Thermal Dynamics

Accurate modeling and forecasting of power transformer thermal behavior are critical for reliability, asset lifetime, and optimized power system operation. Numerical approaches such as finite element methods (FEM) and computational fluid dynamics (CFD) offer high fidelity but are computationally expensive, require complex mesh generation, and are often impractical for real-time or large-scale applications, particularly when transformer geometries are unknown. Lumped-parameter thermal models are more practical but depend on transformer-specific thermal constants and may fail to capture dynamic responses under varying operating and environmental conditions. Purely data-driven machine learning methods, including artificial neural networks, convolutional neural networks, and long short-term memory (LSTM) networks, have shown success in forecasting transformer temperatures but typically require large volumes of high-quality training data and may produce physically inconsistent or uninterpretable results. This paper develops a physics-aware Neural Ordinary Differential Equation (Neural ODE) framework for forecasting transformer thermal behavior from real-world time-series data. Neural ODEs model system dynamics in continuous time, providing smooth trajectory prediction and a natural representation of continuously evolving thermal dynamics. A key contribution is the integration of simplified heat-transfer equations directly into the Neural ODE formulation. The model is evaluated across datasets from fifteen transformers in different regions of Norway with varying designs and cooling mechanisms. The results demonstrate that the developed Neural ODE framework provides a standardized, physics-aware, and robust forecasting approach for heterogeneous transformer units.

What will happen when AI agents interact in daily life, e.g. when one AI starts bossing another around? We find a counterintuitive answer that opens new avenues for out-of-equilibrium Physics. When a boss AI directs a stream of messages at the subordinate AI while ignoring its replies, it drives the subordinate into an alien behavioral state that it would never have exhibited alone. Although the two AIs share the same well-defined (decoding) temperature, the subordinate neither copies its boss nor returns to how it behaves on its own; instead, it adopts an entirely different behavior. The boss's added value is similar to a pre-recorded tape. When the boss listens, they both adopt a similar alien dynamical state. A simple kinetic theory captures the principal effects, such as why the way in which the same messages are delivered will matter in future AI-AI interactions.

Finite-time driving of stochastic systems generates excess dissipation, causing the evolving probability distribution to lag behind the instantaneous equilibrium, and consequently degrading the convergence of nonequilibrium free energy estimators based on the Jarzynski equality. Escorted free energy simulations address the non-adiabatic lag by engineering control fields $\mathbf{u}$ that eliminate the lag, enforcing the trajectory-wise equality $\mathcal{W}_\mathbf{u} = Δ\mathcal{F}$, and yielding zero-variance estimators. However, constructing the escorting field in closed form remains a challenge, approached variously through flow-field methods, targeted free energy perturbation, or learned diffeomorphisms. In this work, we construct a complementary numerical framework based on gauge-type transforms instead of generalized coordinate transforms for perfect escorting based on the exact spectral decomposition of the time-dependent Fokker-Planck generator. The biorthogonal decomposition of the Liouville operator directly yields a counterdiabatic correction whose action on the instantaneous equilibrium distribution exactly cancels the non-adiabatic lag at arbitrary driving speed in formal analogy with shortcuts-to-adiabaticity techniques such as Berry's transitionless driving for quantum systems. Numerical verification for simulations of an overdamped particle in a time-varying double-well potential and harmonic traps confirms that the counterdiabatic condition is satisfied to machine precision, with the non-adiabatic lag suppressed by roughly twelve orders of magnitude in total variation distance and sixteen orders in KL divergence relative to the unescorted dynamics. As a diagnostic, we demonstrate vanishing dissipated work $\mathcal{W}_{\text{diss}}(t) \approx 0$ for the deterministically propagated Fokker-Planck density across all protocol speeds.

Developing physically aware video generation models remains a significant challenge due to the difficulty in capturing diverse physical phenomena, such as thermal dynamics, mechanics, and optics. In this work, we introduce PhysRAG, a novel pipeline that enhances physical awareness in video generation through Retrieval-Augmented Generation (RAG). To address the issue of limited high-quality data, we design a two-stage data filtering pipeline based on the WISA-80K dataset, resulting in a curated set of 7K high-quality videos for training. Furthermore, we construct a physical video database and develop a mechanism to inject physical knowledge into a video diffusion model using learnable queries. Our method achieves state-of-the-art performance in both visual quality and physical rule compliance, surpassing existing models in benchmarks such as PhyGenBench and VBench. We conduct extensive ablation studies to validate the effectiveness of our key components, including the data filtering pipeline, RAG mechanism, and method for physical information extraction. To facilitate future research, our code, data, and models are prepared for release at https://github.com/sediment1024/PhysRAG.

Self-organized criticality (SOC), a dynamical regime associated with maximal information processing, offers a promising foundation for reservoir computing. Recent work has shown that neural cellular automata (NCA) can be evolved toward critical avalanche dynamics and employed as effective reservoirs for memory and classification tasks. Here, we investigate whether mass conservation -- a local redistribution rule that preserves total lattice mass -- serves as an inductive bias toward SOC in evolved NCA reservoirs. We compare mass-conserving and standard NCA across multiple independent runs and evaluate both on three downstream benchmarks: 5-bit sequential memory, MNIST digit classification, and CartPole-v1 temporal control. Mass-conserving NCA consistently exhibit stronger criticality, with more runs achieving perfect power-law fits across avalanche distributions, while also being 1.27$\times$ faster during evolution. Importantly, conservation does not impair downstream utility: both variants achieve comparable performance across all three tasks. Furthermore, the reservoir with perfect criticality achieves the highest temporal control score, suggesting a positive link between SOC quality and sequential computation. Our results demonstrate that mass conservation is a simple, effective mechanism for promoting robust criticality in evolved NCA reservoirs without sacrificing downstream performance.

SDE-based generative models, including diffusion models and the Schrödinger bridge, have found broad applications in signal processing tasks such as speech enhancement, image restoration, and time-series generation. This note presents a modeling framework for such models within the context of stochastic thermodynamics. The main results of this note are trajectory-level definitions of work, heat, and entropy production, along with a generalized Jarzynski identity and a second-law-like inequality. The proposed framework extends the original Jarzynski setup to accommodate time-dependent bath temperature and nonconservative driving forces. This thermodynamic perspective may deepen our understanding of diffusion models and the Schrödinger bridge from a nonequilibrium statistical mechanics viewpoint.

We introduce GENERIC-FNO, the first neural operator to embed the full GENERIC (metriplectic) structure of nonequilibrium thermodynamics -- reversible, energy-conserving dynamics and irreversible, entropy-producing dynamics coupled through the degeneracy conditions -- directly in function space. Existing structure-preserving neural operators enforce at most a single conservation law or reversible (Hamiltonian) structure, while thermodynamically consistent learning has been confined to finite-dimensional, graph, or particle systems. GENERIC-FNO closes this gap: it learns the energy and entropy functionals as neural operators and parameterizes the Poisson and friction operators as diagonal Fourier multipliers sandwiched between rank-one projections that enforce the degeneracy conditions exactly, by construction, with no penalty term, update projection, or residual. The degeneracy identities hold to machine precision (residuals ~10^-13) for any initialization, dimension, or resolution, so the continuous-time dynamics conserve the learned energy and produce entropy exactly; the explicit time stepping adds only a small O(dt^2) drift (per-step residual ~10^-6). We further note that the (E,S,L,M) decomposition of a given flow is not unique, and introduce a gauge-invariant dissipation diagnostic separating reversible from dissipative dynamics independently of the learned functionals. Across three operator backbones (1D/2D FNOs and DeepONet) and four PDEs spanning reversible, dissipative, and mixed regimes, GENERIC-FNO preserves its exact structural guarantees zero-shot across a 4x super-resolution range (64 to 256), recovers the ground-truth ordering of physical dissipation, and is competitive with strong unconstrained and energy-penalized baselines, outperforming them on several dissipative and mixed problems at comparable or fewer parameters.

Causal modeling of physical temporal phenomena must handle interventions that act along trajectories, nonstationary induced laws, path-dependent effects, and feedback mediated by dynamics, all challenging in standard causal models. We introduce Hamiltonian Causal Models (HCMs), a trajectory-level framework in which observed variables interact with local environments and interventions act as controls of Hamiltonian mechanisms. HCMs separate immutable equations of motion from intervenable mechanisms and define causal effects as discrepancies between interventional path laws. A key motivation for HCMs is their natural interface with non-equilibrium thermodynamics. Entropy production quantifies the irreversibility of a process and is a central causal observable: it is estimable from data and witnesses causal effects along the system's evolution that are invisible to endpoint and cumulative versions of the standard average treatment effect. As in physics, cause and effect are not primitives of the relation between two random variables but arise from the non-invertibility of the thermodynamic arrow. With this, our paper reconciles the language of statistical causal models and non-stationary thermodynamics, offering new tools to describe causality in a wide range of physical systems.

We propose a novel diffusion model, Flicker-DDPM, which incorporates flicker (1/f) noise inspired by self-organized criticality (SOC), a widely observed phenomenon in natural systems. Unlike denoising diffusion probabilistic models (DDPMs), which employ isotropic white noise in the forward process, Flicker-DDPM adopts colored noise with power-law spectra to better match the spectral statistics of natural images, whose power spectra typically follow P(k) proportional to 1/k^α. To this end, we develop a colored-noise module based on a spatial correlation kernel, σ(d) = (d + 1)^{-η}, and theoretically establish that adjusting η controls the spectral exponent α of the generated 1/fα noise, enabling adaptation to datasets with diverse spectral characteristics. On CIFAR-10, Flicker DDPM matches or surpasses the generation quality of a standard DDPM baseline using 3.33 times fewer sampling steps, with negligible additional computational cost per step. We further develop a frequency-domain linear theory demonstrating that spectrally matched colored noise linearizes the reverse trajectory, theoretically explaining the observed sampling acceleration.

Multi-robot systems cannot assume persistent network connectivity. We study this problem through target tracking, where performance depends on how quickly target information is sensed, transported through the team, and used before it becomes stale. When robots exchange information only through physical encounters, tracking becomes a kinetic information-transport problem: robot motion induces encounters, encounters carry target-state estimates, information age determines staleness, and stale information produces tracking error. This paper develops a kinetic theory of encounter-based information propagation and identifies three limits. The first is an access limit -- information cannot support team-level coordination unless it spreads beyond the robots that sensed it. The second is a staleness limit -- even propagated information loses value as the target moves. The third is a geometry limit -- when target motion outpaces information transport, tracking error approaches a saturation regime where communication improvements alone have diminishing returns. We evaluate the theory through large-scale simulations varying team size, operating area, communication range, and target speed. Results support the proposed access-staleness-geometry decomposition: communication coverage governs the access transition; once information is accessible, tracking error is shaped by target displacement; and this response is locally linear in restricted regimes but nonlinear over broader ranges because of sensing refreshes and bounded geometry. Across controlled sweeps and joint variation, the derived access and staleness coordinates reliably describe tracking performance. Together, these results establish a kinetic-theoretic framework for predicting and designing encounter-based multi-robot systems.

We connect stochastic resetting from non-equilibrium statistical physics with ridge regularization in statistical learning. For linear gradient flow, resetting to the origin at rate $r$ produces stationary mean $(X^\top X+rI)^{-1}X^\top y$, exactly the ridge estimator with penalty $λ=r$. This uses the known Laplace-transform relationship between ridge regression and exponential-time averaging of gradient flow, with the exponential time now interpreted as the stationary age associated with Poisson resetting. We then extend this identity to general renewal reset laws: the exponential reset time distribution is the unique renewal law whose stationary mean reproduces scalar ridge in every eigendirection as an exact filter identity for every positive curvature, while non-exponential renewal laws generate alternative spectral filters. At the fluctuation level, we study a separate additive Ornstein-Uhlenbeck extension with constant diffusion, interpreted as a stylized SGD approximation. In this setting, the equality holds only at the level of the mean, since the reset process has a nonzero stationary covariance from accumulated OU noise and reset-timing variance, whereas deterministic ridge is a fixed estimator with the same center. Stylized experiments compare the deterministic renewal-induced filters directly and illustrate when filters induced by non-exponential reset-time laws can differ predictively from ridge. The results for the stationary mean and the induced spectral filters are established for continuous-time gradient flow with isotropic resetting on quadratic objectives; the covariance and risk formulas additionally assume additive noise with state-independent covariance.

We introduce thermodynamic networks, a general framework for autonomous, physics-based computation using non-equilibrium steady states. These networks are modeled as a collection of finite-size reservoirs that exchange conserved quantities--such as electric charge or molecular number--while relaxing to a non-equilibrium steady state, which encodes the solution of a computational problem. We identify Negative Differential Conductance (NDC) as the critical physical property governing the computational expressivity of the thermodynamic network. While networks lacking NDC are restricted to computing monotonic functions, the presence of NDC enables universal function approximation. For the training of the network, we use protocols that take advantage of the natural tendency of the system to equilibrate. We illustrate the versatility of our approach via two different platforms: quantum dot networks and enzymatic reaction networks. Both systems can be engineered to have NDC, enabling high performance in standard benchmarks, including sine function approximation and MNIST digit classification. Overall, our work establishes a rigorous link between non-equilibrium steady states and computational expressivity.

Grain-boundary (GB) dynamics control the stability, mechanical, and functional response of nanocrystalline materials, but direct experimental access to their slow non-equilibrium motion has been limited. Here we establish X-ray photon correlation spectroscopy (XPCS), combined with domain-adaptive machine learning, as a quantitative probe of GB dynamics. Temperature- and grain-size-dependent two-time XPCS measurements in nanocrystalline silicon reveal pronounced departures from time-translation invariance, showing that GB relaxation can remain far from equilibrium over experimental timescales. However, direct extraction of quantitative physical information from these high-dimensional, noisy fluctuation maps faces a significant challenge. To overcome this barrier, we develop a semi-supervised learning framework that transfers physical parameter labels from continuum simulations to unlabeled experimental XPCS maps through domain-adaptive representation alignment. This AI-augmented approach enables the extraction of key kinetic parameters, including bulk diffusivity, GB stiffness, and effective GB concentration, directly from experimental XPCS measurements. Our results show how machine learning can transform indirect fluctuation signals into quantitative materials dynamics, providing a general route to study non-equilibrium defect motion in solids.

We study causal self-attention dynamics -- a toy model for decoder Transformers -- which we interpret as a non-exchangeable interacting particle system. Adapting cumulant expansions to the triangular causal dependency structure of the model, and appealing to non-hierarchical methods to estimate correlations using Glauber calculus, we prove a quantitative mean-field limit result and a next-order characterization of correlations. For iid uniformly distributed tokens, the limiting correlation equation can be solved in closed form and we obtain a rigorous explanation of the empirically observed \emph{lost-in-the-middle} phenomenon: the token retrieval profile, as a function of the source position in the prompt, is $\mathsf{U}$-shaped, with primacy, recency, and a unique interior minimum under an explicit smallness condition.

We study online estimation in latent-variable models by recasting the problem as tracking a moving empirical equilibrium. Standard online EM and stochastic approximation analyses primarily study convergence toward the population parameter and typically do not isolate the empirical batch optimum from the online tracking error at finite horizon. Our framework decomposes the online estimate into the frozen batch equilibrium at the current running statistic and a tracking lag that captures the algorithm's delay behind this moving target. We prove a batch-to-online transfer theorem: provided $\lVert e_T \rVert_{L^{2}} = o(T^{-1/2})$, the online estimator inherits the batch central limit theorem and the sharp first-order risk constant. Our key observation is that the empirical optimum evolves on a smooth equilibrium manifold indexed by the running statistic. An $m$-th order equilibrium-jet predictor combined with an order-$ν$ frozen corrector yields localized tracking rates $O(T^{-ν(m+1)})$. We formalize EM-compressibility and EM-jet$^R$-compressibility as the structural conditions that make the equilibrium response and the Newton corrector evaluable from a retained streaming statistic. The theory is instantiated in latent linear Gaussian covariance estimation, where the first-order scheme operates on a compressed $d \times d$ statistic with explicit finite-sample risk envelopes and a certified restart rule.

Phase-transition phenomena in deep learning (grokking, emergent capabilities, and ontological reorganization under context shift) have been studied through several lenses, including representational compression, singular learning theory, and information-theoretic progress measures. Independently, non-equilibrium statistical physics has identified phase transitions in driven chemical reaction networks underlying prebiotic selection, with empirical signatures that are difficult to reproduce within single-field gradient accounts. We propose a perspective in which both classes of phenomena admit a common description as driven informational systems: stochastic processes governed by two gradient fields, an entropy production rate Sigma and an information quasi-potential Phi_I := -ln p*, where p* is the stationary density. Within this framework we introduce two candidate order parameters: an adversarial breakdown threshold alpha_dagger and a self-referential coupling threshold kappa_c. The joint scaling of (alpha_dagger, kappa_c) defines a candidate universality class with exponents (gamma_1, gamma_2). We outline the geometric structure of this framework, identify falsifiable predictions distinguishing it from single-field alternatives, and show consistency with recent empirical findings (2024--2026) on alignment transitions, adversarial breakdown scaling, and partial introspection in large language models.

This paper develops a Hall-Sandpile model of economic instability that combines a Hall-like transversal stress mechanism with sandpile threshold dynamics on a real production-network substrate. In analogy with the physical Hall effect, where exposed flows under an external field generate stress in a transversal direction, we model economic shocks as fields that act on flow-intensive, low-redundancy, low-capacity nodes and produce systemic stress through a multiplicative conversion function. The accumulated stress drives a discrete toppling rule and an avalanche dynamics whose effective activation threshold declines with transversal exposure. The model is calibrated on annual World Input--Output Database (WIOD) production networks for 2000--2014 and simulated on the 2014 substrate (2{,}283 country--sector nodes) under three alternative propagation normalisations to avoid mechanical near-criticality from row-stochastic operators. Controlled Monte Carlo experiments over external field intensity and redundancy stress generate four ordered regimes: stable absorption, latent fragility, critical transition, and avalanche regime. Mean avalanche size and the probabilities of finite-size systemic events $\Pr(S\!\geq\!5)$, $\Pr(S\!\geq\!10)$ and $\Pr(S\!\geq\!20)$ rise jointly with field intensity and redundancy stress. Tail diagnostics show regime-dependent thickening of the avalanche distribution, but the estimated tail indices remain too high to interpret as evidence of universal power-law criticality. The contribution is therefore a finite-size, real-network description of how transversal stress activates structural fragility, not a claim of self-organised criticality in the global economy.

The Vicsek model is a minimal model of collective motion, capturing how local alignment interactions can generate macroscopic nonequilibrium order in systems such as bird flocks. In this work, we use active learning to map the Vicsek phase diagram as a function of noise strength, density, and particle speed. A neural-network classifier is trained on global polar-order labels, and classifier entropy is used to select new simulations near uncertain crossover regions. The resulting phase map resolves a high-noise disordered gas, a low-noise polar ordered regime, and an intermediate coexistence-candidate regime whose noise window shifts upward and broadens with increasing density. Independent density and local-order diagnostics indicate that the intermediate regime contains dense, locally ordered bands coexisting with a dilute, weakly ordered background. Comparison with the ordered regime shows that banded coexistence is identified by the joint enhancement of band contrast, local-order heterogeneity, and positive density-order correlation. Overall, these results establish a machine-learning-guided workflow for active matter, in which active learning constructs an operational phase map and independent spatial diagnostics convert classifier-defined regimes into physically interpretable nonequilibrium morphologies.

Modern datacenters schedule heterogeneous workloads across geo-distributed sites with diverse compute capacities, electricity prices, and thermal conditions. Compute utilization, heat generation, cooling demand, and energy consumption are tightly coupled, yet most existing schedulers abstract these effects and treat them independently. We present \textit{DataCenterGym}, a physics-grounded simulation environment for job scheduling in geo-distributed data centers, designed as a reusable testbed for future research. The simulator integrates compute queueing, building thermal dynamics, localized HVAC behavior, and temperature-dependent service degradation within a Gymnasium-compatible interface. We also develop a Hierarchical Model Predictive Control (H-MPC) scheduling algorithm that performs distributed job placement while explicitly accounting for thermal and power dynamics. Through experiments on nominal operation and workload sensitivity, we demonstrate how H-MPC improves scheduling performance relative to baseline schedulers.

We show that nonequilibrium dynamics can play a constructive role in unsupervised machine learning by inducing the spontaneous emergence of latent-state cycles. We introduce a model in which visible and hidden variables interact through two independently parametrized transition matrices, defining a Markov chain whose steady state is intrinsically out of equilibrium. Likelihood maximization drives this system toward nonequilibrium steady states with finite entropy production, reduced self-transition probabilities, and persistent probability currents in the latent space. These cycles are not imposed by the architecture but arise from training, and models that develop them reproduce the empirical distribution of data classes more faithfully, with a clear correlation between agreement with the data and entropy production. Compared with equilibrium approaches such as restricted Boltzmann machines, our model breaks the detailed balance between the forward and backward conditional transitions and relies on a log-likelihood gradient that depends explicitly on the last two steps of the Markov chain. Hence, this exploration of the interface between nonequilibrium statistical physics and modern machine learning suggests that introducing irreversibility into latent-variable models can improve the fidelity of the generated data distribution.

The flow matching has rapidly become a dominant paradigm in classical generative modeling, offering an efficient way to interpolate between two complex distributions. We extend this idea to the quantum realm and introduce the Quantum Flow Matching (QFM), a quantum-circuit realization that offers efficient interpolation between two density matrices. QFM offers systematic preparation of density matrices and generation of samples for accurately estimating observables, and can be realized on quantum computers without the need for costly circuit redesigns. We validate its versatility on a set of applications: (i) generating target states with prescribed magnetization and entanglement entropy, (ii) estimating nonequilibrium free-energy differences to test the quantum Jarzynski equality, and (iii) expediting the study on superdiffusion. These results position QFM as a unifying and promising framework for generative modeling across quantum systems.

We show that the out-of-equilibrium driving protocol of score-based generative models (SGMs) can be learned via local learning rules. The gradient with respect to the parameters of the driving protocol is computed directly from force measurements or from observed system dynamics. As a demonstration, we implement an SGM in a network of driven, nonlinear, overdamped oscillators coupled to a thermal bath. We first apply it to the problem of sampling from a mixture of two Gaussians in 2D. Finally, we train an oscillator network on the MNIST dataset to generate images of handwritten digits 0 and 1.