arXiv subjects

Cai Dieball

Publications and source records attributed to Cai Dieball.

16 recordsLinked to original sources

arXiv2026

A graph theoretic view on small signal stability of inverter-based power grids

Dynamic grid stability is traditionally ensured with synchronous generators. Modern grids rely substantially more on inverter-based resources, which require grid-forming control to guarantee adequate system-wide synchronization and stability. Small-signal stability has granted various centralized and decentralized stability certificates - but these have primarily been limited to sufficient criteria only. In this work, we construct a necessary and sufficient small-signal stability criterion for lossless inverter-based power grids with arbitrary topology. We show that asymptotic stability is equivalent to the positive definiteness of a single matrix that combines network topology, operating point, and effective droop gains. We derive graph-theoretic stability criteria based on an augmented cone graph and show that the contribution of graph cycles is typically small, as illustrated for three IEEE test cases. The resulting framework yields decentralized stability criteria, quantifies the conservatism introduced by decentralization, and may support the development of future grid codes.

eess.SY↗

arXiv2026

Thermal relaxation asymmetry persists under inertial effects

Relaxation phenomena far from thermal equilibrium feature a rich phenomenology, including the thermal relaxation asymmetry. The latter states that heating occurs faster than cooling in overdamped harmonic systems quantified in terms of excess free energy and entropy production. Upon isolating the relevant relaxational contribution to the entropy production, we here algebraically prove the asymmetry in thermal relaxation in phase space in the entire range from overdamped dynamics to underdamped dynamics. We show that for the same setup as for overdamped dynamics (i.e., motion in harmonic potentials, also known as Ornstein-Uhlenbeck dynamics), even in the more general case of phase-space relaxation, i.e., underdamped dynamics, far-from-equilibrium heating is faster than cooling. The coupling of positions and velocities emerging in this generalization further underscores, in a striking manner, the intricate dynamics of such thermal relaxation processes that do not pass through local equilibria. Investigating the overdamped limit, our generalized approach reveals, interestingly, that an excess free energy contribution from the velocity degrees of freedom does not trivially vanish in the overdamped limit, but is instead affected by the precise interpretation of temperature quenches in overdamped systems.

cond-mat.stat-mech↗

arXiv2025

Permutation-Invariant Spectral Learning via Dyson Diffusion

Diffusion models are central to generative modeling and have been adapted to graphs by diffusing adjacency matrix representations. The challenge of having up to $n!$ such representations for graphs with $n$ nodes is only partially mitigated by using permutation-equivariant learning architectures. Despite their computational efficiency, existing graph diffusion models struggle to distinguish certain graph families and their spectra, unless graph data are augmented with ad hoc features. This shortcoming stems from enforcing the inductive bias within the learning architecture. In this work, we leverage random matrix theory to analytically extract the spectral properties of the diffusion process, allowing us to push most of the inductive bias from the architecture into the dynamics. Building on this, we introduce the Dyson Diffusion Model, which employs Dyson's Brownian motion to capture the spectral dynamics of an Ornstein-Uhlenbeck process on the adjacency matrix. Furthermore, conditioned on the spectral dynamics, we formulate a Lie group diffusion, appropriately modeling the remaining degrees of freedom. Strikingly, the resulting learning problem becomes permutation invariant at the Lie algebra level. We demonstrate that the Dyson Diffusion Model learns graph spectra accurately and outperforms existing graph diffusion models.

stat.ML↗

arXiv2025

Stochastic Calculus for Pathwise Observables of Markov-Jump Processes: Unification of Diffusion and Jump Dynamics

Path-wise observables--functionals of stochastic trajectories--are at the heart of time-average 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 path-wise 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 path-wise 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 path-wise observables of Markov-jump processes. We formulate a "Langevin equation" for jump processes, define general path-wise 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 discus saturation conditions. We determine the response of path-wise observables to general (incl. 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.

cond-mat.stat-mech↗

arXiv2025

Thermodynamic correlation inequalities for finite times and transients

Recently, a thermodynamic bound on correlation times was formulated in [A. Dechant, J. Garnier-Brun, S.-i. Sasa, Phys. Rev. Lett. 131, 167101 (2023)], showing how the decay of correlations in Langevin dynamics is bounded by short-time fluctuations and dissipation. Whereas these original results only address very long observation times in steady-state dynamics, we here generalize the respective inequalities to finite observations and general initial conditions. We utilize the connection between correlations and the fluctuations of time-integrated density functionals and generalize the direct stochastic calculus approach from [C. Dieball and A. Godec, Phys. Rev. Lett. 130, 087101 (2023)] which paves the way for further generalizations. We address the connection between short and long time scales, as well as the saturation of the bounds via complementary spectral-theoretic arguments. Motivated by the spectral insight, we formulate all results also for complex-valued observables.

cond-mat.stat-mech↗

arXiv2025

Precisely controlled colloids: A playground for path-wise non-equilibrium physics

We investigate path-wise observables in experiments on driven colloids in a periodic light field to dissect selected intricate transport features, kinetics, and transition-path time statistics out of thermodynamic equilibrium. These observables directly reflect the properties of individual paths in contrast to the properties of an ensemble of particles, such as radial distribution functions or mean-squared displacements. In particular, we present two distinct albeit equivalent formulations of the underlying stochastic equation of motion, highlight their respective practical relevance, and show how to interchange between them. We discuss conceptually different notions of local velocities and interrogate one- and two-sided first-passage and transition-path time statistics in and out of equilibrium. Our results reiterate how path-wise observables may be employed to systematically assess the quality of experimental data and demonstrate that, given sufficient control and sampling, one may quantitatively verify subtle theoretical predictions.

cond-mat.soft↗

arXiv2025

Perspective: Time irreversibility in systems observed at coarse resolution

A broken time-reversal symmetry, i.e. broken detailed balance, is central to non-equilibrium physics and is a prerequisite for life. However, it turns out to be quite challenging to unambiguously define and quantify time-reversal symmetry (and violations thereof) in practice, that is, from observations. Measurements on complex systems have a finite resolution and generally probe low-dimensional projections of the underlying dynamics, which are well known to introduce memory. In situations where many microscopic states become "lumped" onto the same observable "state" or when introducing "reaction coordinates" to reduce the dimensionality of data, signatures of a broken time-reversal symmetry in the microscopic dynamics become distorted or masked. In this perspective we highlight why in defining and discussing time-reversal symmetry, and quantifying its violations, the precise underlying assumptions on the microscopic dynamics, the coarse graining, and further reductions, are not a technical detail. These assumptions decide whether the conclusions that are drawn are physically sound or inconsistent. We summarize recent findings in the field and reflect upon key challenges.

cond-mat.stat-mech↗

arXiv2024

Thermodynamic bounds on generalized transport: From single-molecule to bulk observables

We prove that the transport of any differentiable scalar observable in $d$-dimensional non-equilibrium systems is bounded from above by the total entropy production scaled by the amount the observation "stretches" microscopic coordinates. The result--a time-integrated generalized speed limit--reflects the thermodynamic cost of transport of observables, and places underdamped and overdamped stochastic dynamics on equal footing with deterministic motion. Our work allows for stochastic thermodynamics to make contact with bulk experiments, and fills an important gap in thermodynamic inference, since microscopic dynamics is, at least for short times, underdamped. Requiring only averages but not sample-to-sample fluctuations, the proven transport bound is practical and applicable not only to single-molecule but also bulk experiments where only averages are observed, which we demonstrate by examples. Our results may facilitate thermodynamic inference on molecular machines without an obvious directionality from bulk observations of transients probed, e.g.\ in time-resolved X-ray scattering.

cond-mat.stat-mech↗

arXiv2023

Asymmetric Thermal Relaxation in Driven Systems: Rotations go Opposite Ways

It was predicted and recently experimentally confirmed that systems with microscopically reversible dynamics in locally quadratic potentials warm up faster than they cool down. This thermal relaxation asymmetry challenged the local-equilibrium paradigm valid near equilibrium. Because the intuition and proof hinged on the dynamics obeying detailed balance, it was not clear whether the asymmetry persists in systems with irreversible dynamics. To fill this gap, we here prove the relaxation asymmetry for systems driven out of equilibrium by a general linear drift. The asymmetry persists due to a non-trivial isomorphism between driven and reversible processes. Moreover, rotational motions emerge that, strikingly, occur in opposite directions during heating and cooling. This highlights that noisy systems do not relax by passing through local equilibria.

cond-mat.stat-mech↗

arXiv2023

Heating and Cooling are Fundamentally Asymmetric and Evolve Along Distinct Pathways

According to conventional wisdom, a system placed in an environment with a different temperature tends to relax to the temperature of the latter, mediated by the flows of heat and/or matter that are set solely by the temperature difference. It is becoming clear, however, that thermal relaxation is much more intricate when temperature changes push the system far from thermodynamic equilibrium. Interestingly, under such conditions heating was predicted to be faster than cooling, which we experimentally confirm using an optically trapped colloidal particle. More strikingly, we show with both experiments and theory that between any pair of temperatures, heating is not only faster than cooling but the respective processes in fact evolve along fundamentally distinct pathways, which we explain with a new theoretical framework we coin "thermal kinematics".

cond-mat.stat-mech↗

arXiv2023

Direct Route to Thermodynamic Uncertainty Relations and Their Saturation

Thermodynamic uncertainty relations (TURs) bound the dissipation in non-equilibrium systems from below by fluctuations of an observed current. Contrasting the elaborate techniques employed in existing proofs, we here prove TURs directly from the Langevin equation. This establishes the TUR as an inherent property of overdamped stochastic equations of motion. In addition, we extend the transient TUR to currents and densities with explicit time-dependence. By including current-density correlations we, moreover, derive a new sharpened TUR for transient dynamics. Our arguably simplest and most direct proof, together with the new generalizations, allows us to systematically determine conditions under which the different TURs saturate and thus allows for a more accurate thermodynamic inference. Finally we outline the direct proof also for Markov jump dynamics.

cond-mat.stat-mech↗

arXiv2023

Feynman-Kac theory of time-integrated functionals: Itô versus functional calculus

The fluctuations of dynamical functionals such as the empirical density and current as well as heat, work and generalized currents in stochastic thermodynamics are usually studied within the Feynman-Kac tilting formalism, which in the Physics literature is typically derived by some form of Kramers-Moyal expansion, or in the Mathematical literature via the Cameron-Martin-Girsanov approach. Here we derive the Feynman-Kac theory for general additive dynamical functionals directly via Itô calculus and via functional calculus, where the latter result in fact appears to be new. Using Dyson series we then independently recapitulate recent results on steady-state (co)variances of general additive dynamical functionals derived recently in Dieball and Godec ({2022 \textit{Phys. Rev. Lett.}~\textbf{129} 140601}) and Dieball and Godec ({2022 \textit{Phys. Rev. Res.}~\textbf{4} 033243}). We hope for our work to put the different approaches to the statistics of dynamical functionals employed in the field on a common footing, and to illustrate more easily accessible ways to the tilting formalism.

cond-mat.stat-mech↗

arXiv2022

On correlations and fluctuations of time-averaged densities and currents with general time-dependence

We present technical results required for the description and understanding of correlations and fluctuations of the empirical density and current as well as diverse time-integrated and time-averaged thermodynamic currents of diffusion processes with a general time dependence on all time scales. In particular, we generalize the results from arXiv:2105.10483 (Phys. Rev. Lett., article in press), arXiv:2204.06553 (Phys. Rev. Research, article in press), and arXiv:2206.04034 to additive functionals with explicit time dependence and transient or non-ergodic overdamped diffusion. As an illustration we apply the results to two-dimensional harmonically confined overdamped diffusion in a rotational flow evolving from a non-stationary initial distribution.

cond-mat.stat-mech↗

arXiv2022

Mathematical, Thermodynamical, and Experimental Necessity for Coarse Graining Empirical Densities and Currents in Continuous Space

We present general results on fluctuations and spatial correlations of the coarse-grained empirical density and current of Markovian diffusion in equilibrium or non-equilibrium steady states on all time scales. We unravel a deep connection between current fluctuations and generalized time-reversal symmetry, providing new insight into time-averaged observables. We highlight the essential role of coarse graining in space from mathematical, thermodynamical, and experimental points of view. Spatial coarse graining is required to uncover salient features of currents that break detailed balance, and a thermodynamically "optimal" coarse graining ensures the most precise inference of dissipation. Defined without coarse graining, the fluctuations of empirical density and current are proven to diverge on all time scales in dimensions higher than one, which has far-reaching consequences for the central-limit regime in continuous space. We apply the results to examples of irreversible diffusion. Our findings provide new intuition about time-averaged observables and allow for a more efficient analysis of single-molecule experiments.

cond-mat.stat-mech↗

arXiv2022

Coarse Graining Empirical Densities and Currents in Continuous-Space Steady States

We present the conceptual and technical background required to describe and understand the correlations and fluctuations of the empirical density and current of steady-state diffusion processes on all time scales -- observables central to statistical mechanics and thermodynamics on the level of individual trajectories. We focus on the important and non-trivial effect of a spatial coarse graining. Making use of a generalized time-reversal symmetry we provide deeper insight about the physical meaning of fluctuations of the coarse-grained empirical density and current, and explain why a systematic variation of the coarse-graining scale offers an efficient method to infer bounds on a system's dissipation. Moreover, we discuss emerging symmetries in the statistics of the empirical density and current, and the statistics in the central-limit regime. More broadly our work promotes the application of stochastic calculus as a powerful direct alternative to Feynman-Kac theory and path-integral methods.

cond-mat.stat-mech↗

arXiv2021

Scattering fingerprints of two-state dynamics

Particle transport in complex environments such as the interior of living cells is often (transiently) non-Fickian or anomalous, that is, it deviates from the laws of Brownian motion. Such anomalies may be the result of small-scale spatio-temporal heterogeneities in, or viscoelastic properties of, the medium, molecular crowding, etc. Often the observed dynamics displays multi-state characteristics, i.e. distinct modes of transport dynamically interconverting between each other in a stochastic manner. Reliably distinguishing between single- and multi-state dynamics is challenging and requires a combination of distinct approaches. To complement the existing methods relying on the analysis of the particle's mean squared displacement, position- or displacement-autocorrelation function, and propagators, we here focus on "scattering fingerprints" of multi-state dynamics. We develop a theoretical framework for two-state scattering signatures -- the intermediate scattering function and dynamic structure factor -- and apply it to the analysis of simple model systems as well as particle-tracking experiments in living cells. We consider inert tracer-particle motion as well as systems with an internal structure and dynamics. Our results may generally be relevant for the interpretation of state-of-the-art differential dynamic microscopy experiments on complex particulate systems, as well as inelastic or quasielastic neutron (incl. spin-echo) and X-ray scattering scattering probing structural and dynamical properties of macromolecules, when the underlying dynamics displays two-state transport.

cond-mat.stat-mech↗