arXiv subjects

Gunnar Pruessner

Publications and source records attributed to Gunnar Pruessner.

At least 19 recordsLinked to original sources

arXiv2026

Large Spin-Wave Fluctuations Suppress Activity in Malthusian Flocks

Novel phases, beyond long-range order in two dimensions, have continued to be discovered within flocking models, establishing flocking as one of the pivotal paradigms in active matter. However, much of the discussion around ``Malthusian'' (constant density) flocks, an analytically more tractable alternative to the Vicsek model, has centred around the scaling exponents governing the intermediate regime prior to the proliferation of asters, leaving open the question of what other phases the model might display. Here, we study the two-dimensional dynamics of Malthusian flocks and identify a previously unnoticed phase, where the dynamics is that of the equilibrium XY Model. By identifying the symmetries of the model, we derive the effective equations of motion for the Goldstone modes and analyse the spin-wave fluctuations. We identify a novel critical point separating two distinct phases and, using a perturbative RG procedure, determine the RG flows in its vicinity. This allows us to calculate the universal scaling behaviour at the critical point, along with its logarithmic corrections. The novel phase transition here is due to the interaction of activity and spin-waves, unlike the equilibrium counterpart, which undergoes a phase transition in effective degrees of freedom, namely vortices. Nevertheless, the RG flows are similar to those of the Berezinskii-Kosterlitz-Thouless transition, and we show that for sufficiently strong noise, the activity becomes irrelevant and the system crosses over to the equilibrium XY universality class.

cond-mat.soft↗

arXiv2026

Partial Entropy production of active particles with hidden states in potentials

Partially observed stochastic systems can appear (almost) time-reversal symmetric while in fact operating far from equilibrium. The present work extends the perturbative framework introduced in [Phys. Rev. Lett. 136, 198302 (2026)] to calculate in a generic confining potential the partial entropy production, which quantifies the time-reversal asymmetry of a generic active particle with hidden self-propulsion. Focusing on the harmonic case, we apply our framework to reproduce an exact result for the partial entropy production rate of an active Ornstein-Uhlenbeck particle and to derive the partial entropy production rate of a run-and-tumble particle.

cond-mat.stat-mech↗

arXiv2026

Critical Dynamics of Non-Reciprocally Coupled Conserved Systems

Non-reciprocal systems have been shown to sustain time-dependent patterns, most prominently travelling waves. The transition into these time-dependent states generally breaks time-translational invariance, representing a clear deviation from equilibrium dynamics. Though common implementations of non-reciprocity lead to such phenomenology, these spatio-temporal patterns are absent in other models. In the same vein, the ensuing scaling behaviour also depends on the precise way non-reciprocity is implemented. To better understand the effects of different non-reciprocal interactions, we study the critical conserved dynamics of non-reciprocally coupled spin systems. Specifically, we consider the dynamics of two $n$-component order parameter fields $\boldsymbol{\phi}_i$ with $i \in\{1,2\}$. Unlike the common implementations of non-reciprocal interactions, we introduce the non-reciprocity solely through the non-linear interaction between the distinct species. Using the field-theoretic renormalisation group (RG) procedure, we perform a one-loop analysis and show that at one-loop level, the critical behaviour depends on the microscopic value of certain quantities. Using the flow functions, we elucidate the behaviour of the fixed points for different bare microscopic values. We also show that for $n \geq 4$, there is a fixed point where the ensuing critical dynamics asymptotically obey detailed-balance, implying the emergent dynamics are agnostic to the microscopic non-reciprocity on large scales. Finally, we show that the conserved dynamics reduces the number of independent scaling exponents, mimicking the effect of a standard fluctuation-dissipation relation.

cond-mat.stat-mech↗

arXiv2026

Effective attraction by repulsion

Repulsive self-propelled particles tend to cluster, leading to Motility-Induced Phase Separation (MIPS). By analogy with equilibrium phase separation, the onset of MIPS has been associated with a transition to effective attraction between particles. Using an exact microscopic theory, we quantify the emergence of effective attraction in a minimal model: two soft run-and-tumble particles in a periodic domain. We show that, as repulsion increases, the leading-order behaviour is that of effective repulsion, while effective attraction emerges as a higher-order contribution to the renormalisation of the pair potential.

cond-mat.stat-mech↗

arXiv2026

Microscopic theory of soft run-and-tumble particles

Soft, repulsive run-and-tumble particles display emergent effective interactions as they appear to stick to each other in spite of the absence of attractive forces. This effective attraction emerges at strong enough repulsion and large self-propulsion. Complementing a companion paper that characterises effective attraction between two soft run-and-tumble particles [Garcia-Millan et al., Effective attraction by repulsion (2026)], here we provide a thorough derivation of our microscopic theory, which is an exact representation of the particle dynamics. We report the systematic calculation of the effective interaction vertices iteratively, in a perturbation expansion about the interaction couplings, by adding, order by order, loop corrections. We use the effective interaction vertices to calculate the two-point correlation function, fully characterising the stationary state. Other observables, such as the structure factor, overlap probability and entropy production rate are calculated as well.

cond-mat.stat-mech↗

arXiv2026

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.

cond-mat.stat-mech↗

arXiv2025

Exact results and instabilities in the harmonic approximation of active crystals

Condensates of active particles such as cells form almost-crystalline lattices which play a central role in many biological systems. Typically, their properties have been determined merely by analogy to the rather trivial one-dimensional case, leaving a gap between experimentally accessible observables and suitable theoretical models. Within a harmonic approximation, we characterise analytically a two-dimensional triangular lattice of active particles that interact with their nearest neighbours through a general pair potential, obtaining exact expressions for the correlators. We study this "active crystal" as a means of characterising active matter in the dense phase. Our treatment correctly approximates arbitrary pair potentials, rather than demanding an unphysical non-singular bilinear form. We retain "off-diagonal" terms that are routinely neglected despite quantifying the anisotropy of the particles' local potential. From the exact expressions for the correlation matrices, we derive exact results that shed light on the presence (or absence) of crystalline order. We further calculate the mean-squared particle separation, energy, entropy production rate and the onset of a pressure-induced instability resulting in the breakdown of the harmonic approximation. The entropy production rate is found to have a general form that is valid for generic active particles and lattice geometries, while resembling that of non-interacting "active modes".

cond-mat.soft↗

arXiv2025

Conditional splitting probabilities for hidden-state inference in drift-diffusive processes

Splitting probabilities quantify the likelihood of particular outcomes out of a set of mutually-exclusive possibilities for stochastic processes and play a central role in first-passage problems. For two-dimensional Markov processes $\{X(t),Y(t)\}_{t\in T}$, a joint analogue of the splitting probabilities can be defined, which captures the likelihood that the variable $X(t)$, having been initialised at $x_0 \in \mathbb{L}$, exits $\mathbb{L}$ for the first time via either of the interval boundaries \emph{and} that the variable $Y(t)$, initialised at $y_0$, is given by $y_{\rm exit}$ at the time of exit. We compute such joint splitting probabilities for two classes of processes: processes where $X(t)$ is Brownian motion and $Y(t)$ is a decoupled internal state, and unidirectionally coupled processes where $X(t)$ is drift-diffusive and depends on $Y(t)$, while $Y(t)$ evolves independently. For the first class we obtain generic expressions in terms of the eigensystem of the Fokker-Planck operator for the $Y$ dynamics, while for the second we carry out explicit derivations for three paradigmatic cases (run-and-tumble motion, diffusion in an intermittent piecewise-linear potential and diffusion with stochastic resetting). Drawing on Bayes' theorem, we subsequently introduce the related notion of conditional splitting probabilities, defined as the posterior likelihoods of the internal state $Y$ \emph{given} that the observable degree of freedom $X$ has undergone a specific exit event. After computing these conditional splitting probabilities, we propose a simple scheme that leverages them to partially infer the assumedly hidden state $Y(t)$ from point-wise detection events.

math-ph↗

arXiv2025

Stochastic cloaking: concealing a region from diffusive particles

We introduce "stochastic cloaking," where a region of space is concealed from an ensemble of diffusing particles whose individual trajectories are governed by a stochastic (Langevin) equation. Our simulations reveal how different interpretations of the Langevin equation affect the cloaking performance of an annular single-layer invisibility cloak of smoothly varying diffusivity in two dimensions. Near-perfect cloaking is achieved under the Ito convention, indicated by the cloak preventing particles from accessing an inner core without disturbing the particle density outside the cloak. The cloak's performance can be further improved by regularising its singular behaviour. We believe our demonstration of stochastic cloaking is a significant milestone, comparable to earlier developments that extended cloaking from optics and acoustics to thermodynamics.

cond-mat.mtrl-sci↗

arXiv2025

Self-propulsion symmetries determine entropy production of active particles with hidden states

Entropy production distinguishes equilibrium from non-equilibrium. Calculating the entropy production rate (EPR) is challenging in systems where some degrees of freedom cannot be observed. Here we introduce a perturbative framework to calculate the ``partial EPR'' of a canonical hidden-state system, a generic self-propelled active particle with hidden self-propulsion. We find that the parity symmetry, P, and (time-)reversibility, T, of the hidden variable determine partial entropy production. Non-trivial entropy production appears at least at sixth order in the self-propulsion velocity. We apply our framework to two processes which break P- and T-symmetries respectively: an asymmetric telegraph process and diffusion with stochastic resetting.

cond-mat.stat-mech↗

arXiv2025

Hyperuniformity at the Absorbing State Transition: Perturbative RG for Random Organization

Hyperuniformity, where the static structure factor obeys $S(q)\sim q^ς$ with $ς> 0$, emerges at criticality in systems having multiple, symmetry-unrelated, absorbing states. Important examples arise in periodically sheared suspensions and amorphous solids; these lie in the random organisation (RO) universality class, for which analytic results for $ς$ are lacking. Here, using Doi-Peliti field theory and perturbative RG about a Gaussian model, we find $ς= 0^+$ and $ς= 2ε/9 + O(ε^2)$ in dimension $d>d_c=4$ and $d=4-ε$ respectively. Our calculations assume that renormalizability is sustained via a certain pattern of cancellation of strongly divergent terms. These cancellations allow the upper critical dimension to remain $d_c = 4$, as is known for RO, while generic perturbations (e.g., those violating particle conservation) would typically flow to a fixed point with $d_c=6$. The assumed cancellation pattern is closely reminiscent of a long-established one near the tricritical Ising fixed point. (This has $d_c=3$, although generic perturbations flow towards the Wilson-Fisher fixed point with $d_c = 4$.) We show how hyperuniformity in RO emerges from anticorrelation of strongly fluctuating active and passive densities. Our calculations also yield the remaining exponents to order $ε$, surprisingly without recourse to functional RG. These exponents coincide as expected with the Conserved Directed Percolation (C-DP) class which also contains the Manna Model and the quenched Edwards-Wilkinson (q-EW) model. Importantly however, our $ς$ differs from one found via a mapping to q-EW. That mapping neglects a conserved noise in the RO action, which we argue to be dangerously irrelevant. Thus, although other exponents are common to both, the RO and C-DP universality classes have different exponents for hyperuniformity.

cond-mat.stat-mech↗

arXiv2025

Looking Back: Field theory of transiently chiral active particles

We derive a Doi-Peliti Field Theory for transiently chiral active particles in two dimensions, that is, active Brownian particles that undergo tumbles via a diffusing reorientation angle. Using this framework, we compute the mean squared displacement for both uniformly distributed and fixed initial reorientations. We also calculate an array of orientation-based observables, to quantify the transiently chiral behaviour observed.

cond-mat.stat-mech↗

arXiv2025

Eph-ephrin-mediated differential persistence as a mechanism for cell sorting

The phenomenon of cell sorting/segregation, by which cells organise spatially into clusters of specific cell type or function, is essential for tissue morphogenesis. This self-organization process involves an interplay between mechanical, biochemical, and cellular mechanisms that act across various spatial and temporal scales. Several mechanisms for cell sorting have been proposed; however, the physical nature of these mechanisms and how they lead to symmetric or asymmetric cell sorting remains unclear. Here, using experimental data from cocultures of genetically modified Human Embryonic Kidney (HEK293) cells and numerical simulations, we show the existence of a cell sorting mechanism based on transient increases in the persistence of motion of cells. This mechanism is activated on cells overexpressing the ephrinB1-related receptor EphB2 after their interaction with cells overexpressing ephrinB1. We show that this mechanism is sufficient to cause cell sorting, breaking the symmetry of the sorting dynamics, and show that the duration of this transient differential persistence state is optimal for enhancing sorting. Furthermore, we show that in combination with other interaction mechanisms, such as changes in direction-also known as contact inhibition of locomotion-and adhesion forces, differential persistence significantly reduces the timescale of sorting. Our findings offer insights into the behaviour of cell mixtures, the relevance of non-reciprocal interactions, and may provide insight into developmental processes and tissue patterning.

physics.bio-ph↗

arXiv2025

Numerical investigation of the Brownian $q=2$ Potts Model

In active matter, such as the Vicsek Model of flocking, particles possesses an internal degree of freedom, such as their director, which is subject to interaction with other particles, provided they are within a certain range. In an effort to understand better the interplay between spatial and internal degrees of freedom, we study numerically a variation of the $q=2$ Potts Model on and off the lattice, where particles are additionally subject to Brownian motion. The lack of a feedback of the internal degrees of freedom to the spatial degrees of freedom renders this model generically non-equilibrium. We confirm previous work that showed that the static exponents of the phase transition are unaffected by the diffusion. In contrast to previous work, we show that the formation of ordered clusters is not undermined by diffusion, but should rather be thought of as an effective form of interaction. We demonstrate how our numerical findings can be understood on the basis of the well-established Model A, B and C: Off lattice, the Brownian $q=2$ Potts Model is Model C. On the lattice, it is Model A with an additional (irrelevant, conserved) Model B noise.

cond-mat.stat-mech↗

arXiv2025

Field theories of active particle systems and their entropy production

Active particles that translate chemical energy into self-propulsion can maintain a far-from-equilibrium steady state and perform work. The entropy production measures how far from equilibrium such a particle system operates and serves as a proxy for the work performed. Field theory offers a promising route to calculating entropy production, as it allows for many interacting particles to be considered simultaneously. Approximate field theories obtained by coarse-graining or smoothing that draw on additive noise can capture densities and correlations well, but they generally ignore the microscopic particle nature of the constituents, thereby producing spurious results for the entropy production. As an alternative we demonstrate how to use Doi-Peliti field theories, which capture the microscopic dynamics, including reactions and interactions with external and pair potentials. Such field theories are in principle exact, while offering a systematic approximation scheme, in the form of diagrammatics. We demonstrate how to construct them from a Fokker-Planck equation and show how to calculate entropy production of active matter from first principles. This framework is easily extended to include interaction. We use it to derive exact, compact and efficient general expressions for the entropy production for a vast range of interacting conserved particle systems. These expressions are independent of the underlying field theory and can be interpreted as the spatial average of the local entropy production. They are readily applicable to numerical and experimental data. In general, the entropy production due to any pair interaction draws at most on the three point, equal time density; and an $n$-point interaction on the $(2n-1)$-point density. We illustrate the technique in a number of exact, tractable examples, including some with pair-interaction as well as in a system of many interacting ABPs.

cond-mat.stat-mech↗

arXiv2023

Memoryless Chemotaxis with Discrete Cues

A wide array of biological systems can navigate in shallow gradients of chemoattractant with remarkable precision. Whilst previous approaches model such systems using coarse-grained chemical density profiles, we construct a dynamical model consisting of a chemotactic cell responding to discrete cue particles. For a cell without internal memory, we derive an effective velocity with which the cell approaches a point source of cue particles. We find that the effective velocity becomes negative beyond some homing radius, which represents an upper bound on the distance within which chemotaxis can be reliably performed. This work lays the foundation for the analytical characterisation of more detailed models of chemotaxis.

physics.bio-ph↗

arXiv2023

Correlation, crossover and broken scaling in the Abelian Manna Model

The role of correlations in self-organised critical (SOC) phenomena is investigated by studying the Abelian Manna Model (AMM) in two dimensions. Local correlations of the debris left behind after avalanches are destroyed by re-arranging particles on the lattice between avalanches, without changing the one-point particle density. It is found that the spatial correlations are not relevant to small avalanches, while changing the scaling of the large (system-wide) ones, yielding a crossover in the model's scaling behaviour. This crossover breaks the simple scaling observed in normal SOC.

cond-mat.stat-mech↗

arXiv2023

Field theory of survival probabilities, extreme values, first passage times, and mean span of non-Markovian stochastic processes

We provide a perturbative framework to calculate extreme events of non-Markovian processes, by mapping the stochastic process to a two-species reaction diffusion process in a Doi-Peliti field theory combined with the Martin-Siggia-Rose formalism. This field theory treats interactions and the effect of external, possibly self-correlated noise in a perturbation about a Markovian process, thereby providing a systematic, diagrammatic approach to extreme events. We apply the formalism to Brownian Motion and calculate its survival probability distribution subject to self-correlated noise.

cond-mat.stat-mech↗