AI for Science

Locally probing pairing in fermionic superfluids, ranging from micro- to macroscopic scales, has been a long-standing challenge. Here, we investigate a new approach that uses Rydberg impurities as a spectroscopic sensor of the surrounding strongly correlated state of ultracold paired fermions. The extended wavefunction of the Rydberg electron induces a finite-range potential that can bind atoms from the BCS medium, forming molecular states. As a consequence, the optical absorption spectrum of the impurity encodes key many-body properties. Using the functional determinant approach, we provide a direct measure of the superfluid gap through frequency shifts of dimer and trimer peaks. The spectra also reveal whether the Cooper pairs are broken or trapped intact. For static Rydberg atoms, we relate this signature of pairing to the suppression of the orthogonality catastrophe due to the superconducting gap resulting in the formation of well-defined polaron quasiparticles. Our work establishes Rydberg atom spectroscopy as a powerful local probe of strongly correlated matter.

We present PEPSKit$.$jl, a Julia package for simulating two-dimensional quantum many-body systems with infinite projected entangled-pair states (iPEPS). PEPSKit$.$jl builds on the TensorKit$.$jl package for tensor computations and provides high-level algorithms for iPEPS simulations that support both Abelian and non-Abelian symmetries, as well as fermionic systems. This work gives an overview of the main package features, which include support for ground-state, time-evolution, and finite-temperature simulations in systems with different physical symmetries and lattice geometries. These capabilities are illustrated through various examples and technical benchmarks.

Physics-informed neural networks (PINNs) often become difficult to optimize for incompressible flow problems with large spatial domains, multiscale stresses, or long-time invariant dynamics. We propose an invariant-guided PINN (IG-PINN) framework that uses partitioned training as a conservative preconditioning stage rather than as the final piecewise representation. A globally defined architecture is trained successively on spatial subdomains or temporal slabs; selected field traces, structural information, and conservative diagnostics are then transferred to a final global correction, yielding a single neural field on the full spatial or space-time domain. The framework is tested on two incompressible flow problems: steady Oldroyd--B flow past a confined cylinder and a rotational Newtonian flow with helicity diagnostics. In the Oldroyd--B case, IG-PINN transfers velocity, polymeric stress, and mass-flux information while avoiding pressure traces at artificial interfaces. In the helicity case, endpoint velocity is transferred through a hard temporal constraint and kinetic energy is controlled during slab training and residual global correction. The experiments demonstrate improved optimization robustness, reduced conservation errors for the cylinder wake, and controlled energy and helicity diagnostics for the transient rotational flow.

Nonreciprocal interactions that violate Newton's law 'actio=reactio' are ubiquitous in nature and are currently intensively investigated in active matter, chemical reaction networks, population dynamics, and many other fields. An outstanding challenge is the thermodynamically consistent formulation of the underlying stochastic dynamics that obeys local detailed balance and allows for a rigorous analysis of the stochastic thermodynamics of non-reciprocally interacting particles. Here, we present such a framework for a broad class of active systems and derive by systematic coarse-graining exact expressions for the macroscopic entropy production. Four independent contributions to the thermodynamic dissipation can be identified, among which the energy flux sustaining vorticity currents manifests the presence of non-reciprocal interactions. Then, Onsager's non-reciprocal relations, the fluctuation-response relation, the fluctuation relation and the thermodynamic uncertainty relations for non-reciprocal systems are derived. Finally, we demonstrate that our general framework is applicable to a plethora of active matter systems and chemical reaction networks and opens new paths to understand the stochastic thermodynamics of non-reciprocally interacting many-body systems.

We introduce SoliDualSPHysics, a novel open-source and GPU-accelerated software that extends DualSPHysics to enable the numerical simulation of hyperelastic, finite-strain plastic, and brittle fracture behavior in deformable solids within a unified smoothed particle hydrodynamics (SPH) software framework. The software implements a total Lagrangian formulation for solid mechanics that allows direct application of external loads and boundary conditions, enabling independent solid mechanics simulations. Brittle fracture is modeled through a phase-field approach coupled with SPH, allowing crack initiation, propagation, and branching under dynamic loading without explicit crack tracking, ad hoc crack-path criteria, or local refinement. The framework also supports user-defined mathematical expressions to prescribe time- and space-dependent quantities, complementing the solid and fracture extensions and enhancing flexibility across existing and future DualSPHysics applications. Leveraging DualSPHysics' native CPU/GPU parallel architecture, the software achieves substantial computational acceleration for large-scale simulations, and the implementation is verified and validated against benchmark numerical problems and experimental data, demonstrating accuracy, robustness, and favorable scaling performance. Comprehensive implementation details and user documentation are provided to ensure reproducibility and to support further development by the community. The framework and source code are freely available through a public GitHub repository.

In the present paper, we construct a theoretical description of a three-dimensional photonic structure in the form of a tetragonal lattice of bianisotropic resonators applying a dyadic Green's function approach. By representing the resonators as point electric and magnetic dipoles, we obtain the Bloch Hamiltonians for the approximations considering the interactions between the nearest, next-nearest, and next-to-next-nearest resonators, and construct the corresponding real-space tight-binding models. We analyze the band diagrams, spatial structure of the eigenmodes, and their localization, revealing quadratic degeneracies in the vicinity of high-symmetry points in the absence of bianisotropy and the emergence of in-gap states localized at a domain wall upon the introduction of bianisotropy. Finally, we compare the theoretical results with full-wave numerical simulations for an array of bianisotropic resonators.

Using mean-field theory, we determine the electronic phase diagram of undoped AB-stacked bilayer graphene in the presence of a transverse electric field. In addition to multiple competing electronic instabilities characterized by excitonic order parameters, our framework incorporates the long-range Coulomb energy associated with interlayer polarization. This long-range interaction plays a crucial role, as it significantly influences both the structure and the relative energies of the competing ordered states. We derive a set of self-consistency equations and solve them both numerically and analytically. Our findings reveal that, as the bias field is varied, the bilayer undergoes a cascade of first-order transitions between several ordered insulating phases for which order-parameter structures are explicitly identified. Some of these phases are characterized by two inequivalent single-particle gaps, whose magnitudes depend on the valley and spin quantum numbers. Field-driven transitions are accompanied by discontinuous and non-monotonic variations of the single-electron gap. We relate our results to Hartree-Fock numerical calculations and to experimental research, including observations of fractional metallic phases that emerge upon doping the bilayer system.

We study the quantum field theory of zero temperature perfect fluids. Such systems are defined by quantizing a classical field theory of scalar fields $ϕ^I$ that act as Lagrange coordinates on an internal spatial manifold of fluid configurations. Invariance under volume preserving diffeomorphisms acting on these scalars implies that the long-wavelength spectrum contains vortex (transverse modes) with an exact $ω_T=0$ dispersion relation. As a consequence, physically interpreting the results obtained via perturbative quantization of this theory has proven to be challenging. In this paper, we show that correlators evaluated in a class of semi-classical (Gaussian) initial states prepared at $t=0$ are well-defined and accessible via perturbation theory. The width of the initial state effectively acts as an infrared regulator without explicitly breaking diffeomorphism invariance of the classical action. As an application, we compute the stress tensor two-point correlators and show that vortex modes give a non-trivial contribution to the response function, non-local in both space and time.

In this paper we present a newly developed GRPIC code framework called FPIC, providing a detailed description of the Maxwell-equations solver, of the particle ``pushers'', and of the other algorithms that are needed in this approach. We describe in detail the code, which is written in Fortran and exploits parallel architectures using MPI directives both for the fields and particles. FPIC adopts spherical Kerr-Schild coordinates, which encode the overall spherical topology of the problem while remaining regular at the event horizon. The Maxwell equations are evolved using a finite-difference time-domain solver with a leapfrog scheme, while multiple particle ``pushers'' are implemented for the evolution of the particles. In addition to well-known algorithms, we introduce a novel hybrid method that dynamically switches between the most appropriate scheme based on the violation of the Hamiltonian energy. We first present results for neutral particles orbiting around black holes, both in the Schwarzschild and Kerr metrics, monitoring the evolution of the Hamiltonian error across different integration schemes. We apply our hybrid approach, showing that it is capable of achieving improved energy conservation at reduced computational cost. We apply FPIC to investigate the Wald solution, first in electrovacuum and subsequently in plasma-filled configurations. In the latter case, particles with negative energy at infinity are present inside the ergosphere, indicating that the Penrose process is active. Finally, we present the split-monopole solution in a plasma-filled environment and successfully reproduce the Blandford-Znajek luminosity, finding very good agreement with analytical predictions.

This paper investigates density driven flow in porous media, focusing on the roles of viscosity contrast, density contrast, and linear adsorption. In this setup, the fluid on top is heavier and more viscous than the fluid below. Under the effect of gravity, this system becomes unstable, and finger-like structures appear. The phenomenon is described mathematically by coupling Darcy's law with a convection-diffusion reaction equation. The nonlinearity in this model arises mainly from the concentration dependence of viscosity and the convective transport term. The existence of a unique pair of weak solutions is shown using the Galerkin approximation method and truncation technique. Moreover, an application of the maximum principle shows non-negativity of the concentration. Additionally, we analyze the long-time behavior of the solution and prove that the concentration converges exponentially to zero in the $L^p$-norm for all $1 \le p \le \infty$ as $t \to \infty.$ To complement the theoretical analysis, we perform numerical simulations based on a pressure formulation. By tracking total kinetic energy and mixing measures over time, we discuss the instability and the mixing efficiency, respectively. The present study reveals that although increasing the density contrast amplifies the total kinetic energy, the marginal impact diminishes with successive increments of density contrast. Similarly, while adsorption acts to suppress mixing, its efficiency in doing so tends to saturate with further increases. These behavior are consistent with the numerical simulations.

We present an attention-based foundation model architecture for learning and predicting quantum states across Hamiltonian parameters, system sizes, and physical systems. Using only basis configurations and physical parameters as inputs, our trained neural network is able to produce highly accurate ground state wavefunctions. For example, we build the phase diagram for the 2D square-lattice $t-V$ model with $N$ particles, from only 18 parameters $(V/t,N)$. Thus, our architecture provides a basis for building a universal foundation model for quantum matter.

Resonances associated with complex-frequency poles are ubiquitous across physics and can arise in any open system, ranging from subwavelength particles and cavities to biological structures. When two such resonances coalesce, they form exceptional points (EPs), non-Hermitian singularities known to produce unusual spectral and dynamical behavior. However, the dynamics of the response of such resonances and exceptional points to complex frequency drive remained largely unexplored. Here, we experimentally observe the temporal response of complex-frequency resonances and theoretically study this for exceptional points. We unveil a universal transient phenomenon of open cavities driven at complex frequencies: the system's initial response grows linearly, with enhanced growth at exceptional points (EPs), even though the system is passive and the excitation decays. Closed-form theory for general resonators, extended to higher-order modes, predicts efficient power transfer with $t$ and $t^2$ scaling for complex single poles and exceptional points (EPs), respectively, at all times. We demonstrate these effects in subwavelength optical scatterers and experimentally in an electrical circuit analogue, with excellent agreement, and explore configurations that capture EP-enhanced growth.

In this work we present a pedagogically motivated analysis of spin-correlation calculations in a quantum system composed of two spin-$1/2$ particles. Rather than aiming at new physical results, our purpose is to clarify and bring attention to different strategies for evaluating expectation values of the form $\langle ψ| S^{(1)}_{\hat{\boldsymbol{u}}} S^{(2)}_{\hat{\boldsymbol{v}}} | ψ\rangle$, which play an important role in discussions of entanglement and Bell-type correlations. We compare three complementary approaches. The first follows a direct algebraic evaluation in the product basis, closely related to standard textbook methods. The second uses a matrix representation of bipartite states, in which the tensor-product structure is expressed in terms of $2\times2$ complex matrices. This representation keeps the calculation close to the familiar Pauli-matrix algebra and makes the independent action of operators on each subsystem more transparent. The third explores a symmetry-based argument, highlighting both its usefulness and its limitations when applied beyond the singlet state. We show explicitly that the singlet state is rotationally invariant, which explains why the symmetry argument successfully reproduces its correlation function, while a naive extension fails for triplet states. The discussion illustrates how entanglement, tensor-product structure, and rotational symmetry interplay in spin correlations.

Nuclear quantum effects and non-Born--Oppenheimer effects play a vital role in many chemical and biological processes, motivating the incorporation of such effects into dynamical simulations. In real-time nuclear--electronic orbital time-dependent density functional theory (RT-NEO-TDDFT), the electronic and nuclear densities are propagated numerically in time according to the time-dependent Schrödinger equation. In this framework, specified protons are treated quantum mechanically on the same level as the electrons. The classical nuclei can be propagated on the instantaneous NEO vibronic surface using Ehrenfest dynamics. A traveling proton basis (TPB) can be used to describe the dynamics of moving protons in conjunction with Gaussian-type protonic and electronic basis sets for each quantum proton. Herein, we present a constrained TPB (c-TPB) approach that ensures each protonic basis function center coincides with the corresponding proton position expectation value during the dynamics. This approach produces accurate nuclear--electronic quantum dynamics and rigorously conserves energy. We demonstrate the accuracy and stability of this approach for computing molecular vibrational frequencies as well as simulating excited-state intramolecular proton transfer and double proton transfer in the o-hydroxybenzaldehyde and [2,2$'$-bipyridyl]-3,3$'$-diol molecules. These applications show that the c-TPB method provides accurate dynamics, conserves energy, and is computationally efficient.

We introduce a simplicial and categorical formulation of Aharonov-Bohm (AB) type arbitrage in filtered market systems. Given a filtration modeled as a contravariant functor $F : \mathcal T^{op} \to \mathbf{Prob},$ we consider the associated conditional expectation transport functor $\mathcal E \circ F : \mathcal T^{op} \to \mathbf{Ban},$ and the canonical distortion $dF(i) := (\mathcal E \circ F)(i)(1),$ which measures the failure of constant functions to be preserved under non-measure-preserving transitions. Motivated by the multiplicative transport structure of $dF$, we introduce a simplicial distortion operator defined recursively on the nerve $N_\bullet(\mathcal T)$ of the time category. This construction describes recursively accumulated transported distortions along composable chains of morphisms and leads naturally to a notion of holonomy along loops. We interpret non-trivial holonomy as a global inconsistency invisible at the level of individual transitions, analogous to the Aharonov-Bohm effect in physics. This yields a notion of AB arbitrage, in which arbitrage opportunities arise from global loop effects rather than local price discrepancies. We further introduce simplicial admissibility conditions ensuring that recursively accumulated distortions remain integrable, and show how non-trivial holonomy can be translated into predictable self-financing trading strategies through executable loop dynamics. This establishes a connection between categorical holonomy structures and economically realizable arbitrage. The framework developed here suggests a global and homological perspective on arbitrage theory, in which market inconsistencies are encoded by recursively accumulated simplicial distortions and their holonomy along loops in the underlying time category.

We present a physics-based neural network framework for the discovery of constitutive models in fully coupled thermomechanics. In contrast to classical formulations based on the Helmholtz energy, we adopt the internal energy and a dissipation potential as primary constitutive functions, expressed in terms of deformation and entropy. This choice avoids the need to enforce mixed convexity--concavity conditions and facilitates a consistent incorporation of thermodynamic principles. In this contribution, we focus on materials without preferred directions or internal variables. While the formulation is posed in terms of entropy, the temperature is treated as the independent observable, and the entropy is inferred internally through the constitutive relation, enabling thermodynamically consistent modeling without requiring entropy data. Thermodynamic admissibility of the networks is guaranteed by construction. The internal energy and dissipation potential are represented by input convex neural networks, ensuring convexity and compliance with the second law. Objectivity, material symmetry, and normalization are embedded directly into the architecture through invariant-based representations and zero-anchored formulations. We demonstrate the performance of the proposed framework on synthetic and experimental datasets, including purely thermal problems and fully coupled thermomechanical responses of soft tissues and filled rubbers. The results show that the learned models accurately capture the underlying constitutive behavior. All code, data, and trained models are made publicly available via https://doi.org/10.5281/zenodo.19248596.

This work presents the application of parametric Operator Inference (OpInf) -- a nonintrusive reduced-order modeling (ROM) technique that learns a low-dimensional representation of a high-fidelity model -- to the numerical model of the purging process in semiconductor manufacturing. Leveraging the data-driven nature of the OpInf framework, we aim to forecast the flow field within a plasma-enhanced chemical vapor deposition (PECVD) chamber using computational fluid dynamics (CFD) simulation data. Our model simplifies the system by excluding plasma dynamics and chemical reactions, while still capturing the key features of the purging flow behavior. The parametric OpInf framework learns nine ROMs based on varying argon mass flow rates at the inlet and different outlet pressures. It then interpolates these ROMs to predict the system's behavior for 25 parameter combinations, including 16 scenarios that are not seen in training. The parametric OpInf ROMs, trained on 36\% of the data and tested on 64\%, demonstrate accuracy across the entire parameter domain, with a maximum error of 9.32\%. Furthermore, the ROM achieves an approximate 142-fold speedup in online computations compared to the full-order model CFD simulation. These OpInf ROMs may be used for fast and accurate predictions of the purging flow in the PECVD chamber, which could facilitate effective particle contamination control in semiconductor manufacturing.

We prove, within the probabilistic framework of Khinchin families, that the generating function $P_k$ of partitions into $k$-th powers is strongly Gaussian in the sense of Báez-Duarte, and even further that it is a Hayman function. Thus the Hardy--Ramanujan asymptotic formula for the number $p_k(n)$ of partitions of $n$ into $k$-th powers which reads \[ p_k(n) \sim \frac{α_k}{n^{(3k+1)/(2k+2)}} \exp\!\Big(β_k\, n^{1/(k+1)}\Big), \qquad n\to\infty, \] where $α_k$ and~$β_k$ are explicit constants depending only on $k$, follows directly from Hayman's asymptotic formula for strongly Gaussian power series. The proof of strong Gaussianity of $P_k$ combines a Gaussianity criterion for Khinchin families with certain bounds of Tenenbaum, Wu and Li on the generating function; the asymptotic formula is recovered by computing asymptotic approximations of the mean and variance of the associated family. Analogous results are presented for the generating function $Q_k$ of partitions into distinct $k$-th powers.

We present a systematic construction of non-Hermitian tight-binding lattices whose Bloch spectra are $n$th roots of those of Hermitian parent two-dimensional (2D) lattices, namely graphene and the Lieb lattice. The $n$-roots of these models are constructed from connecting loop modules of unidirectional couplings whose geometrical arrangements match that of the corresponding parent system. Their energy spectrum is shown to consist of $n$ rotated and equivalent branches in the complex energy plane, each matching the real spectrum of the parent model when raised to the $n$th power, together with extra zero-energy flat bands (FBs) accounted for by the generalized index theorem. We show how the low-energy Dirac cones of the parent models translate, for an appropriate choice of phase configuration for the couplings of the $n$-root lattices, as what we call an "exceptional horn" appearing at each branch, with the central Dirac point (DP) converted into zero-energy exceptional points (EPs) of order $n$ or higher at high-symmetry momenta. These exceptional horns reflect the behavior of low-lying excitations that scale with momentum as $E\sim\vert \mathbf{q}\vert^{\frac{1}{n}}$, with $n\geq 3$, as opposed to the linear massless modes that characterize a Dirac cone. Moreover, we derive analytic expressions for the associated Landau levels (LLs), whose energies scale with magnetic flux as $E\simϕ^{\frac{1}{2n}}$. For the case of the $n$-root Lieb lattice, the zeroth LL is shown to be exceptional. These results are analytically derived for both $n$-root models and numerically demonstrated for certain values of $n$. Finally, we propose a realistic photonic implementation based on coupled ring resonators with a split configuration of optical gain and loss.

We develop a systematic framework for the model reduction of multivariate geometric Brownian motions (GBMs), a fundamental class of stochastic processes with broad applications in mathematical finance, population biology, and statistical physics. Our approach leverages the interplay between the method of invariant manifolds and adiabatic elimination to derive closed-form reduced equations for the deterministic drift. An extended formulation of the fluctuation-dissipation theorem is subsequently employed to characterize the stochastic component of the reduced description. As a concrete application, we apply our reduction scheme to a GBM arising from a two-state quantum system, showing that the reduced dynamics accurately capture the localization properties of the original model while significantly simplifying the analysis.

This paper presents an adaptive observer design for semilinear hyperbolic rolling contact ODE-PDE systems with uncertain friction characteristics parameterized by a matrix of unknown coefficients appearing in the nonlinear (and possibly non-smooth) PDE source terms. Under appropriate assumptions of forward completeness and boundary sensing, an adaptive observer is synthesized to simultaneously estimate the lumped and distributed states, as well as the uncertain friction parameters, using only boundary measurements. The observer combines a finite-dimensional parameter estimator with an infinite-dimensional description of the state error dynamics, and achieves exponential convergence under persistent excitation. The effectiveness of the proposed design is demonstrated in simulation by considering a relevant example borrowed from road vehicle dynamics.

The component-wise dimensionally reduced real Schur flows (RSFs) associated to the classical compressible Euler equation [J.-Z. Zhu, J. Math. Phys. \textbf{62}, 083101 (2021)] is reformulated alternatively in terms of mode-truncation, with the untruncated Fourier modes preserving the original interaction structure and thus other important derivatives. A number of results are set up for the mathematical physics of component-wise dimensionally reduced flows (CWDRFs, including those with further dimensional reductions of RSFs); and, it is particularly shown that previous proofs of the helicity invariance in barotropic ideal flows were overkilling in the sense of using the unnecessary condition of local mass conservation, while our new ``sharper'' proof without invoking the latter carries over to our CWDRFs and the inviscid Burgers equation, verified using recent results [S.~G.~Chefranov \& A.~S.~Chefranov, Phys. Scr. \textbf{94}, 054001 (2019)] for the latter case in the infinite domain.

We consider a nonlinear Klein-Gordon equation in the nonrelativistic limit regime with initial data in the form of a modulated highly oscillatory exponential. In this regime of a small scaling parameter $\varepsilon\ll 1$, the solution exhibits rapid oscillations in both time and space. The solution is approximated, up to $\mathcal{O}(\varepsilon)$, by a superposition of two polarized solutions, which are wave packets that move with opposite group velocities proportional to $\varepsilon^{-1}$. The equations for polarized solutions are formulated in co-moving coordinates and are then discretized by an explicit and an implicit exponentially weighted finite difference method. While the explicit weighted leapfrog method needs to satisfy a CFL-type stability condition, the implicit weighted Crank-Nicolson method is unconditionally stable. Both methods achieve second-order accuracy with time steps and mesh sizes that are not restricted in magnitude by $\varepsilon$. For the approximation of polarized solutions, the methods are uniformly convergent in the range from arbitrarily small to moderately bounded $\varepsilon$. Numerical experiments illustrate the theoretical results.

We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis. Our algorithm provides the exact solution to this recovery problem and improves upon current approaches by an order of magnitude. It relies on generalized normal forms and stabilizers of group actions via matrix-tensor congruence. We apply randomized transformation techniques that avoid the task of solving nonlinear polynomial systems associated to degenerate paths, and accompany our methods with an efficient implementation in the computer algebra system OSCAR.

We introduce a nonperturbative framework for quantizing chiral solitons in interacting quantum spin chains. This approach provides a direct lattice extension of the well-established $S$-duality between the sine-Gordon and Thirring models, thereby bridging the gap between continuum dualities and their lattice counterparts. By constructing the quantum chiral-soliton operators explicitly, we show how their unconventional dynamics appear in the excitation spectrum and correlation functions across the full Brillouin zone. A key result is that the dominant soliton tunneling amplitude alternates in sign, $\operatorname{sgn}(t_{1+}) = (-1)^{2S+1}$, sharply distinguishing half-odd-integer from integer spin chains. We further identify characteristic signatures of these chiral excitations in the dynamical spin structure factor, demonstrating their visibility in inelastic neutron scattering. Our results open a route to experimentally probing nonperturbative features of dual quantum field theories in condensed-matter settings.

Random-matrix theory helps disentangle signal from noise in large data sets. We analyze rectangular $p \times q$ matrices $W = W_0 + M$ in which the noise $M$ generates a Marchenko-Pastur bulk, whereas the signal $W_0$ injects an extensive set of degenerate singular values. Keeping $\mathrm{rank}$ $W_0/q$ finite as $p,q \to \infty$, we show that the trace of the resolvent of $W^{\top} W$ obeys a quartic equation for one degenerate signal, yielding an exact spectral density, and derive explicit asymptotics in the strong-signal regime. We map out a detailed generalized Baik-Ben Arous-Péché (BBP) phase diagram and clarify how a finite density of spikes reshapes the bulk edges. We further derive a $1/3$-scaling law for the critical signal strength in terms of the rank ratio for rectangular matrices in the finite-to-extensive-rank crossover. Numerical simulations validate the theory and illustrate its relevance for high-dimensional inference tasks with multiple degenerate signals and more general signal distributions.

Renormalization is an essential technique in field-theoretic descriptions of natural phenomena, where the absence of a UV-complete description yields an abundance of divergent quantities. While the renormalization prescription has been thoroughly refined for equilibrium systems, consistently extending it to out-of-equilibrium systems is an active area of research. In this paper, we identify a mutual information-based measure of renormalizability that applies to quantum field theories both in and out of equilibrium. Specifically, we use mutual information to characterize correlations between infinitesimal shells in momentum space and show that the logarithmic derivative of mutual information with mode separation, at large mode separation, is a measure of renormalizability. We first consider Minkowski spacetime, where we introduce dynamics by performing an interaction quench, initializing the field in the free theory vacuum and then turning on the interaction. We show that the late-time mutual information relaxes to that for the interacting vacuum and the logarithmic derivative at large mode separation is negative for super-renormalizable theories, zero for renormalizable (marginal) theories, and positive for non-renormalizable theories. We then consider a conformally-coupled scalar field on the Poincaré patch of de Sitter spacetime, initializing the field in the Bunch-Davies vacuum in the asymptotic past. For different self-interactions and at any finite time, we find that the resulting mutual information has the same qualitative behavior as a function of mode separation, demonstrating that it can be used as a reliable indicator of renormalizability.

The Boltzmann distribution for an equilibrium system constrains the statistics of the system by the energetics. Despite the non-equilibrium generalization of the Boltzmann distribution being studied extensively, a unified framework valid for far-from-equilibrium discrete state systems is lacking. Here, we derive an exact path-integral representation for discrete state processes and represent it using the exponential of the action for stochastic transition dynamics. Solving the variational problem, the effective action is shown to be equal to the inferred entropy production rate (a thermodynamic quantity) and a non-quadratic dissipation function of the thermodynamic length (TL) defined for microscopic stochastic currents (a dynamic quantity). This formulates a far-from-equilibrium analog of the Boltzmann distribution, namely, the minimum action principle. The non-quadratic dissipation function is physically attributed to incorporating non-Gaussian fluctuations or far-from-equilibrium non-conservative driving. Further, an exact large deviation dynamical rate functional is derived. The equivalence of the variational formulation with the information geometric formulation is proved. The non-quadratic TL recovers the non-quadratic thermodynamic-kinetic uncertainty relation (TKUR) and the speed limits, which are tighter than the close-to-equilibrium quadratic formulations. Moreover, if the transition affinities are known, the non-quadratic TL recovers the fluctuation relation (FR). The minimum action principle manifests the non-quadratic TKUR and FR as two faces corresponding to the thermodynamic inference and partial control descriptions, respectively. In addition, the validity of these results is extended to coarse-grained observable currents, strengthening the experimental/numerical applicability of them.

The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these processes and the diversity of the modeled systems. While results about their steady state are well-known, very few exact results about their finite-time evolution exist. Here, we introduce the conditional entropy of heat diffusion in graphs, and outline a mathematical framework that contextualizes diffusion and conditional entropy within the theories of continuous-time Markov chains and information theory. In particular, we highlight that this entropic measure satisfies an information-theoretical version of the second law of thermodynamics, thereby providing a parallelism between diffusion dynamics on networks and their physical counterparts. Furthermore, we obtain explicit results for its evolution on complete, path, and circulant graphs, as well as a mean-field approximation for Erdös-Rényi graphs. We also obtain asymptotic results for general networks and provide bounds for the evolution of conditional entropy. Finally, we experimentally demonstrate several properties of conditional entropy for diffusion over random graphs, such as the Watts-Strogatz model.

Simulation Based Inference (SBI) is shown to yield more accurate resonance parameter estimates than traditional chi-squared minimization in certain cases of model misspecification, demonstrated through a case study of pi-pi scattering and the rho(770) resonance. Models fit to some data sets using chi-squared minimization can predict inaccurate pole positions for the rho(770), while SBI provides more robust predictions across the same models and data. This result is significant both as a proof of concept that SBI can handle model misspecification, and because accurate modeling of pi-pi scattering is essential in the study of many contemporary physical systems (e.g., a1(1260), omega(782)). The method of Simulation Based Inference is shown to lead to a more accurate resonance parameter estimation than traditional chi-squared minimization in certain cases of model misspecification in a case-study of pi-pi scattering and the rho(770)-resonance. Models fit to certain data sets using chi-squared minimization can make inaccurate predictions for the pole position of the rho(770). SBI is shown to make a more robust predictions for the pole positions. This is significant, both as a proof of concept that the SBI method can be used in cases of model misspecification, and because models of pi-pi scattering are a crucial part to many physical systems of contemporary interest (e.g., a1(1260), omega(782)).