We establish universal relations between pattern formation and dissipation with a geometric approach to nonequilibrium thermodynamics of deterministic reaction-diffusion systems. We first provide a way to systematically decompose the entropy production rate based on the orthogonality of thermodynamic forces, thereby identifying the amount of dissipation caused by each factor. This enables us to extract the excess entropy production rate that genuinely contributes to the time evolution of patterns. We also show that a similar geometric method further decomposes the entropy production rate into detailed contributions, e.g., the dissipation from each point in real or wavenumber space. Second, we relate the excess entropy production rate to the details of the change in patterns through two types of thermodynamic trade-off relations for reaction-diffusion systems: thermodynamic speed limits and thermodynamic uncertainty relations. The former relates dissipation and the speed of pattern formation, and the latter bounds the excess entropy production rate with partial information on patterns, such as specific Fourier components of concentration distributions. In connection with the derivation of the thermodynamic speed limits, we also extend optimal transport theory to reaction-diffusion systems, which enables us to measure the speed of the time evolution. This extension of optimal transport also solves the minimization problem of the dissipation associated with the transition between two patterns, and constructs energetically efficient protocols for pattern formation. We numerically demonstrate our results using chemical traveling waves in the Fisher–Kolmogorov–Petrovsky–Piskunov equation and changes in symmetry in the Brusselator model. Our results apply to general reaction-diffusion systems and contribute to understanding the relations between pattern formation and unavoidable dissipation.

Forming an interface between immiscible fluids incurs a free-energy cost that usually favors minimizing the interfacial area. An emulsion droplet of fixed volume therefore tends to form a sphere, and pairs of droplets tend to coalesce. Surfactant molecules adsorbed to the droplets' surfaces stabilize emulsions by providing a kinetic barrier to coalescence. Here, we show that the pressure exerted by bound surfactant molecules also competes with the droplet's intrinsic surface tension and can reverse the sign of the overall surface free energy. The onset of negative surface tension favors maximizing surface area and therefore favors elongation into a wormlike morphology. Analyzing this system in the Gibbs grand canonical ensemble reveals a phase transition between spherical and wormlike emulsions that is governed by the chemical potential of surfactant molecules in solution. Predictions based on this model agree with the observed behavior of an experimental model system composed of lipid-stabilized silicone oil droplets in an aqueous surfactant solution.

Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching complex datasets of high-dimensional patterns. Within the class of hierarchical self-organized systems, we investigate the interplay of structure and function associated with the emergence of complex tree structures in disordered environments. Using an algorithm that creates and searches trees of real-world patterns, our work stands at the intersection of statistical physics, machine learning, and network theory. We resolve the network properties over multiple phase transitions and across a continuity of scales, using the von Neumann entropy, its generalized susceptibility, and the recent definition of thermodynamic-like quantities, such as work, heat, and efficiency. We show that scaleinvariance, i.e., power-law Laplacian spectral density, is a key feature for constructing trees capable of combining fast information flow and sufficiently rich internal representation of information, enabling the system to achieve its functional task efficiently. Moreover, the complexity of the environmental conditions the system has adapted to is encoded in the value of the exponent of the power-law spectral density, which is inherently related to the network spectral dimension and directly influences the traits of those maximally functionally efficient networks. Thereby, we provide a novel metric to estimate the complexity of high-dimensional datasets.

We introduce a framework for engineering active quantum matter that involves mimicking the role of self-propulsion through an external trapping potential that is moving along imposed trajectories traced by classical active dynamics. This approach in the presence of dissipation not only recovers essential dynamical behavior of classical activity, including the ballistic to diffusive crossover of its mean-square displacement, but also reveals additional features of activity that are of quantum origin. These quantum-active features are revealed in nondissipative systems, and manifest as novel exponents of the mean-square displacement at short timescales.

Open dissipative systems of quantum fluids have been well studied numerically. In view of a complementary analytical description, we extend here the variational optimization method for Bose-Einstein condensates of closed systems to open-dissipative condensates. The resulting projection optimization method is applied to a complex Gross-Pitaevskii equation, which models a photon Bose-Einstein condensate. Together with known methods from hydrodynamics, we obtain an approximate vortex solution, which depends on the respective open system parameters and has the same properties as obtained numerically in the literature.

The interplay between chaos and thermalization in weakly nonintegrable systems is a rich and complex subject. Interest in this area is further motivated by a desire to develop a unified picture of chaos for both quantum and classical systems. In this work, we study the adiabatic gauge potential (AGP), an object typically studied in quantum mechanics that describes deformations of a quantum state under adiabatic variation of the Hamiltonian, in classical Fermi-Pasta-Ulam-Tsingou (FPUT) and Toda models. We show how the time variance of the AGP over a trajectory probes the longtime correlations of a generic observable and can be used to distinguish among nearly integrable, weakly chaotic, and strongly chaotic regimes. We draw connections between the evolution of the AGP and diffusion and derive a fluctuation-dissipation relation that connects its variance to longtime correlations of the observable. Within this framework, we demonstrate that strongly and weakly chaotic regimes correspond to normal and anomalous diffusion, respectively. The latter gives rise to a marked increase in the variance as the time interval is increased, and this behavior serves as the basis for our probe of the onset times of chaos, which is interpreted as a “mixing” time. Numerical results are presented for FPUT and Toda systems that highlight integrable, weakly chaotic, and strongly chaotic regimes. Further, a hierarchy of $t_{\text{Lyapunov}}<t_{\text{chaos}}<t_{\text{thermalization}}$ is found in these models. We conclude by commenting on the wide applicability of our method to a broader class of systems.

Combinatorial mechanical metamaterials are made of anisotropic, flexible blocks, such that multiple metamaterials may be constructed using a single block type, and the system's response depends on the frustration (or its absence) due to the mutual orientations of the blocks within the lattice. Specifically, any minimal loop of blocks that may not simultaneously deform in their softest mode defines a mechanical defect at the vertex (in two dimensions) or edge (in three dimensions) that the loop encircles. Defects stiffen the metamaterial, and allow one to design the spatial patterns of stress and deformation as the system is externally loaded. We study the ability to place defects at arbitrary positions in metamaterials made of a family of block types that we recently introduced for the square, honeycomb, and cubic lattices. Alongside blocks for which we show that any defect configuration is possible, we identify situations in which not all sets are realizable as defects. One of the restrictions is that in three dimensions, defected edges form closed curves. Even in cases when not all geometries of defect lines are possible, we show how to produce defect lines of arbitrary knottedness.

Combinatorial mechanical metamaterials are made of anisotropic, flexible blocks, such that multiple metamaterials may be constructed using a single block type, and the system's response strongly depends on the mutual orientations of the blocks within the lattice. We study a family of possible block types for the square, honeycomb, and cubic lattices. Blocks that are centrally symmetric induce holographic order, such that mechanical compatibility (meaning that blocks do not impede each other's motion) implies bulk-boundary coupling. With them, one can design a compatible metamaterial that will deform in any desired texture only on part of its boundary. With blocks that break holographic order, we demonstrate how to design the deformation texture on the entire boundary. Correspondingly, the number of compatible holographic metamaterials scales exponentially with the boundary, while in nonholographic cases we show that it scales exponentially with the bulk.

A realistic description of active particles should include interactions with the medium, commonly a momentum-conserving simple fluid, in which they are suspended. In this work, we consider a multispecies suspension of self-diffusiophoretic Janus colloids interacting via chemical and hydrodynamic fields. Through a systematic coarse-graining of the microscopic dynamics, we calculate the multicomponent contribution to the hydrodynamic stress tensor of the incompressible Stokesian fluid in which the particles are immersed. For a single species, we find that the strength of the stress produced by the gradients of the number density field is determined by the particles' self-propulsion and chemotactic alignment, and can be tuned to be either contractile or extensile. For a multispecies system, we unveil how different forms of activity modify the stress tensor and how it can acquire nonreciprocal couplings due to phoretic effects.

We present a method for realizing various zero-energy localized states on disorder-free hypercube graphs. Previous works have already indicated that disorder is not essential for observing localization phenomena in noninteracting systems, with some prominent examples including the one-dimensional Aubry-André model, characterized solely by incommensurate potentials, or two-dimensional incommensurate moiré lattices, which exhibit localization due to the flat-band spectrum. Moreover, flat-band systems with translational invariance can also possess so-called compact localized states, characterized by exactly zero amplitude outside a finite region of the lattice. Here, we demonstrate that both compact and noncompact (i.e., Anderson-like) localized states naturally emerge in disorder-free hypercubes, which can be systematically constructed using Cartan products. This construction ensures the robustness of these localized states against perturbations. Furthermore, we show that the hypercubes can be associated with the Fock space of interacting spin systems exhibiting localization. Viewing localization from the hypercube perspective, with its inherently simple eigenspace structure, offers a clearer and more intuitive understanding of the underlying Fock-space many-body localization phenomena. Our findings can be readily tested on existing experimental platforms, where hypercube graphs can be emulated, e.g., by photonic networks of coupled optical cavities or waveguides. The results can pave the way for the development of quantum information protocols and enable effective simulation of quantum many-body localization phenomena.

Accurate gradient sensing is crucial for efficient chemotaxis in noisy environments. Many eukaryotic cells migrate in chemical gradients by active deformation, yet the relationship between cell shape deformations and sensing accuracy remains largely unexplored. Using a theoretical framework based on maximum likelihood estimation, we show that the receptor dispersion, quantified by cell shape convex hull, fundamentally limits gradient sensing accuracy. Cells with a concave shape and isotropic error space achieve optimal performance in gradient detection. This concave shape, resulting from active protrusions or contractions, can significantly improve gradient sensing accuracy at the cost of increased energy expenditure. By balancing sensing accuracy and deformation cost, we predict that a concave, three-branched shape is optimal for cells in shallow gradients. To achieve efficient chemotaxis, our theory suggests that a cell should adopt a repeating “run-and-expansion” cycle. Our theoretical predictions align well with experimental observations, implying that fast amoeboid cell motion is optimized near the physical limit for chemotaxis. This study highlights the crucial role of active cell shape deformation in facilitating accurate chemotaxis.

Nonlinear disordered media uniquely combine multiple scattering and second-harmonic generation. Here, we investigate the statistical properties of the nonlinear light generated within such media. We report super-Rayleigh statistics of the second-harmonic speckle intensity, and demonstrate that it is caused by the mesoscopic correlations arising in extreme scattering conditions. The conductance measured is exceptionally low for an isotropically scattering three-dimensional medium, enabling applications in broadband second-harmonic generation, wavefront shaping in nonlinear disordered media, and photonic computing.

Acoustically vaporizable droplets are phase-change agents that can improve the effectiveness of ultrasound-based therapies. In this study, we demonstrate that the compression phase of an acoustic wave contributes to the generation of the negative pressure that initiates vaporization. This counterintuitive process is explained by separately evaluating the contribution of the compression and rarefaction phase of the incoming acoustic wave to the acoustic pressure field inside the droplet. Our analysis unifies the existing theories for acoustic droplet vaporization under a single framework and is supported by experiments and simulations. This different interpretation can be employed to identify governing parameters that allow one to vaporize droplets using predominantly compression waves, which are safer in medical use.

The study of charge current fluctuations (noise) can give useful insights into the properties of nanoscale systems. In this work, the peculiar properties of noise in multiterminal hybrid normal-superconducting systems are explored in the thermal out-of-equilibrium regime, i.e., when temperature biases are present ($\mathrm{\Delta }T$-noise). Using the Landauer-Büttiker approach, we identify two contributions: background noise and excess noise, analyzing them when both electrical and thermal biases are applied. When temperature biases are present, and superconducting terminals are grounded, we find that the first contribution depends not only on the electrical conductance, as the Johnson-Nyquist at equilibrium, but also on a quantity strictly related to the heat conductance. This is our first main result. On the other hand, the second contribution shows, as expected, additional terms originating from the partitioning of currents into different transport channels, including the ones associated with Andreev reflection processes. However, noise induced by the temperature differences unveils also interference terms that cannot be present either in voltage bias or in the absence of any Andreev processes. Finally, we apply the results obtained to two different specific physical situations. The first is a generic three-terminal normal-superconductor-normal system and the second is a device based on spin-resolved copropagating chiral channels in the integer quantum Hall regime with a superconducting region. In these example setups, we investigate mainly the shot-noise regimes, when high-voltage or high-temperature biases are applied. We find remarkable differences between the two limits, which ultimately show the different nature of electrically and thermally induced charge current fluctuations.

In this paper, we introduce a class of highly entangled real quantum states that cannot be approximated by circuits with $log$-many non-Clifford gates and prove that Bell sampling enables efficient cross-device verification (or distributed inner product estimation) for these states. That is, two remote parties can estimate the inner product $tr\left(\rho \sigma \right)$, each having black-box access to copies of a state $\rho$ (or respectively $\sigma$) in this class. This is significant because it is clear that this task can be achieved in those cases (such as low entanglement or low non-Clifford gate count) where one can independently learn efficient classical descriptions of each state using established techniques and share the description to compute the overlap. Instead, our results demonstrate that this is possible even in more complex scenarios where these “learn and share” methods are insufficient. Our proposal is scalable, as it just requires a number of two-copy Bell measurements and single-copy Pauli measurements that grows polynomially with both the number of qubits and the desired inverse error, and can be implemented in the near term. Moreover, the required number of samples can be efficiently experimentally determined by the parties in advance, and our findings are robust against preparation errors. We anticipate that these results could have applications in quantum cryptography and verification.

The many-body electron-electron interaction in cuprates causes broadening of the electronic bands in $\mathit{k}$ space, leading to a deviation from the standard Fermi liquid. While a $\mathit{k}$-dependent anisotropic electronic scattering ($\mathit{k}$-DAES) has been assessed by photoemission, its fingerprint in $\mathit{Q}$ space has been scarcely considered. Here, we explore the $\mathit{Q}$-dependent electron dynamics in optimally doped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ through the evolution of low-energy charge excitations as measured by resonant inelastic x-ray scattering (RIXS). In the normal state, the RIXS spectra display a continuum of excitations down to 0 meV, while the superconducting state features a spectral weight suppression below 80 meV without any enhancement at higher energies. To interpret the energy and $\mathit{Q}$ evolution of our data, we introduce a phenomenological expression of the charge susceptibility by including the $\mathit{k}$-DAES. We show that only the charge susceptibility with $\mathit{k}$-DAES captures the RIXS data, highlighting the importance of $\mathit{k}$-DAES when describing the $\mathit{Q}$ dependence of charge excitations from 0 to a few eV scale. Furthermore, we also find that the inclusion of $\mathit{k}$-DAES is essential when quantitative parameters such as the electronic energy gap are extracted from RIXS data.

We explore the stability of supersolid striped waves, plane-wave boselets, and other extended states in one-dimensional spin-orbit-coupled Bose-Einstein condensates with repulsive three-body interactions (R3BIs), modeled by quintic terms in the framework of the corresponding Gross-Pitaevskii equations. In the absence of R3BIs, the extended states are susceptible to the modulational instability (MI) induced by the cubic attractive nonlinearity. Using the linearized Bogoliubov-de-Gennes equations, we identify multiple new types of MI, including baseband, passband, mixedband, and zero-wavenumber-gain ones, which give rise to deterministic rogue waves and complex nonlinear wave patterns. Our analysis reveals that R3BIs eliminate baseband and zero-wavenumber-gain MIs, forming, instead, phonon modes that enable stable boselets. Additionally, mixedband and passband MIs are suppressed, which results in a latticelike phonon-roton mode that supports a stable supersolid phase. These stable supersolids can be realized using the currently available ultracold experimental setup.

Finding reliable approximations to the quantum many-body problem is one of the central challenges of modern physics. Elemental to this endeavor is the development of advanced numerical techniques pushing the limits of what is tractable. One such recently proposed numerical technique are neural quantum states. This new type of wave-function-based Ansatz utilizes the expressivity of neural networks to tackle fundamentally challenging problems, such as the Mott transition. In this paper, we aim to gauge the universalness of one representative of neural network Ansätze, the hidden-fermion slater determinant approach. To this end, we study five different fermionic models each displaying volume law scaling of the entanglement entropy. For these, we correlate the effectiveness of the Ansatz with different complexity measures. Each measure indicates a different complexity in the absence of which a conventional Ansatz becomes efficient. We provide evidence that whenever one of the measures indicates proximity to a parameter region in which a conventional approach would work reliably, the neural network approach also works reliably and efficiently. This highlights the great potential of neural network approaches, but also the inherent challenges: finding suitable points in theory space around which to construct the Ansatz in order to be able to efficiently treat models unsuitable for their current designs.