1,932 papers
Run, Tumble and Paint
The visit probability, quantifying whether a particle has reached a given point for the first time by a specified time, provides access to various extreme value statistics and serves as a fundamental tool for characterising active matter models. However, previous studies have largely neglected how the visit probability depends on the internal degree of freedom driving the active particle. To address this, we calculate the "state-dependent'' visit probability for a Run-and-Tumble particle, that is the probability that the particle first passes through $x$ before time $t$, keeping track of its internal state during first passage. This process may be thought of as the particle "painting'' the positions it passes through for the time in the colour of its self-propulsion state. We perform this calculation in one dimension using Doi-Peliti field theory, by extending the tracer mechanism from previous works to incorporate such "polar deposition'' and demonstrate that state-dependent visit probabilities can be elegantly captured within this field-theoretic framework. We further derive the total volume covered by a right- (or left-) moving Run-and-Tumble particle and compare our results with known expressions for Brownian motion.
2603.24277Mar 2026
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Dynamical thermalization and turbulence in social stratification models
We study the nonlinear chaotic dynamics in a system of linear oscillators coupled by social network links with an additional stratification of oscillator energies, or frequencies, and supplementary nonlinear interactions. It is argued that this system can be viewed as a model of social stratification in a society with nonlinear interacting agents with energies playing a role of wealth states of society. The Hamiltonian evolution is characterized by two integrals of motion being energy and probability norm. Above a certain chaos border the chaotic dynamics leads to dynamical thermalization with the Rayleigh-Jeans (RJ) distribution over states with given energy or wealth. At low energies, this distribution has RJ condensation of norm at low energy modes. We point out a similarity of this condensation with the wealth inequality in the world countries where about a half of population owns only a couple of percent of the total wealth. In the presence of energy pumping and absorption, the system reveals features of the Kolmogorov-Zakharov turbulence of nonlinear waves.
2603.24190Mar 2026
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Digitally Optimized Initializations for Fast Thermodynamic Computing
Thermodynamic computing harnesses the relaxation dynamics of physical systems to perform matrix operations. A key limitation of such approaches is the often long thermalization time required for the system to approach equilibrium with sufficient accuracy. Here, we introduce a hybrid digital-thermodynamic algorithm that substantially accelerates relaxation through optimized initializations inspired by the Mpemba effect. In the proposed scheme, a classical digital processor efficiently computes an initialization that suppresses slow relaxation modes, after which the physical system performs the remaining computation through its intrinsic relaxation dynamics. We focus on overdamped Langevin dynamics for quadratic energy landscapes, analyzing the spectral structure of the associated Fokker-Planck operator and identifying the corresponding optimal initial covariances. This yields a predictable reduction in thermalization time, determined by the spectrum of the encoded matrix. We derive analytic expressions for the resulting speedups and numerically analyze thermodynamic implementations of matrix inversion and determinant computation as concrete examples. Our results show that optimized initialization protocols provide a simple and broadly applicable route to accelerating thermodynamic computations.
2603.24183Mar 2026
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2603.24151Universality of order statistics for Brownian reshuffling
We discuss the order statistics of the particle positions of a gas of $N$ identical independent particles performing Brownian motion in one dimension in a potential that asymptotically behaves like $V(x) \sim x^γ$ for $x\rightarrow+\infty$, with a positive power $γ>0$. We show that in the stationary state, the order statistics that describe how the leaders are reshuffled are universal and independent of $γ$. What depends on $γ$ is the timescale of the leaders' reshuffling, which scales as a power of the logarithm of the population size: $t \sim (\ln N)^\frac{2(1-γ)}γ τ$, where $τ$ is of order one. We derive the probability that the particle which has the $k$th largest value of $x$ at some time $t_1$ will have the $j$th largest value at time $t_2=t_1+t$ in the form of an explicit expression for the generating function for the reshuffling probabilities for all $k\ge 1$ and $j\ge 1$. The generating function, expressed in scaled time $τ$, is independent of $γ$. In particular, we show that the average percentage overlap coefficient of leader lists takes the universal, $γ$-independent form ${\rm erfc}(\sqrtτ)$ for long lists.
2603.24151Mar 2026
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Mpemba effect in a two-dimensional bistable potential
We present an exactly solvable model of the Mpemba effect in an overdamped Langevin system confined in a two-dimensional radially symmetric bistable potential. The potential is constructed as a piecewise quadratic-logarithmic function that is continuous and differentiable at the matching radii, enabling an exact mapping of the corresponding Fokker-Planck operator to a Schroedinger-type eigenvalue problem. The relaxation spectrum and eigenmodes are obtained analytically in each region in terms of confluent hypergeometric functions, with eigenvalues determined from matching conditions. Focusing on isotropic equilibrium initial states at inverse temperature $β_{\rm ini}$ quenched to a bath at inverse temperature $β$, we derive explicit expressions for the mode amplitudes governing long-time relaxation. We demonstrate that the coefficient of the slowest mode exhibits non-monotonic dependence on $β_{\rm ini}$ and identify a sufficient crossing condition for the Kullback-Leibler divergence in terms of the two slowest modes, if the global minimum of the potential is located far away from the origin and the second minimum exists near the origin. For corresponding parameters, we demonstrate that the Mpemba effect can be realized. Our results provide a rare example of an analytically tractable two-dimensional model exhibiting anomalous relaxation without any confining walls, extending previous one-dimensional constructions with a hard wall and clarifying the role of radial geometry in nonequilibrium relaxation phenomena.
2603.24148Mar 2026
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Universal scaling laws for dynamical-thermal hysteresis
Dynamic hysteresis, the rate-dependent lagged response of materials to external fields, underpins applications from energy-efficient transformers to gas storage systems. A fundamental yet unresolved question is how the hysteresis loop area $A$ scales with the field sweep rate $R$. Here, we reveal that a competition between the field sweep and thermal fluctuations governs a universal crossover between two scaling regimes: $A - A_0 \propto R^{1/3}$ for $R < R^*$ and $A - A_0 \propto R^{2/3}$ for $R > R^*$, where $A_0$ is the quasi-static area and the crossover rate $R^* \propto T/T_c$ depends on the temperature $T$ and the material's critical temperature $T_c$. We demonstrate these scaling laws universally across experiments of magnetic materials, simulations of Ising and metal-organic framework models, and analytical solutions of a stochastic Langevin equation. This framework not only resolves the long-standing non-universality of reported scaling exponents but also provides a direct design principle for the application of dynamic hysteresis.
2603.24007Mar 2026
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Fading ergodicity and quantum dynamics in random matrix ensembles
Recent work has proposed fading ergodicity as a mechanism for many-body ergodicity breaking. Here, we show that two paradigmatic random matrix ensembles -- the Rosenzweig-Porter model and the ultrametric model -- fall within the same universality class of ergodicity breaking when embedded in a many-body Hilbert space of spins-1/2. By calibrating the parameters of both models via their Thouless times, we demonstrate that the matrix elements of local observables display similar statistical properties, allowing us to identify the fractal phase of the Rosenzweig-Porter model with the fading-ergodicity regime. This correspondence is further supported through the analyses of quantum-quench dynamics of local observables, their temporal fluctuations and power spectra, and survival probabilities. Our findings reveal that local observables thermalize within the fading-ergodicity regime on timescales shorter than the Heisenberg time, thus providing a unified framework for understanding ergodicity breaking across these distinct models.
2603.23616Mar 2026
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The Fermi-Pasta-Ulam-Tsingou problem after 70 years: Universal laws of thermalization in lattice systems
Over the past decade, substantial progress has been made in clarifying a central question of the Fermi-Pasta-Ulam-Tsingou problem: whether weakly nonlinear lattice systems thermalize and, if so, through what mechanisms. The current understanding is as follows. (a) Classical lattice systems fall into two universal classes. In the first, the Hamiltonian has extended normal modes. For sufficiently large systems, the thermalization time scales as $T_{\rm eq}\sim g^{-γ}$ with $γ=2$, where $g$ denotes the effective nonlinear strength, i.e., the perturbation strength or degree of non-integrability. Thus, in the thermodynamic limit, these systems inevitably thermalize. Typical examples include common one-, two-, and three-dimensional lattice models. In the second class, all normal modes are localized. Here the relaxation time is essentially independent of system size. Although one may still formally write $T_{\rm eq}\sim g^{-γ}$, the exponent $γ$ diverges as $g\to0$, implying that arbitrarily weak nonlinear perturbations cannot induce thermalization. For sufficiently small $g$, such systems may therefore be viewed, in a theoretical sense, as thermal insulators. (b) In systems of the first class, disorder does not obstruct thermalization. Rather, by breaking translational symmetry and relaxing wave-vector resonance constraints, it increases the number of quasi-resonant processes and can therefore accelerate thermalization. (c) In systems of the second class, when both on-site potentials and disorder are present, all normal modes become localized in sufficiently large systems, suppressing thermalization. The perturbative framework underlying these conclusions will also be presented systematically, with particular emphasis on the thermalization criterion based on resonance-network connectivity, an approach rooted in weak wave turbulence theory.
2603.23347Mar 2026
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Internal stress drives ferromagnetic-like ordering in networks of proliferating bacteria
Proliferation is a defining feature of life. Through growth, division, and death, living systems consume energy and inject mass, breaking conservation laws and driving collective phenomena from biofilm formation to embryonic development. Yet, while active matter physics has advanced our understanding of self-propelled agents, quantitative frameworks for proliferating systems are still emerging, and most work focuses on simplified settings. Here, we study \textit{E.coli} bacteria growing inside a network of single-file microchannels as a minimal model of structured environments. Competition for free volume drives the spontaneous emergence of coherent growth patterns that persist across generations but vanish when the channel links exceed the typical cell size at birth. Despite the strongly out-of-equilibrium character of the dynamics, the observed phenomenology can be quantitatively captured by an effective equilibrium description in which the flow state at each node is represented by a spin variable with ferromagnetic interactions. Simulations of growing elastic cells show that this coupling arises from internal stress accumulated at network nodes due to dynamical constraints. Our results reveal a surprising correspondence between proliferating active matter and equilibrium statistical mechanics, highlighting open fundamental questions and offering a first step toward describing growth phenomena in real-world complex environments.
2603.23320Mar 2026
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A $q$-Caputo Fractional Generalization of Tsallis Entropy: Series Representation and Non-Negativity Domains
We introduce a fractional generalization of Tsallis entropy by acting with a $q$-Caputo operator on the generating family $\sum_i p_i^{\,x}$ evaluated at $x=1$. Concretely, we define $S_{q}^α$ through the $q$-Caputo differintegral of order $0<α<1$ and derive a closed series representation in terms of the $q$-Gamma function. The construction is anchored at the evaluation point, which ensures well-behaved limits: as $α\!\to\!1$ we recover the standard Tsallis entropy $S_q$. Finally we perform a numerical calculation to show the regions where the obtained $q$-fractional entropy $S^α_q$ can be non-negative (or negative) through the fractional parameter $α$ and the non extensive index $q$.
2603.23254Mar 2026
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Dynamics of O(2) excitations in a non-reciprocal medium
We investigate emergent dynamics due to non-reciprocity in the $\mathcal{O}(2)$ model. The lattice XY model, where non-reciprocity stems from vision cone like couplings, can be described by a continuum description in which non-reciprocity translates into a new term depending on the rotational of the orientation field. We argue that non-reciprocity is akin to activity and we highlight the connection between our hydrodynamic equation and the constant density Toner-Tu framework. The active force advects and reshapes patterns, a generic feature found in many non-reciprocal systems. We show how $1d$ excitations in the non-reciprocal $\mathcal{O}(2)$ model can be described by a generalized Burgers equation, derived from our continuum model. We then extend the results to $2d$ perturbations. As such, we establish the first principles of excitation trajectory control in a non-reciprocal $\mathcal{O}(2)$ medium. Concretely, we explain how tuning the degree of non-reciprocity and the orientation of the background medium impacts the time evolution of excitations. We also showcase how initially different excitations lead to very different dynamical behavior. Non-reciprocity also affects the stability of defect-free excitations with non-zero winding numbers and, unlike in its equilibrium $O(2)$ counterpart, enables the system, above a certain threshold, to relax to its ground state.
2603.23225Mar 2026
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Amplification based on the noise-induced negative differential resistance in a Zener diode
A voltage biased Zener diode always exhibit positive differential resistance, thus cannot be used as an element to provide amplification of a signal. We show how to induce negative differential resistance in the reverse bias regime of a 12V Zener diode by noise feedback. We use this to build a voltage amplifier in the audio frequency range, which we characterize by providing bandwidth, gain, power consumption, gain compression and output noise spectral density.
2603.23169Mar 2026
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Basis dependence of eigenstate thermalization
Eigenstate thermalization refers to the property that an energy eigenstate of a many-body system is indistinguishable from a thermal equilibrium ensemble at the same energy as far as expectation values of local observables are concerned. In systems with degeneracies, the choice of an energy eigenbasis is not unique and the fraction of basis states exhibiting eigenstate thermalization can vary. We present a simple example where this fraction vanishes in the thermodynamic limit for one basis choice, but remains nonzero for another choice. In other words, the weak eigenstate thermalization hypothesis is satisfied in the first, but violated in the second basis. We furthermore prove that degeneracies must abound whenever a system is simultaneously symmetric under spatial translations and reflection. Finally, we derive general bounds on how strongly eigenstate thermalization may depend on the choice of the basis, and we reveal some interesting implications regarding the temporal relaxation properties of such systems.
2603.23058Mar 2026
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Dynamics of Aligning Active Matter: Mapping to a Schrödinger Equation and Exact Diagonalization
There has been recent interest in the relaxational modes of small-scale fully connected systems of aligning self-propelled particles (Spera et al., Phys. Rev. Lett. {\bf 132}: 078301 (2024)). We revisit the classical connection between Fokker-Planck and Schrödinger equations to address this by means of exact diagonalization, allowing for rigorous analytical insight into the full spectrum. This allows us to extract exact results which we compare to the existing result from linearized statistical field theory. We derive asymptotically correct analytical results that improve upon the prior approximations. We show that this methodology can fruitfully be extended to the case of non-reciprocal interactions which gives rise to a non-Hermitian Schrödinger problem akin to those in open quantum mechanics. While the non-reciprocity can be chosen such as not to alter the stationary distribution, it fundamentally changes the nature of the steady state which we quantify via the entropy production. We discuss the case of low particle numbers as well as the emergence of mean-field dynamics at large numbers.
2603.23021Mar 2026
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Genuine and spurious (non-)ergodicity in single particle tracking
In single-particle tracking experiments measuring anomalous diffusion dynamics, understanding ergodicity is crucial, as it ensures that the time average of an observable matches the ensemble average, and can thus be fitted with known ensemble-averaged observables. A commonly used criterion for assessing the ergodicity of a stochastic process is based on the comparison of the mean-squared displacement (MSD) with the time-averaged MSD (TAMSD). This approach has been widely applied and proves effective in cases of weak ergodicity breaking across various systems in both theoretical and experimental studies. However, there is relatively little discussion regarding the theoretical justification and limitations of this definition. Here, we demonstrate that this widely accepted criterion to some extent contradicts the classical definition of ergodicity as well as physical intuition, leading to spurious (non-)ergodicity results when applied to several well-known stochastic models. To address this limitation, we propose using the mean-squared increment (MSI) instead of the MSD for comparison of ensemble- and time-averaged observables. Several well-established examples demonstrate that our MSI-TAMSD criterion not only effectively reveals weak ergodicity breaking, equivalent to the MSD-TAMSD approach, but also provides a more accurate characterization of the genuine (non-)ergodicity of systems where the MSD-TAMSD method fails. Additionally, for systems exhibiting "ultraweak" ergodicity breaking, the MSI can reveal the asymptotic stationarity and ergodic nature of the process' increments. Our findings emphasize the important role of the MSI observable for SPT experiments and anomalous diffusion studies.
2603.22989Mar 2026
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Pseudospectral phenomena and the origin of the non-Hermitian skin effect
The non-Hermitian skin effect (NHSE), characterized by a macroscopic accumulation of eigenstates at the edge of a system with open boundaries, is often ascribed to a non-trivial point-gap topology of the Bloch Hamiltonian. We revisit this connection and show that the eigenspectrum of non-normal operators is highly sensitive to boundary conditions and generic perturbations, and therefore does not constitute a stable object encoding topological information. Instead, topological properties are reflected in the singular-value spectrum of finite systems and, in the semi-infinite limit, correspond to boundary-localized eigenmodes implied by the index of the corresponding Toeplitz operator. For a Hatano-Nelson ladder, where point-gap winding and non-normality can be varied independently, we demonstrate that the NHSE can occur without point-gap winding and, conversely, that point-gap winding can persist without the NHSE. These results establish that the NHSE originates from spectral instability and non-reciprocity rather than topology, and that the commonly assumed relation between spectral winding and boundary localization relies on translational invariance and is therefore not generic.
2603.22643Mar 2026
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Geometric Thermodynamics of Cycles: Curvature and Local Thermodynamic Response
Classical thermodynamics contains familiar geometric relations associated with cyclic processes, most notably the identification of mechanical work with the area enclosed by a trajectory in the $(P,V)$ plane. We show that the area laws for work and reversible heat arise as projections of a single canonical two--form defined on the equilibrium thermodynamic manifold, providing a unified description of thermodynamic cycles in both the $(P,V)$ and $(T,S)$ representations. The same structure yields a direct link between cycle geometry and thermodynamic response: the work generated by infinitesimal cycles is set locally by the mixed curvature $U_{SV}$ of the equilibrium energy surface, which can be expressed in terms of measurable susceptibilities. This identifies thermodynamic work as a local geometric field over state space rather than solely a global property of cyclic processes. More broadly, the framework connects classical cycle geometry to stochastic thermodynamic trajectories, providing a geometric interpretation of nonequilibrium work relations such as the Jarzynski equality.
2603.22559Mar 2026
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The damage spreading transition: a hierarchy of renormalization group fixed points
Deterministic classical cellular automata can be in two phases, depending on how irreversible the dynamical rules are. In the strongly irreversible phase, trajectories with different initial conditions coalesce quickly, while in the weakly irreversible phase, trajectories with different initial conditions can remain different for a time exponential in the system volume. The transition between these phases is referred to as the damage-spreading transition (the "damaged" sites are those that differ between the trajectories). We develop a theory for this transition. In the simplest and most generic setting, the transition is known to be related to directed percolation, one of the best-studied nonequilibrium phase transitions. However, we show that full theory of the damage-spreading critical point is richer than directed percolation, and contains an infinite hierarchy of sectors of local observables. Directed percolation describes the first level of the hierarchy. The higher observables include "overlaps" for multiple trajectories, and may be labeled by set partitions. (These higher observables arise naturally if, for example, we consider decay of entropy under the irreversible dynamics.) The full hierarchy yields a hierarchy of nonequilibrium fixed points for reaction-diffusion-type processes, all of which contain directed percolation as a subsector, but which possess additional universal critical exponents. We analyze these higher fixed points using a field theory formulation and renormalization group arguments, and using simulations in 1+1 dimensions.
2603.22439Mar 2026
View2603.22424How active field theories couple to external potentials
We study the simplest terms that need to be included in active field theories to couple them to external potentials. To do so, we consider active Brownian particles and implement a systematic perturbative expansion in the particle persistence time. The result is a non-trivial coupling between density and potential gradients, which accounts for the nonequilibrium features of active particles in the presence of an external potential, from boundary accumulation to far-field density modulation. We show how the method can be applied to particles interacting via pairwise forces and to spatial modulations of the propulsion speed.
2603.22424Mar 2026
View2603.22163Dissipative free fermions in disguise
Recently, a class of spin chains known as ``free fermions in disguise'' (FFD) has been discovered, which possess hidden free-fermion spectra even though they are not solvable via the standard Jordan-Wigner transformation. In this work, we extend this FFD framework to open quantum systems governed by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. We establish a general class of exactly solvable open quantum systems within the FFD framework: if the Liouvillian frustration graph is claw-free and has a simplicial clique, the Liouvillian possesses a hidden free-fermion spectrum. In particular, the (even-hole, claw)-free condition automatically guarantees this, enabling exact computation of the Liouvillian gap and an infinite-temperature autocorrelation function. Our results provide the first realization of the FFD mechanism in open quantum systems.
2603.22163Mar 2026
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