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Clemens Bechinger

Publications and source records attributed to Clemens Bechinger.

At least 19 recordsLinked to original sources
arXiv2026

Equivalence classes of finite-time transitions in optimal control and non-equilibrium relaxation

We present a theory for the optimal control of stochastic systems in structured environments, represented by penalty terms in the cost functional. We show that such control problems generically feature sharp finite-time transitions associated with a qualitative change in the control strategy at a critical time. Starting from an overdamped Langevin equation and a quadratic cost functional, we show that all resulting problems fall into three canonical equivalence classes (parabolic, hyperbolic, and elliptic), distinguished by the sign of the determinant of the control Hamiltonian. For each class, we obtain the optimal protocol, the cost function, and the critical time in closed form, and show that the transition exhibits features of a continuous phase transition at mean-field level. We then establish a mapping between the optimal control cost and the large-deviation rate function governing non-equilibrium relaxation after a potential quench. The mapping covers the parabolic and hyperbolic classes, while the elliptic class has no simple relaxation counterpart. This correspondence implies that recently discovered finite-time dynamical phase transitions, which are exponentially costly to sample directly, are accessible through ordinary averages over optimally controlled trajectories. To validate our theoretical findings, we report three experiments with optically trapped colloidal particles: a control transition for the mean stochastic work, and the finite-time dynamical phase transitions in free diffusion and in harmonic relaxation.

cond-mat.stat-mech↗
arXiv2026

Memory with Onsager-Casimir symmetry: Rotating particle in a viscoelastic fluid

We study the stochastic dynamics of a rotating Brownian particle in a non-Markovian fluid. Experimentally, we find that rotation enhances the long-time diffusivity of the particle and generates time-antisymmetric cross-correlations between orthogonal displacement components in the plane perpendicular to the rotation axis. To rationalize these observations, we introduce a minimal linear model in which a tracer is coupled to a slow bath degree of freedom and rotation enters through an advective coupling. Eliminating the bath variable yields a generalized Langevin equation with a non-reciprocal memory kernel. This kernel rotates in time, forming a logarithmic spiral, and it obeys Onsager-Casimir symmetry under reversal of the rotation vector, and the corresponding fluctuation-response relation. From the latter we obtain a geometric construction that links two-time cross-correlations to the transverse response of the particle in bulk. Unlike the ordinary Einstein relation, this relation involves the antisymmetric sector of the response. Our experiments and theory are in qualitative agreement, establishing rotating colloids in viscoelastic fluids as a minimal realization of Onsager-Casimir symmetry in time-nonlocal stochastic dynamics

cond-mat.stat-mech↗
arXiv2026

Bath-modes quantitatively capture the nonlinear microrheology of micellar solutions

Active microrheology experiments, in which a probe is driven through a complex fluid, often exhibit nonlinear responses that cannot be captured by generalized Langevin equations. Models that couple the probe to a Gaussian field reproduce such nonlinear effects qualitatively, but their large number of parameters hinders direct comparison with experiments. Here, we restrict these models to a small number of field modes and demonstrate that this reduced description quantitatively reproduces a broad range of active microrheology experiments in a micellar solution using a single set of parameters. We further show that the same framework extends naturally to multi-probe systems, such as colloidal dumbbells.

cond-mat.soft↗
arXiv2026

Work Extraction via Backward Motion in Optimal Closed-Loop Stochastic Control

We experimentally realize finite-time feedback control in an overdamped colloidal system using real-time optical tweezers with in situ reinforcement learning (RL). By varying the protocol duration tf for displacing the optical trap between prescribed positions, the optimal strategies identified by RL reveal a crossover from deterministic dragging toward the target to feedback-assisted exploitation of thermal fluctuations, reducing and eventually overcoming the energetic cost. The resulting policies agree quantitatively with the exact optimal closed-loop solution. By extending the approach to spatially localized external forcing, we further show that RL can identify optimal feedback strategies in heterogeneous stochastic environments where direct analytical control design is challenging.

cond-mat.stat-mech↗
arXiv2026

Finite-time transitions in optimal control and non-equilibrium relaxation

We theoretically and experimentally study finite-time optimal control of a colloidal particle steered through a spatially inhomogeneous environment, modeled by a position-dependent energetic cost at the final state. The competition between this state-dependent penalty and path-dependent dissipation gives rise to a sharp transition in the control strategy at a critical control duration. We further show that this transition can be linked to a dynamical phase transition in nonequilibrium relaxation after a quench, where the control cost maps onto the rate function governing rare trajectories.

cond-mat.stat-mech↗
arXiv2026

Energy-Efficient Control of Interacting Microscopic Systems: When Longer Paths Save Energy

We experimentally and theoretically study the thermodynamically optimal control of interacting multiple-particle systems, focusing on collections of colloidal particles individually confined in optical traps. We investigate protocols that transport the system between prescribed trap configurations within a fixed time in the most energy efficient way. For Markovian systems with conservative pairwise interactions, we establish a general result in the low-noise limit: optimal particle trajectories are linear in space and time, corresponding to steady straight-line motion, irrespective of the specific interaction potential, even for nonlinear forces. Thus, conservative interactions do not modify the geometry of the optimal paths. This property breaks down in the presence of strong noise or nonconservative interactions. For the paradigmatic case of hydrodynamic coupling, we demonstrate experimentally that optimal control can involve curved trajectories that significantly reduce the energetic cost by exploiting collectively generated fluid flows. The emergence of curved paths as optimal solutions highlights a fundamental distinction between non-interacting and interacting systems and reveals a cooperative mechanism for energy-efficient control.

cond-mat.soft↗
arXiv2026

Extracting work from hidden degrees of freedom

Thermodynamics establishes that information acquired through measurement can be converted into work, as exemplified by Maxwell's demon and Szilard engines. Most experimental realizations of information engines, however, implicitly assume Markovian environments, in which information exchanged with the surroundings is irreversibly lost. Many physical systems instead exhibit environmental memory, with hidden degrees of freedom retaining correlations with the system's past and giving rise to non Markovian dynamics. Whether and how such concealed memory can be harnessed as a thermodynamic resource has remained an open question. Here we experimentally demonstrate work extraction from environmental memory. Using time resolved measurements on an optically trapped Brownian particle in equilibrium, we implement a time delayed double measurement protocol that retrieves information via backflow from hidden bath degrees of freedom. We show that this information backflow alters relaxation dynamics, can be quantified independently of initial state effects, and when appropriately exploited enhances work extraction. Notably, we identify regimes in which the extracted work exceeds the energy stored in the observable degree of freedom alone. Our results establish environmental memory as an experimentally accessible thermodynamic resource and reveal how non Markovian dynamics can be systematically explored to improve the performance of information engines operating in time-correlated environments.

cond-mat.soft↗
arXiv2026

Nonmonotonic Magnetic Friction from Collective Rotor Dynamics

Amontons' law postulates a monotonic relationship between frictional force and the normal load applied to a sliding contact. This empirical rule, however, fails in systems where internal degrees of freedom - such as structural or electronic order - play a central role. Here, we demonstrate that friction can emerge entirely from magnetically driven configurational dynamics in the absence of physical contact. Using a two-dimensional array of rotatable magnetic dipoles sliding over a commensurate magnetic substrate, we observe a pronounced non-monotonic dependence of friction on the interlayer separation, and thus on the effective load. The friction peaks at an intermediate distance where competing ferromagnetic and antiferromagnetic interactions induce dynamical frustration and hysteretic torque cycles during sliding. Molecular dynamics simulations and a simplified two-sublattice model confirm that energy dissipation is governed by collective magnetic reorientations and their hysteresis. Our results establish the occurrence of sliding-induced changes in collective magnetic order, which has a strong impact on friction, and thus open new possibilities for contactless friction control, magnetic sensing, and the design of reconfigurable, wear-free frictional interfaces and metamaterials.

cond-mat.mtrl-sci↗
arXiv2026

Reservoir computing from collective dynamics of active colloidal oscillators

Physical reservoir computing is a computational framework that offers an energy- and computation-efficient alternative to conventional training of neural networks. In reservoir computing, input signals are mapped into the high-dimensional dynamics of a nonlinear system, and only a simple readout layer is trained. In most physical implementations, the interactions that give rise to the dynamics cannot be tuned directly and high dimensionality is typically achieved through time-multiplexing, which can limit flexibility and efficiency. Here we introduce a reservoir composed of hundreds of hydrodynamically coupled active colloidal oscillators forming a fully parallel physical reservoir and whose coupling strength and fading-memory time can be tuned in situ. The collective dynamics of the active oscillators allow accurate predictions of chaotic time series from single reservoir readouts without time-multiplexing. We further demonstrate real-time detection of subtle hidden anomalies that preserve all instantaneous statistical properties of the signal yet disrupt its underlying temporal correlations. These results establish interacting active colloids as a reconfigurable platform for physical computation and edge-integrated intelligent sensing for model-free detection of irregularities in complex time signals.

cond-mat.soft↗
arXiv2025

Negative drag force on beating flagellar-shaped bodies in active fluids

We experimentally investigate the drag force exerted by a suspension of light-induced active particles (APs) on a translating and beating idealized flagellum-shaped object realized through negative phototactic interactions with the APs. We observe both positive and negative drag forces, depending on the beating frequency and translational velocity, driven by the dynamic redistribution of APs in response to the object's motion. These findings are supported by numerical simulations and an analytical model, extendable to a range of slender geometries. Our results illustrate the complex interplay between geometric body changes and the density distribution in active baths, which may also be relevant for microrobotic applications.

cond-mat.soft↗
arXiv2025

Equilibrium trajectories quantify second order violation of fluctuation dissipation theorem without need of a model

Quantifying and characterizing fluctuations far away from equilibrium is a challenging task. We discuss and experimentally confirm a series expansion for a driven classical system, relating the different non-equilibrium cumulants of the observable conjugate to the driving protocol. This series is valid from micro- to macroscopic length scales, and it encompasses the fluctuation dissipation theorem. We apply it in experiments of a Brownian probe particle confined and driven by an optical potential and suspended in a nonlinear and non-Markovian fluid. The expansion states that the form of FDT remains valid away from equilibrium for Gaussian observables, up to the order presented. We show that this expansion agrees with the expansion of a known fluctuation theorem up to an unresolved difference regarding moments versus cumulants.

cond-mat.stat-mech↗
arXiv2024

The 2024 Motile Active Matter Roadmap

Activity and autonomous motion are fundamental aspects of many living and engineering systems. Here, the scale of biological agents covers a wide range, from nanomotors, cytoskeleton, and cells, to insects, fish, birds, and people. Inspired by biological active systems, various types of autonomous synthetic nano- and micromachines have been designed, which provide the basis for multifunctional, highly responsive, intelligent active materials. A major challenge for understanding and designing active matter is their inherent non-equilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Furthermore, interactions in ensembles of active agents are often non-additive and non-reciprocal. An important aspect of biological agents is their ability to sense the environment, process this information, and adjust their motion accordingly. It is an important goal for the engineering of micro-robotic systems to achieve similar functionality. With many fundamental properties of motile active matter now reasonably well understood and under control, the ground is prepared for the study of physical aspects and mechanisms of motion in complex environments, of the behavior of systems with new physical features like chirality, of the development of novel micromachines and microbots, of the emergent collective behavior and swarming of intelligent self-propelled particles, and of particular features of microbial systems. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter poses major challenges, which can only be addressed by a truly interdisciplinary effort involving scientists from biology, chemistry, ecology, engineering, mathematics, and physics.

cond-mat.soft↗
arXiv2024

Counterfactual rewards promote collective transport using individually controlled swarm microrobots

Swarm robots offer fascinating opportunities to perform complex tasks beyond the capabilities of individual machines. Just as a swarm of ants collectively moves a large object, similar functions can emerge within a group of robots through individual strategies based on local sensing. However, realizing collective functions with individually controlled microrobots is particularly challenging due to their micrometer size, large number of degrees of freedom, strong thermal noise relative to the propulsion speed, complex physical coupling between neighboring microrobots, and surface collisions. Here, we implement Multi-Agent Reinforcement Learning (MARL) to generate a control strategy for up to 200 microrobots whose motions are individually controlled by laser spots. During the learning process, we employ so-called counterfactual rewards that automatically assign credit to the individual microrobots, which allows for fast and unbiased training. With the help of this efficient reward scheme, swarm microrobots learn to collectively transport a large cargo object to an arbitrary position and orientation, similar to ant swarms. We demonstrate that this flexible and versatile swarm robotic system is robust to variations in group size, the presence of malfunctioning units, and environmental noise. Such control strategies can potentially enable complex and automated assembly of mobile micromachines, programmable drug delivery capsules, and other advanced lab-on-a-chip applications.

cs.RO↗
arXiv2023

Average negative heat in a non-Markovian bath

We experimentally study the motion of a colloidal particle, translated back and forth within a viscoelastic, i.e. non-Markovian bath. The particle starts in equilibrium before the forward motion, but only partially relaxes at the turning point. During the backward motion, we measure a systematic (negative) heat flow from the bath to the particle. Our observations are in good agreement with a simple model that describes the time-delayed response of the fluid. We expect our results to be important for the realization and optimization of novel types of micro-engines in non-Markovian surroundings.

cond-mat.soft↗
arXiv2023

Universal symmetry of optimal control at the microscale

Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge of optimal driving protocols is particularly valuable at the microscale, where energy supply is often limited. Here we investigate experimentally and theoretically the paradigmatic optimization problem of moving a potential carrying a load through a fluid, in a finite time and over a given distance, in such a way that the required work is minimal. An important step towards more realistic systems is the consideration of memory effects in the surrounding fluid, which are ubiquitous in real-world applications. Therefore, our experiments were performed in viscous and viscoelastic media, which are typical environments for synthetic and biological processes on the microscale. Despite marked differences between the protocols in both fluids, we find that the optimal control protocol and the corresponding average particle trajectory always obey a time-reversal symmetry. We show that this symmetry, which surprisingly applies here to a class of processes far from thermal equilibrium, holds universally for various systems, including active, granular, and long-range correlated media in their linear regimes. The uncovered symmetry provides a rigorous and versatile criterion for optimal control that greatly facilitates the search for energy-efficient transport strategies in a wide range of systems. Using a machine learning algorithm, we demonstrate that the algorithmic exploitation of time-reversal symmetry can significantly enhance the performance of numerical optimization algorithms.

cond-mat.soft↗
arXiv2023

Motility-induced clustering of active particles under soft confinement

We investigate the structural and dynamic properties of active Brownian particles (APs) confined within a soft annulus-shaped channel. Depending on the strength of the confinement and the P\'eclet number, we observe a novel re-entrant behavior that is not present in unconfined systems. Our findings are substantiated by numerical simulations and analytical considerations, revealing that this behavior arises from the strong coupling between the P\'eclet number and the effective confining dimensionality of the APs. Beyond highlighting the important influence of soft boundaries on APs, our research holds significance for future applications of micro-robotic systems.

cond-mat.soft↗
arXiv2023

Memory-induced alignment of colloidal dumbbells

When a colloidal probe is forced through a viscoelastic fluid which is characterized by a long stress-relaxation time, the fluid is excited out of equilibrium. This is leading to a number of interesting effects including a non-trivial recoil of the probe when the driving force is removed. Here, we experimentally and theoretically investigate the transient recoil dynamics of non-spherical particles, i.e., colloidal dumbbells. In addition to a translational recoil of the dumbbells, we also find a pronounced angular reorientation which results from the relaxation of the surrounding fluid. Our findings are in good agreement with a Langevin description based on the symmetries of a director (dumbbell) as well as a microscopic bath-rod model. Remarkably, we find a frustrated state with amplified fluctuations when the dumbbell is oriented perpendicular to the direction of driving. Our results demonstrate the complex behavior of non-spherical objects within a relaxing environment which are of immediate interest for the motion of externally but also self-driven asymmetric objects in viscoelastic fluids.

cond-mat.soft↗
arXiv2023

Environmental effects on emergent strategy in micro-scale multi-agent reinforcement learning

Multi-Agent Reinforcement Learning (MARL) is a promising candidate for realizing efficient control of microscopic particles, of which micro-robots are a subset. However, the microscopic particles' environment presents unique challenges, such as Brownian motion at sufficiently small length-scales. In this work, we explore the role of temperature in the emergence and efficacy of strategies in MARL systems using particle-based Langevin molecular dynamics simulations as a realistic representation of micro-scale environments. To this end, we perform experiments on two different multi-agent tasks in microscopic environments at different temperatures, detecting the source of a concentration gradient and rotation of a rod. We find that at higher temperatures, the RL agents identify new strategies for achieving these tasks, highlighting the importance of understanding this regime and providing insight into optimal training strategies for bridging the generalization gap between simulation and reality. We also introduce a novel Python package for studying microscopic agents using reinforcement learning (RL) to accompany our results.

physics.bio-ph↗