In order to describe the nonisothermal dynamics of two-phase flows or binary mixtures such as colloidal suspensions consisting of colloidal particles and solvent on a microscopic level, we derive a new extended dynamical density functional theory (EDDFT) that includes the total mass density, the local concentration of one species, the total momentum density, and the energy density as variables using the Mori-Zwanzig-Forster projection operator technique. Through the incorporation of the momentum density into EDDFT, not only the diffusive but also the convective dynamics is taken into account. We derive an exact entropy and free-energy functional for the case of hard spheres. The hydrodynamic limit of our new EDDFT and its relation to the mode-coupling theory of the glass transition are discussed. It is shown that EDDFT allows to obtain the correct value for the speed of sound.

Active colloidal microparticles require reliable actuation to sustain directed motion. Light-based propulsion is particularly attractive as it provides persistent energy supply and enables direct spatiotemporal control. Here, we introduce 3D-printable particles with symmetry-broken refractive index profiles (SBRIP particles) that achieve propulsion through direct momentum transfer from asymmetric light refraction. Internal refractive-index gradients provide optical symmetry breaking independent of external shape, fundamentally decoupling propulsion from particle geometry. Geometrically symmetry-broken particles with a homogeneous refractive index are another special case, where propulsion originates from refractive contrast at the boundary instead of within the particle. Unlike conventional systems relying on absorption or reflection, this transparency-based mechanism minimizes heating and mitigates shadowing in bulk suspensions. We present a theoretical framework for refractive propulsion as well as numerical simulations of the SBRIP particles using raytracing and the finite volume method. This is complemented by experiments, validating the momentum transfer mechanism using particles with geometric symmetry breaking. The high transparency of our particles ensures deep light penetration, enabling the realization of volumetric active matter. This opens pathways toward adaptive nonlinear optical materials where light-driven particle reorganization modulates the local refractive index, establishing a dynamic feedback loop between the optical field and the material structure.

Imitating the shape-encoded tactics of natural microswimmers—organisms that flip, roll, and rheotaxis through viscous fluids—could transform microfluidics, micromanufacturing, and targeted therapy. However, translating those geometric navigation cues into actively driven microrobots is an open, largely unexplored challenge. Here, inspired by the structure of sperm cells, we introduce a sound-propelled head-helix microparticle (“microrobot”) featuring an elliptical head and a spiral tail. This asymmetrical design interacts with the incident acoustic field, generating complex secondary flows that induce a torque, enabling the particle to reorient around its cross-section. The microparticle exhibits a preferred direction of propulsion and orientation when exposed to a traveling sound wave, reorienting if its initial alignment deviates from this preference. Both the preferred direction and orientation can be modulated by adjusting the sound frequency, and they further adapt to background flow fields in the environment. Furthermore, the microparticle exhibits rheotaxis-like motion, exhibiting wall-following motion with frequency-dependent sliding behavior. By moving towards the channel wall, it enters the region with the smallest flow velocities, allowing it to move antiparallel to the fluid. These findings contribute to the engineering of the trajectories of sound-propelled microparticles and to the development of next-generation microrobots for medical and other innovative applications. ### Competing Interest Statement The authors have declared no competing interest. European Research Council (ERC), 853309 ETH Research grant, 535275785 China Scholarship Council, 202206020125

The measurement of stresses and forces at the tissue level has proven to be an indispensable tool for the understanding of complex biological phenomena such as cancer invasion, embryo development or wound healing. One of the most versatile tools for force inference at the cell and tissue level are elastic force sensors, whose biocompatibility and tunable material properties make them suitable for many different experimental scenarios. The evaluation of those forces, however, is still a bottleneck due to the numerical methods seen in literature until now, which are usually slow and render low experimental yield. Here we present BeadBuddy, a ready-to-use platform for the evaluation of deformation and stresses from fluorescently labelled sensors within seconds. The strengths of BeadBuddy lie in the pre-computed analytical solutions of the elastic problem, the abstraction of data into Spherical Harmonics, and a simple user interface that creates a smooth workflow for force inference. ### Competing Interest Statement The authors have declared no competing interest.

The measurement of stresses and forces at the tissue level has proven to be an indispensable tool for the understanding of complex biological phenomena such as cancer invasion, embryo development, or wound healing. One of the most versatile tools for force inference at the cell and tissue level are elastic force sensors, whose biocompatibility and tunable material properties make them suitable for many different experimental scenarios. The evaluation of those forces, however, is still a bottleneck due to the numerical methods seen in the literature until now, which are usually slow and render low experimental yield. Here, we present BeadBuddy, a ready-to-use platform for the evaluation of deformation and stresses from fluorescently labeled sensors within seconds. The strengths of BeadBuddy lie in the precomputed analytical solutions of the elastic problem, the abstraction of data into spherical harmonics, and a simple user interface that creates a smooth workflow for force inference.

Crystalline or polycrystalline systems governed by odd elastic responses are known to exhibit complex dynamical behaviors involving self-propelled dynamics of topological defects with spontaneous self-rotation of chiral crystallites. Unveiling and controlling the underlying mechanisms require studies across multiple scales. We develop such a type of approach that bridges between microscopic and mesoscopic scales, in the form of a phase field crystal model incorporating transverse interactions. This continuum density field theory features two-dimensional parity symmetry breaking and odd elasticity, and generates a variety of interesting phenomena that agree well with recent experiments and particle-based simulations of active and living chiral crystals, including self-rotating crystallites, dislocation self-propulsion and proliferation, and fragmentation in polycrystals. We identify a distinct type of surface cusp instability induced by self-generated surface odd stress that results in self-fission of single-crystalline grains. This mechanism is pivotal for the occurrence of various anomalous grain dynamics for odd crystals, particularly the predictions of a transition from normal to reverse Ostwald ripening for self-rotating odd grains, and a transition from grain coarsening to grain self-fragmentation in the dynamical polycrystalline state with an increase of transverse interaction strength. We also demonstrate that the single-grain dynamics can be maneuvered through the variation of interparticle transverse interactions. This allows to steer the desired pathway of grain locomotion and to control the transition between grain self-rotation, self-rolling, and self-translation. Our results provide insights for the design and control of structural and dynamical properties of active odd elastic materials.

In the past years, the amount of research on active matter has grown extremely rapidly, a fact that is reflected in particular by the existence of more than 1000 reviews on this topic. Moreover, the field has become very diverse, ranging from theoretical studies of the statistical mechanics of active particles to applied work on medical applications of microrobots and from biological systems to artificial swimmers. This makes it very difficult to get an overview over the field as a whole. Here, we provide such an overview in the form of a metareview article that surveys the existing review articles and books on active matter. Thereby, this article provides a useful starting point for finding literature about a specific topic.

Inspired by Richard Feynman's 1959 lecture and the 1966 film Fantastic Voyage, the field of micro/nanorobots has evolved from science fiction to reality, with significant advancements in biomedical and environmental applications. Despite the rapid progress, the deployment of functional micro/nanorobots remains limited. This review of the technology roadmap identifies key challenges hindering their widespread use, focusing on propulsion mechanisms, fundamental theoretical aspects, collective behavior, material design, and embodied intelligence. We explore the current state of micro/nanorobot technology, with an emphasis on applications in biomedicine, environmental remediation, analytical sensing, and other industrial technological aspects. Additionally, we analyze issues related to scaling up production, commercialization, and regulatory frameworks that are crucial for transitioning from research to practical applications. We also emphasize the need for interdisciplinary collaboration to address both technical and nontechnical challenges, such as sustainability, ethics, and business considerations. Finally, we propose a roadmap for future research to accelerate the development of micro/nanorobots, positioning them as essential tools for addressing grand challenges and enhancing the quality of life.

In this book chapter, we review how systems of simple motile agents can be used as a pathway to intelligent systems. It is a well known result from nature that large groups of entities following simple rules, such as swarms of animals, can give rise to much more complex collective behavior in a display of emergence. This begs the question whether we can emulate this behavior in synthetic matter and drive it to a point where the collective behavior reaches the complexity level of intelligent systems. Here, we will use a formalized notion of "intelligent matter" and compare it to recent results in the field of active matter. First, we will explore the approach of emergent computing in which specialized active matter systems are designed to directly solve a given task through emergent behavior. This we will then contrast with the approach of physical reservoir computing powered by the dynamics of active particle systems. In this context, we will also describe a novel reservoir computing scheme for active particles driven ultrasonically or via light refraction.

The worldwide COVID-19 pandemic has led to a significant growth of interest in the development of mathematical models that allow to describe effects such as social distancing measures, the development of vaccines, and mutations. Several of these models are based on concepts from soft matter theory. Considerably less well investigated is the reverse direction, i.e., how results from epidemiological research can be of interest for the physics of colloids and polymers. In this work, we consider the SIR-DDFT model, a combination of the susceptible-infected-recovered (SIR) model from epidemiology with dynamical density functional theory (DDFT) from nonequilibrium soft matter physics, which allows for an explicit modeling of social distancing. We extend the SIR-DDFT model both from an epidemiological perspective by incorporating vaccines, asymptomaticity, reinfections, and mutations, and from a soft matter perspective by incorporating noise and self-propulsion and by deriving a phase field crystal (PFC) model that allows for a simplified description. On this basis, we investigate via computer simulations how epidemiological models are affected by the presence of non-reciprocal interactions. This is done in a numerical study of a zombie outbreak.

The hydrodynamics of thin films is typically described using phenomenological models whose connection to the microscopic particle dynamics is a subject of ongoing research. Existing methods based on density functional theory provide a good description of static thin films, but are not sufficient for understanding nonequilibrium dynamics. In this work, we present a microscopic derivation of the thin film equation using the Mori-Zwanzig projection operator formalism. This method allows to directly obtain the correct gradient dynamics structure along with microscopic expressions for the mobility and the free energy. Our results are verified against molecular dynamics simulations for both simple fluids and polymers.

Supplemental data for the following manuscript: Stephan Bröker, Michael te Vrugt, Raphael Wittkowski, "Collective dynamics and pair-distribution function of active Brownian ellipsoids"

The mechanical forces that cells experience from the tissue surrounding them are crucial for their behavior and development. Experimental studies of such mechanical forces require a method for measuring them. A widely used approach in this context is bead deformation analysis, where spherical particles are embedded into the tissue. The deformation of the particles then allows to reconstruct the mechanical stress acting on them. Existing approaches for this reconstruction are either very time-consuming or not sufficiently general. In this article, we present an analytical approach to this problem based on an expansion in solid spherical harmonics that allows us to find the complete stress tensor describing the stress acting on the tissue. Our approach is based on the linear theory of elasticity and uses an ansatz specifically designed for deformed spherical bodies. We clarify the conditions under which this ansatz can be used, making our results useful also for other contexts in which this ansatz is employed. Our method can be applied to arbitrary radial particle deformations and requires a very low computational effort. The usefulness of the method is demonstrated by an application to experimental data.

In the past years, the amount of research on active matter has grown extremely rapidly, a fact that is reflected in particular by the existence of more than 600 review articles on this topic. Moreover, the field has become very diverse, ranging from theoretical studies of the statistical mechanics of active particles to applied work on medical applications of microrobots and from biological systems to artificial swimmers. This makes it very difficult to get an overview over the field as a whole. Here, we provide such an overview in the form of a metareview article that surveys the existing review articles on active matter. Thereby, this article provides an introduction to the various subdisciplines of active matter science and constitutes a useful starting point for finding literature about a specific topic.

Nonreciprocal forces violating Newton's third law are common in a plethora of nonequilibrium situations ranging from predator-prey systems to the swarming of birds and effective colloidal interactions under flow. While many recent studies have focused on two species with nonreciprocal coupling, much less is examined for the basic single-component system breaking the actio and reactio equality of force within the same species. Here, we systematically derive the fundamental field theory of single-species nonreciprocal interactions from microscopic dynamics, leading to a generic framework termed Active Model N (N denoting nonreciprocity). We explore the rich dynamics of pattern formation in this intrinsic nonreciprocal system and the emergence of self-traveling states with persistent variation and flowing of active branched patterns. One particular new characteristic pattern is an interwoven self-knitting "yarn" structure with a unique feature of simultaneous development of micro- and bulk phase separations. The growth dynamics of a "ball-of-wool" active droplet towards these self-knitted yarn or branched states exhibits a crossover between different scaling behaviors. The mechanism underlying this distinct class of active phase separation is attributed to the interplay between force nonreciprocity and competition. Our predictions can be applied to various biological and artificial active matter systems controlled by single-species nonreciprocity.

Self-propelled particles in anisotropic environments can exhibit a motility that depends on their orientation. This dependence is relevant for a plethora of living organisms but difficult to study in controlled environments. Here, we present a macroscopic system of self-propelled vibrated granular particles on a striated substrate that displays orientation-dependent motility. An extension of the active Brownian motion model involving orientation-dependent motility and inertial effects reproduces and explains our experimental observations. The model can be applied to general n-fold symmetric anisotropy and can be helpful for predictive optimization of the dynamics of active matter in complex environments.

Recently, there has been much progress in the formulation and implementation of methods for generic many-particle simulations. These models, however, typically either do not utilize shared memory hardware or do not guarantee data-race freedom for arbitrary particle dynamics. Here, we present both a abstract formal model of particle dynamics and a corresponding domain-specific programming language that can guarantee data-race freedom. The design of both the model and the language are heavily inspired by the Rust programming language that enables data-race-free general-purpose parallel computation. We also present a method of preventing deadlocks within our model by a suitable graph representation of a particle simulation. Finally, we demonstrate the practicability of our model on a number of common numerical primitives from molecular dynamics.

The pair-distribution function, which provides information about correlations in a system of interacting particles, is one of the key objects of theoretical soft matter physics. In particular, it allows for microscopic insights into the phase behavior of active particles. While this function is by now well studied for two-dimensional active matter systems, the more complex and more realistic case of three-dimensional systems is not well understood by now. In this work, we analyze the full pair-distribution function of spherical active Brownian particles interacting via a Weeks-Chandler-Andersen potential in three spatial dimensions using Brownian dynamics simulations. Besides extracting the structure of the pair-distribution function from the simulations, we obtain an analytical representation for this function, parametrized by activity and concentration, which takes into account the symmetries of a homogeneous stationary state. Our results are useful as input to quantitative models of active Brownian particles and advance our understanding of the microstructure in dense active fluids.

The study of active soft matter has developed into one of the most rapidly growing areas of physics. Field theories, which can be developed either via phenomenological considerations or by coarse-graining of a microscopic model, are a very useful tool for understanding active systems. Here, we provide a detailed review of a particular coarse-graining procedure, the interaction-expansion method (IEM). The IEM allows for the systematic microscopic derivation of predictive field theories for systems of interacting active particles. We explain in detail how it can be used for a microscopic derivation of active model B+, which is a widely used scalar active matter model. Extensions and possible future applications are also discussed.

Employing acoustofluidic simulations, we study the propulsion of cone-shaped nano- and microparticles by a traveling ultrasound wave. In particular, we investigate how the acoustic propulsion of the particles depends on their size and the energy density and frequency of the ultrasound wave. Our results reveal that the flow field generated around the particles depends on all three of these parameters. The results also show that the propulsion velocity of a particle increases linearly with the particle size and energy density and that an increase of the sound frequency leads to an increase of the propulsion velocity for frequencies below about 1 MHz but to a decrease of the propulsion velocity for larger frequencies. These findings are compared with preliminary results from the literature.