ideas raises questions about expressivity (the range of problems that cellular phase transitions might be able to solve) and learning (how these systems could adapt and evolve to solve different problems). This emerging area of research presents diverse opportunities across molecular biophysics, soft matter, and embodied computation.

In statistical physics, it is well established that the liquid-gas (LG) phase transition with divergent critical fluctuations belongs to the Ising universality class. Whether nonequilibrium effects can alter this universal behavior remains a fundamental open question. In this work, we theoretically prove that nonequilibrium hyperuniform (HU) fluids with additional center-of-mass conservation exhibit LG criticality different from the Ising universality class. As a specific case, we investigate a 2D HU fluid composed of active spinners, where phase separation is driven by dissipative collisions. Strikingly, at the critical point, the 2D HU fluid displays finite density fluctuations $S(q)\sim q^{\eta }\sim \mathrm{const}$ with $\eta =0$, rather than the expected divergence $S(q)\sim q^{\eta -2}$ with $\eta =1/4$ as in the Ising model, while the compressibility still diverges. The critical point is thus calm yet highly susceptible, in fundamental violation of the conventional fluctuation-dissipation relation. Consistently, we observe short-range pair correlation functions coexisting with quasi-long-range response functions at the critical point. Based on a generalized model $B$ and renormalization-group analysis, we prove that hyperuniformity reduces the upper critical dimension $d_c$ from 4 to 2. Moreover, the critical point exhibits Gaussian density fluctuations indicated by Binder cumulant, distinct from non-Gaussian critical behaviors of the mean-field Ising universality class. The system also exhibits nondivergent energy fluctuations rather than logarithmic divergence as expected in the Ising universality class at $d=d_c$. Furthermore, the HU fluid undergoes nonconventional spinodal decomposition, where the decomposition time diverges but the characteristic length scale remains finite as the critical point is approached. The origin of the above anomalies lies in the nonequilibrium nature of the system which obeys a generalized fluctuation-dissipation relation $2\mathrm{Im}\chi (q,\omega )=\omega C(q,\omega )/k_B{T}_{\mathrm{eff}}(q)$ with a scale-dependent effective temperature $T_{\mathrm{eff}}(q)\propto q^2$. These findings establish a striking exception to conventional paradigms of critical phenomena and illustrate how nonequilibrium forces can fundamentally reshape universality classes.

Hydrogels are widely used in applications that require durability under cyclic loading, yet fatigue fracture often limits their reliability. The underlying physical principles of hydrogel fatigue remain elusive due to the complex interplay between molecular-scale events and macroscopic crack propagation. Here, we harness folded protein domains as reversible, mechanically defined sacrificial units within polyprotein crosslinkers to directly correlate single-molecule unfolding with bulk fatigue behavior. By engineering hydrogels with protein domains that have tunable unfolding forces (100–1500 pN) and varying the number of domains per crosslink, we demonstrate that random networks incorporating weaker protein domains can achieve unexpectedly high fatigue thresholds through distributed energy dissipation. Moreover, we develop a force response model—introducing a generalized force-decay law and integrating unfolding or refolding kinetics—to establish a quantitative framework for understanding fatigue behavior. This combined approach offers a versatile strategy for designing next-generation, fatigue-resistant hydrogels that retain low stiffness and high extensibility.

Intertwined orders refer to strongly coupled and mutually dependent orders that coexist in correlated electron systems, often underpinning key physical properties of the host materials. Among them, polar, chiral, and ferro-rotational orders have been theoretically known to form a closed set of intertwined orders. However, experimental investigation into their mutual coupling and physical consequences has remained elusive. In this work, we employ the polar-chiral insulator ${\mathrm{Ni}}_3{\mathrm{TeO}}_6$ as a platform and utilize a multimodal optical approach to directly probe and reveal the intertwining among polarity, chirality, and ferro-rotational order. We demonstrate how their coupling governs the formation of domains and dictates the nature of domain walls. Within the domains, we identify spatial inversion symmetry as the operation connecting two domain states of opposite polarity and chirality, with a homo-ferro-rotational state serving as the prerequisite for these interlocked configurations. At the domain walls, we observe a pronounced enhancement of in-plane polarization accompanied by a suppression of chirality. By combining with Ginzburg-Landau theory within the framework of a preexisting homo-ferro-rotational background, we uncover the emergence of mixed Néel- and Bloch-type domain walls. Our findings highlight the critical role of intertwined orders in defining domain and domain-wall characteristics and open pathways for domain switching and domain-wall control via intertwined order parameters.

Graphene is an ideal platform for supporting ballistic, spin-coherent transport—crucial ingredients for spin-based quantum technologies. Here, we demonstrate a spin-dependent electron-optic mechanism that enables spin-transistor-like control of spin transport in a graphene spin valve, in the absence of spin-orbit coupling in the transport channel. Using transverse magnetic focusing in a high-mobility graphene device, we couple spin and orbital degrees of freedom through charge transfer doping and proximity exchange at ferromagnetic contacts. This coupling allows for gate-tunable modulation of both the amplitude and polarity of the spin signal, reminiscent of the functionality of a Datta-Das spin field-effect transistor. Measurements confirm that spin-coherent ballistic transport is observable up to room temperature. Our results demonstrate an operational principle for spintronic devices based on spin-dependent electron optics in low spin-orbit coupling materials such as graphene.

Hyperuniform structures are spatial patterns whose fluctuations disappear on long length scales, making them effectively homogeneous when observed from afar. Mathematically, this means that their spectral density $\tilde{\rho }(\mathbf{k})$ approaches zero for low wave number $|\mathbf{k}|$. Crystalline lattices are hyperuniform, as are certain quasicrystals, maximally random jammed packings of spheres, and electrons in the fractional quantum Hall state. Stealthy hyperuniformity is an even stronger constraint on the spectral density: It requires that $\tilde{\rho }(\mathbf{k})$ is strictly zero in a finite range of wave vectors around $\mathbf{k}=\mathbf{0}$, called the stealthy regime, or exclusion region. Since the degree of scattering by disorder is, to leading order, proportional to $\tilde{\rho }(\mathbf{k})$, waves propagating through such structures may do so without scattering for sufficiently long wavelengths and short distances. Here, we measure scattering by disorder in photonic crystal slabs with stealthy-hyperuniform disorder by measuring the linewidths of the photonic bands. We observe the transition between the stealthy and nonstealthy regimes, marked by a sharp increase in linewidth. We also observe the effects of multiple scattering in the stealthy regime, which implies diminishing transparency. Moreover, we show that residual single scattering in the stealthy regime arises from an intrinsically non-Hermitian effect: Propagating light has a complex effective mass due to radiative loss out of the slab.

Quantum information is typically fragile under measurements and environmental coupling. Remarkably, we find that its lifetime can scale exponentially with system size when the environment is continuously monitored via midcircuit measurements—regardless of bath size. Starting from a maximally entangled state with a reference, we analytically prove this exponential scaling for typical Haar-random unitaries and confirm it through numerical simulations in both random unitary circuits and chaotic Hamiltonian systems. In the absence of bath monitoring, the lifetime exhibits a markedly different scaling: It grows at most linearly—or remains constant—with system size and decays inversely with the bath size. We further extend our findings numerically to a broad class of initial states. In the intermediate regime of partial monitoring, we identify and prove a two-scale transition, where the quantum mutual information decays logarithmically at microscopic timescales but linearly at macroscopic timescales. We discuss implications for monitored quantum circuits in the weak-measurement limit, quantum algorithms such as quantum diffusion models and quantum reservoir computing, and quantum communication. Finally, we experimentally verify the gap of persisted information on IBM Quantum hardware.

Hydroplastification offers an eco-friendly route to plasticize hydrophilic polymers by enhancing chain mobility, yet it remains ineffective for rigid crystalline nanomaterials. Here, we report a novel plasticity mechanism governed by mesopores acting as structural free volume between rigid hydrophilic nanocrystals, cellulose nanocrystals (CNCs). During the mechanosorptive vapor training process to change the mesopores, the plasticity arises from a dynamic competition between external tensile stress and internal capillary forces. We establish a semiquantitative constitutive relationship revealing that the network’s wet-state yield strength is critically regulated by the aspect ratio and surface chemistry of the nanocrystals. Specifically, the weak acidity of carboxyl groups ($pKa\sim 3.2$) combined with high aspect ratios creates a defect-dominated soft skeleton; here, the internal Laplace pressure ($\sim 26\mathrm{MPa}$) exceeds the yield strength, driving the splitting of bottlelike mesopores into smaller domains until a geometric locking limit defined by the nanocrystal diameter is reached. In contrast, strong electrostatic repulsion from sulfonates ($pKa\sim 1.0$) or spatial jamming in short nanorods results in rigid networks that resist this capillary-driven densification. This novel hydroplastification mechanism by capitalizing on mesopores with competing capillary force, opposing network stress, and external stress enables shaping CNC films into stable geometries, rather than lattice disruption. Moreover, such findings extend hydroplasticity concepts to rigid matter, establishing mesopore engineering as a physical pathway to regulate the plasticity of crystalline nanomaterials.

One of the roadblocks toward the implementation of a fault-tolerant superconducting quantum processor is impacts of ionizing radiation with the qubit substrate. Such impacts temporarily elevate the density of quasiparticles (QPs) across the device, leading to correlated qubit error bursts. The most damaging errors, $T_1$ errors, stem from QP tunneling across the qubit Josephson junctions (JJs). Recently, we demonstrated [M. McEwen, K. Miao, et al., Phys. Rev. Lett. 133, 240601 (2024)] that this type of error can be strongly suppressed by engineering the profile of superconducting gap at the JJs in a way that prevents QP tunneling. In this work, we identify a new type of impact-induced correlated error that persists in the presence of gap engineering. We observe that impacts shift the frequencies of the affected qubits, and thus lead to correlated phase errors. The frequency shifts are systematically negative, reach values up to 3 MHz, and last for $\sim 1\mathrm{ms}$. We provide evidence that the shifts originate from QP-qubit interactions in the JJ region. Further, we demonstrate that the shift-induced phase errors can be detrimental to the performance of quantum error correction protocols.

Superionic conductors (SICs) exhibit liquidlike ionic diffusivities while maintaining a periodic crystalline lattice, making them promising candidates for applications in fuel cells, solid-state electrolytes, and thermoelectric materials. The transient local structures of mobile ions and their cooperative interactions with the host lattice are of pivotal importance regarding both the ion and heat conduction in SICs. However, accurately capturing the structural evolution of mobile ions remains a significant challenge due to the inherent complexities involved. Here, we employed ultrafast electron diffraction (UED) with femtosecond-temporal and angstrom-spatial resolution to resolve the structural evolution of mobile ${\mathrm{Ag}}^{+}$ ions in ${\mathrm{AgCrSe}}_2$. Our experiments identify a critical process originating from localized ${\mathrm{Ag}}^{+}$ vibrations at the long-range-ordered lattice sites to a formation of short-range-correlated ${\mathrm{Ag}}^{+}$ trimer structures through a drastic contraction of the ${\mathrm{Ag}}^{+}─{\mathrm{Ag}}^{+}$ bond from approximately 3.68 to approximately 3.00 Å in 1.97 ps. Combining real-time time-dependent density-functional-theory and molecular dynamics simulation, we further reveal the crucial role of these contracted trimer structures in enabling fast ${\mathrm{Ag}}^{+}$ diffusion by opening up excess free volume and reducing local energy barriers. Such an intimate relation between fast diffusion and local lattice variations is not exclusive and can be extended beyond ${\mathrm{AgCrSe}}_2$ to materials such as ${\mathrm{Li}}_{10}X{\mathrm{P}}_2{\mathrm{S}}_{12}$ ($X=\mathrm{Si}$, Ge, Sn). The ability to track ion diffusion with UED also provides new avenues for exploring the atomistic mechanisms of fast ion diffusion in next-generation solid-state electrolytes, fuel cells, and ion transport membranes.

Cell extrusion is an essential mechanism for controlling cell density in epithelial tissues. Another essential element of epithelia is curvature, which is required to achieve complex shapes, like in the lung or intestine. Here, we introduce a three-dimensional bubbly vertex model to study the interplay between extrusion and curvature. We find a generic cellular bulging instability at topological defects, which is much stronger than for standard vertex models. Analyzing cell shapes in three-dimensional imaging data of spherical mouse colon organoids, we infer that pentagonal cells have an increased basal interfacial tension, suggesting that cells at topological defects react to the different force conditions. Using the bubbly vertex model, we show that such basal tensions stabilize against the predicted instability and result in better cell shape control than tissue-scale mechanisms such as lumen pressure and spontaneous curvature. Our theory suggests that epithelial curvature naturally leads to bulged and extrusionlike cell shapes because the interfacial curvature of individual cells at the defects strongly amplifies buckling effected by tissue-scale topological defects in elastic sheets. Our results highlight the complex interplay of forces across scales in three-dimensional tissue organization.

Relaxor ferroelectrics exhibit exceptional dielectric and electromechanical properties, yet their microscopic origins remain elusive due to the interplay of hierarchical polar structures and chemical complexity. While models based on polar nanoregions or nanodomains offer valuable phenomenological insights, they often lack the first-principles predictive capability necessary for quantitatively describing functional properties such as piezoelectric coefficients. Here, we use large-scale molecular dynamics simulations, enabled by a universal first-principles-based machine-learning interatomic potential, to investigate atomic-scale polar dynamics in canonical Pb-, Bi-, and Ba-based relaxors. Across all systems, we uncover a universal dipolar nematic state, characterized by long-range orientational order of local polarizations without local alignment, challenging conventional polar-cluster-based paradigms. We introduce a universal order parameter, derived from the skewness of the distributions of the local polarization autocorrelation functions, that captures the thermal evolution of both lead-based and lead-free systems within a single master curve. This nematic order, and its robust structural memory under electric field cycling, underpins key relaxor phenomena, including diffuse phase transition, frequency-dependent dielectric dispersion, and reversible giant piezoelectricity. Our findings establish a unified microscopic framework for relaxors and present a broadly applicable statistical approach to understanding complex disordered materials.

Ultrastable glasses prepared from the physical vapor deposition of organic molecules present a very low density of two-level states, the kind of glass defects that determine their peculiar low-temperature thermal properties. Numerical simulations suggest that quasilocalized harmonic vibrational modes emerge in the soft regions associated with two-level states. However, the connection between the low-frequency vibrational modes and the local structural instabilities of glasses remains unexplained. Here, we exploit a recently developed spectrograph for nuclear resonant analysis of inelastic x-ray scattering to probe the density of vibrational states of amorphous thin films of ultrastable and conventional glasses down to an exceptionally low frequency of approximately 70 GHz. We show that the glass stability does not affect the harmonic vibrational modes at the lowest frequencies, despite a reduction of almost an order of magnitude in the density of two-level states. At the same time, the vibrational modes at higher frequencies, around the boson peak maximum, are extremely sensitive to the glass stability. Although we cannot exclude the possible existence of quasilocalized modes in glasses, we show that their presence is not strictly necessary to describe the measured density of low-frequency vibrations. The experimental developments here presented pave the way to the solution to the long-standing debate on the low-frequency vibrations in glasses.

The thermodynamic limit is foundational to statistical mechanics, underlying our understanding of many-body phases. It assumes that, as the system size grows infinitely at fixed density of particles, unambiguous macroscopic phases emerge that are independent of the system’s boundary shape. We present explicit quantum spin and dimer Hamiltonians whose ground states violate this principle. Our construction relies on the previous mathematical work on classical dimers on the Aztec diamond and the square-octagon fortress, where geometry-dependent phase behaviors are observed in the infinite-size limit. We reverse engineer quantum spin Hamiltonians on the square and the square-octagon lattices whose ground states at the Rokhsar-Kivelson points are described by classical dimer coverings. On diamond-shaped domains, we find macroscopic boundary regions exhibiting distinct quantum phases from those on square-shaped domains. We study the nature of these phases by calculating the dimer-dimer and vison correlators and adapt Kasteleyn matrix based analytical and numerical methods for computing the vison correlator, which are significantly more efficient than standard Monte Carlo techniques. Our results show that the square-octagon lattice supports a single gapped short-range entangled phase, with exponentially decaying dimer correlators and a constant vison correlator. When the same model is considered on a diamond-shaped domain, two additional macroscopic regions emerge, with one near the corners and exhibiting staggered dimer order, and another exhibiting critical correlations.