Papers

Using diffuse-interface theory, we uncover unexpected phase-change phenomena that are absent from widely used models of evaporation and condensation. In the inviscid limit, the same adjacent thermodynamic states admit stationary evaporation and condensation with equal and opposite mass fluxes, even when the vapor pressure lies below saturation. Viscosity breaks this reversibility but gives rise to multiple stationary condensation rates for the same vapor state. Lattice Boltzmann simulations dynamically recover these states, showing that these phenomena are dynamically realized by the diffuse-interface equations rather than arising solely as mathematical solutions of the reduced interfacial relations. Our results reveal previously unexplored behavior in a well-established theory of liquid–vapor interfaces.

Tissues are composites of living cells and extracellular matrix (ECM), that jointly determine their unique mechanical behavior. Here, we experimentally demonstrate that contractile cells remodel the ECM by generating long-range bands of aligned and densified fibers that mechanically couple cells into multicellular clusters. Using a finite-element model, we quantify the collective mechanical interactions mediated by these ECM bands for various volume fractions of cells. The model incorporates contractile particles that mimic cell-active forces within a nonlinear biological gel, inducing stiffening internally rather than through external loading. We find that even a small volume fraction of contractile particles (approximately 10%), much below what is expected for percolation of sphere contacts, leads to internal stiffening, mediated by the high-concentrated stress bands between cells and is strongly dependent on the nonlinear mechanical response of the ECM. Percolation analysis of the band network reveals sharp transitions at a critical particle volume fraction, that aligns with the onset of internal stiffening. These results demonstrate that long-range interaction between contractile cells through the deformation of the medium has the potential to globally shape the structure and mechanics of the bulk gel, leading to a functional structure with modified properties. These modified macroscopic changes can define organizing principles in tissue patterning and morphogenesis.

Polymers are widely used as functional insulating materials, but predicting their dielectric behavior is challenging because multiple mechanisms, acting across different spatial and temporal scales, contribute to their response. In polyethylene (PE), one of the most common polymers, electronic, atomic, and mesoscale dynamics must all be considered. In this work, semicrystalline models of polyethylene were developed and investigated using a multiscale approach. Quantum simulations were employed to describe electronic and vibrational contributions to the dielectric response, while classical molecular dynamics simulations captured the behavior of polymer chains at room temperature and frequencies down to the 10-100 MHz range. The study focuses on the impact of radio-oxidation defects on the dielectric properties of polyethylene. Quantum calculations reveal how electronic and vibrational contributions depend on the local atomic environment surrounding these defects. Comparison with molecular dynamics results highlights the influence of temperature on the static dielectric constant. Structural analyses further assess the effect of each defect type on PE crystallinity. Analysis of dipolar correlation functions shows that different defects interact with one another and with the polymer matrix in distinct ways, affecting permittivity and dielectric loss peaks. For all defect types, defect-defect interactions provide the largest contribution to dielectric response. While most oxidized groups exhibit positive coupling with the PE matrix, alcohol defects display a negative cross-correlation, partially offsetting their impact on the dielectric properties. Our results also show that ketone groups produce the largest dielectric loss between the defects studied.

We show that a linear damped elastic system can display a Mpemba-like reversal of vibrational relaxation without any nonlinear constitutive response or amplitude-dependent damping. The mechanism is purely modal. For a one-dimensional Kelvin–Voigt elastic medium, the decay rate of the $n$-th vibrational mode scales as $\gamma_n\propto n^2$. We formulate relaxation in terms of a positive modal envelope energy, thereby excluding crossings caused merely by oscillation phase. A one-parameter family of initial states is then constructed such that increasing the initial elastic excitation simultaneously reduces the projection onto the slow fundamental mode. In the invariant two-mode subspace, the relaxation-order crossing is obtained analytically and, for this family, occurs at a universal dimensionless time independent of the selected pair of initial states. In the limiting case where the slowest mode is absent, the dominant relaxation rate changes discontinuously, yielding a direct vibrational analogue of the strong Mpemba effect. We further show that the same relaxation-order reversal occurs in the ordinary mechanical vibrational energy, which decreases monotonically despite retaining the oscillatory dynamics of the underlying modes.

A ball bouncing on a thicker cushion should bounce less. We show that this is not always so . Measuring the coefficient of restitution $e$ of a steel ball dropped on a stack of $N$ sheets of standard A4 printer paper, we find that $e$ first drops, then rises to a pronounced maximum, and only then decreases towards a minimum. The maximum occurs where the acoustic round trip through the stack matches the contact time of the impact. For a contact set by the stack itself, one recovers the classical bar-impact condition of a stack-to-ball mass ratio of order one. Bar impact, however, predicts only a weak recovery, insensitive to the surrounding gas. For paper stacks, the recovery is large and no maximum is resolved when the stack is evacuated: the air trapped between the sheets, not the paper alone, makes the stack a trampoline.

Weakly flexible, directed polymers can adopt a potentially infinite variety of conformations, some of them chiral. We develop a second-virial theory for semi-rigid polymers embedded in a nematic environment based on the assumption that the chains possess no intrinsic molecular chirality but can take on weakly helical conformations of either handedness. We demonstrate how these transient helical fluctuations can be exploited to predict the degree of chain stiffening induced by molecular crowding. The theoretical predictions are in good agreement with large-scale molecular dynamics simulations of bead-spring polymers with tunable backbone flexibility. Although both theory and simulations rule out spontaneous global chiral symmetry breaking imparted by chain conformations alone, they do reveal that polymers can develop pronounced enantiomeric shapes. Nematic fluids of semi-rigid polymers can be viewed as compensated cholesterics composed of transiently helical polymers with zero enantiomeric excess. By quantifying the degree of compensated chiral order developed over a broad range of concentrations and persistence lengths, two distinct regimes of weak and strong enantiomerism can be identified. A crossover between the two occurs when the chain persistence length drops below roughly three times the contour length.

Light sheet microscopy is ideal for the 3D imaging of large biological specimens, yet systematic documentation on adapting microscope designs to diverse experimental requirements remains limited. We present the iterative process used to design and build a modular light-sheet microscope and adapt it to different sample types and experimental conditions. Starting from a stripped-down OpenSPIM platform, we gradually make our microscope more versatile by implementing new hardware, such as additional laser channels and optical filters, and new protocols for sample handling. In its final iteration, FlowSPIM is a new flow-based incubation technique for 3D tissue culture.

Motile active matter systems, from animal groups to synthetic particles, exhibit spontaneous self-organized transitions between disordered and ordered collective states. These transitions are driven by continuous energy injection, yet how energy consumption and dissipation change during these transitions remains poorly understood due to the challenge of measuring individual energetic fluxes. Here, we introduce a minimal experimental system of synthetic motile spheres that enables the first time-resolved power-budget characterization of collective motion. We show that the transition to an ordered state is accompanied by increased locomotion efficiency and a reorganization of dissipation pathways, shifting dissipation from internal friction to external slip with the environment. Leveraging this energetic reorganization, we construct an active engine powered by collective motion, capable of performing mechanical work against an external load. These findings establish energetic fluxes as quantitative observables for understanding collective state transitions and demonstrate how collective order can be harnessed for work extraction in active matter.

The discovery of the twist-bend nematic phase in liquid crystals composed of bent-core and dimeric molecules has revealed an unexpected mechanism for the spontaneous formation of nanoscale periodic structures in soft condensed matter. Unlike conventional liquid-crystalline phases, the twist-bend phase exhibits a nanoscale heliconical modulation despite the absence of molecular chirality. In this note, dedicated to the late R. Meyer, we discuss a Landau phenomenological interpretation of this phenomenon. The central idea is that a short-range orientational order parameter undergoes condensation, giving rise to a heliconical structure characterized by a finite wave vector. We emphasize that the conventional nematic order is already long-ranged, whereas the additional order parameter describes local orientational correlations hidden within the nematic state. The resulting phase transition bears a close analogy to the de Gennes theory of the nematic–smectic-A transition. Fluctuation effects are expected to drive the transition weakly first order. The theory also predicts a new Goldstone mode associated with the spontaneously broken continuous symmetry of the heliconical state

I present a discrete-element approach developed to study the collisional and gravitational evolution of small self-gravitating granular aggregates. Each body is represented as a composite of cohesively bonded spherical grains, so that fragmentation and reaccumulation emerge from the microscopic competition between short-range dissipative contact forces, an irreversible bond-breaking criterion, and pairwise Newtonian self-gravity summed over every particle pair, including those internal to a single body. A numerical experiment is described: a random-sequential packing procedure that generates two bonded spherical aggregates, a controlled two-body encounter with tunable approach speed and impact parameter, and a systematic parameter sweep designed to map the conditions under which two bodies launched from rest under their mutual gravity alone either merge into a single remnant or fail to settle after a low-speed encounter. Of the 125 simulated collisions, 56.8% result in the formation of a single residue. The cohesive network remains intact for $\Pi_\sigma\lesssim0.036$, is partially damaged with dispersion determined by the contact damping ratio, and breaks completely for $\Pi_\sigma\approx3.59$

Liquid crystal displays (LCDs) employ thin pixels of a paraelectric nematic, confined between two glass plates with transparent indium tin oxide (ITO) electrodes. A voltage applied to the electrodes realigns the molecules, changing the optical appearance of the pixel. Here we demonstrate that a similar molecular realignment can be triggered by low-power light irradiation when the paraelectric nematic in the cell with ITO electrodes is replaced with a ferroelectric nematic (NF). Irradiation creates an intrinsic electric field that is strong enough to realign the NF but too weak to affect the paraelectric nematic. The extraordinary sensitivity of the ITO/NF pair to light irradiation creates a platform for optical control of ferroelectric polarization and applications in photonics, sensing, smart windows, and beyond.

We study the structural, thermophysical and dynamical properties of molten MgCl2 over a wide temperature range using Ab Initio Molecular Dynamics (AIMD) and molecular dynamics simulations based on machine-learning interaction potentials (MLIPs). MLIPs can achieve near-AIMD accuracy at a fraction of the computational cost, enabling simulations of larger systems and longer timescales. This opens up the possibility of studying the system under out-of-equilibrium conditions, which in turn allows for the calculation of physical properties, such as the thermal conductivity or viscosity, that cannot be obtained reliably for the typical time and length scales accessible to AIMD. We follow two complementary approaches to develop and evaluate the MLIPs. Firstly, we develop a Deep Potential (DP) from scratch using AIMD trajectories at different temperatures. Secondly, we also evaluate two out-of-the-box foundation models and a fine-tuned version of one of them. The fine-tuning is performed using configurations from the AIMD trajectories originally used to train the Deep Potential. We compare the predictions of the trained DP, the foundation models and AIMD simulations with the available experimental data and provide a comprehensive calculation of the most important physical quantities of molten MgCl2. We compute densities, radial and angular distribution functions, thermal conductivity, heat capacity, viscosity and diffusion coefficients over the 1000-1600 K temperature range. This range is relevant to important technological applications such as thermal energy storage, generation IV nuclear reactors and concentrated solar power systems. Finally, we briefly review the accuracy and performance of the different MLIPs versions used throughout the work.

The mechanical properties of network-based materials have been extensively studied under qui- escent conditions, yet their self-assembly in nature occurs mainly in a mechanically stressed envi- ronment. Here, we show that the stiffness of collagen networks, one of the main building blocks of the mammalian extracellular matrix, can be tuned by applying shear stress during gelation, which first strains and aligns the material, then triggers a dramatic irreversible increase in the elastic modulus. This stiffening is anchored by maintaining the stress until the gel is fully matured. Using particle-based simulations, we show that the underlying microscopic mechanism is likely generic to a broad class of network-based systems and arises from two synergetic effects: changes in the network orientation and topology through the formation of permanent contacts that stabilize the system. Our findings are rationalized using a rigidity percolation framework and offer a general principle for encoding elasticity in biological and synthetic networks.

I show that the initial conditions imposed by Balan [Phys. Fluids 35, 113108 (2023)] are incompatible with a nonzero retardation time, so that the problem solved is not impulsive start-up, but, as I prove exactly, the start-up of a plate ramped as $1 - \mathrm{e}^{-t/\lambda_2}$ on the retardation timescale $\lambda_2$ (a material parameter, not a setting in a rheometer). Values digitized from that paper's viscoelastic figures fall on the ramped-plate solution, not on Tanner's start-up solution. The large negative wall normal stress reported for the corotational model is a grid-dependent artifact due to the same error in the initial data. An open-source code repository provides annotated notebooks reproducing every figure and number in this Comment.

Molecular dynamics simulations are used to compute the potential of mean force (PMF) between two united-atom methane molecules at several temperatures and integration time-steps. At a fixed time-step, the contact minimum of the PMF deepens with increasing temperature, as expected for hydrophobicity driven association. Compared with a time-step of 0.5 fs, one that preserves equipartition, larger time-steps alter the PMF and make the contact minimum more favorable. Thus even relative free energy values are sensitive to time-steps that break equipartition. Using quasichemical theory, we partition the free energy of association into hydrophobic and hydrophilic contributions. The hydrophilic contribution opposes association and is insensitive to the time-step. Thus the artificial enhancement of association at larger time-steps comes entirely from the hydrophobic contribution. We explain this behavior through the temperature dependence of the internal pressure of the liquid. The same analysis also accounts for earlier observations of the liquid's p-V behavior under conditions that break equipartition.

Janus-particle arrays provide a soft-matter platform in which particle orientations act as classical spins with anisotropic, bond-dependent interactions. Motivated by recent experiments on triangular arrays of metallodielectric Janus particles exhibiting sixfold orientational order and directly observable vortices and antivortices, we study effective models beyond the isotropic XY description. A classical $120^\circ$ compass model captures the minimal bond-directional interaction, while an effective Kern–Frenkel model incorporates the geometry of the Janus surface interaction more directly. Monte Carlo simulations show that both models exhibit a low-temperature sixfold ordered phase, a high-temperature disordered phase, and an intermediate quasi-long-range-ordered regime consistent with two Berezinskii–Kosterlitz–Thouless transitions. In both cases, the sixfold order arises through thermal order-by-disorder from a continuously degenerate ferromagnetic manifold. We further show that higher-order extensions of the $120^\circ$ interaction can alter the orientational selection: a quadratic term reverses the fluctuation-induced sixfold anisotropy, while a cubic term lifts the degeneracy energetically and selects the lattice-aligned directions that coincide with those observed experimentally. These results connect the microscopic anisotropy of Janus-particle interactions to emergent XY-like vortex physics and illustrate how distinct microscopic mechanisms can produce similar sixfold orientational order.

Strikingly, when hydrogel particles are embedded in ice in a temperature gradient, they move through the solid ice towards warmer temperatures, while swelling as they warm up. This motion comes from a flow of unfrozen water through the hydrogel mesh, driven by a process known as `cryosuction'. Here, we show how one can use this behavior to measure – with extremely high resolution – a range of different hydrogel transport properties, and how these change as a hydrogel deswells. These properties include permeability, compressibility, and poroelastic diffusivity: all of which are challenging to measure, but widely important for phenomena involving swelling, dehydration, transpiration and filtration. We demonstrate the measurement technique using poly(ethylene glycol) diacrylate (PEGDA) hydrogels. The technique uses picoliter-scale hydrogel volumes, and yields measurements of hydrogel properties that are consistent with existing literature data. The high resolution of our measurements also allows us to test commonly-used, classical predictions for hydrogel properties (derived assuming an idealized, homogeneous polymer network in the hydrogel). We show that these classical predictions do not work well, highlighting the need for new models that can accurately describe real hydrogels.

We study the relaxation dynamics of a one-dimensional system of hard rods at the level of one-body fields using superadiabatic dynamical density functional theory, and compare the results with Brownian dynamics simulations. The theory uses the exact equilibrium excess free energy functional and incorporates superadiabatic effects from first principles via an adiabatic closure relation at the three-particle level. The predicted superadiabatic response shows very good agreement with simulation data, provided that initial-state ensemble differences between theory and simulations remain small. Furthermore, we evaluate an approximate power functional theory based on a velocity-gradient expansion, which also yields an accurate superadiabatic response, although requiring a memory kernel extracted from simulation data.

Entangled polymer melts exhibit the robust two-branch Baumgärtel-Schausberger-Winter (BSW) relaxation spectrum, while related spectra occur in nonpolymeric monodisperse disordered systems. In spite of the successful application of BSW to many different materials, a molecular derivation of these spectra is lacking. We construct a molecular theory in which a chain segment moves relative to a screened, dynamically responding multichain environment. Gaussian-chain preaveraging gives $M_{\rm seg}(\Delta m)\sim(\Delta m)^{-1/2}$, hence $\lambda_p\sim p^{3/2}$ and, after stress projection, $H(\tau)\sim\tau^{-2/3}$. Independently, longitudinal primitive-path diffusion gives contour-length fluctuations with $H(\tau)\sim\tau^{1/4}$. A molecular-weight-constrained implementation is tested simultaneously against experimental $G'(\omega)$ and $G''(\omega)$ data for four monodisperse polybutadiene (PBD) melts, without fitting spectral exponents or individual modal weights. The resulting BSW spectrum exhibits a continuous transfer from the fast cooperative to the slow constraint-renewal cascade before a finite-chain terminal edge. A common two-sector caged dynamics then connects polymers to particle rafts without assuming identical microscopic mechanisms.

We analyze the transport of rod-like particles by diffusion and drift in a three-dimensional channel with varying circular or elliptic cross section. Applying the Fick-Jacobs approximation to the transport equation of the particles' probability distribution, we derive an effective one-dimensional substitute model and the associated free energy profile. Our results show that the data for the mean first passage time of rods, once expressed as a function of the effective free energy barrier, collapse onto the same master curve as obtained for point or spherical particles. The observed universality provides a simple framework for predicting transport times of anisotropic particles in confined geometries without resolving the full multidimensional dynamics.

Diffusivity of passive tracers in complex mixtures is widely relevant for industrial applications and for probing biological systems. Interactions with the surrounding medium typically generate a drag force that suppresses tracer diffusion, although self-propulsion can accelerate tracers via active fluctuations. Similar effects are not understood in mixtures with particle conversion and exchange, although these are particularly relevant in biological contexts, where actively driven reactions prevail. By studying a thermodynamically consistent model of chemical reactions in mixtures, we show that reactions provide an additional relaxation pathway that suppresses interaction-induced memory, reducing the drag on tracers and restoring their diffusivity toward the value expected in the absence of solutes. Moreover, active reactions generate nonequilibrium fluctuations that can push tracer diffusivity beyond this limit, an effect we confirm with particle-based simulations. Our results identify chemical activity as a distinct route to controlling mass transport and offer a framework for interpreting microrheology experiments in chemically active mixtures.

Mechanical metamaterials are materials that, by virtue of their microstructural architectures, exhibit mechanical properties not often found in nature: for example, auxetic mechanical metamaterials are materials that possess a negative Poisson's ratio in response to deforming forces. However, outside of relatively simple crystalline, lattice-based, or repeating-pattern architectures composed of mostly identical unit cells, mechanical metamaterials like auxetics are notoriously difficult to design, particularly across all three dimensions. Here we show that, for any structure that can be decomposed into triangular or tetrahedral meshes, those structures can be subjected to a simple transformation that that creates conditions within those triangular or tetrahedral simplexes that, regardless of their individual geometries, introduces a counter-rotating polygon/polyhedron mechanism that both guarantees a negative Poisson ratio and allows locally programmable mechanical properties. We apply this "shrink-and-wrap" construction to generate mechanical metamaterials from increasingly complex 3D structures, first from simple (convex) polyhedrons; then, to designs with arbitrarily large numbers of vertices and designed using constructive solid geometry (CSG) and 3D scanning; and, ultimately to 3D objects generated from videos captured by mobile phone camera – making potentially any object or geometric structure designed or found in the real world transformable into a mechanical metamaterial. We show that these monolithic auxetic constructions remain readily 3D-printable via additive manufacturing techniques. We expect this piecewise approach to designing arbitrarily complex mechanical metamaterial structures can enable numerous potential applications where programmable internal reconfigurations and/or force redirection are required across and throughout their 3D geometries.

Self-similar dynamics are often described in terms of a single asymptotic scaling regime. Here we experimentally investigate the post-breakup recovery of a hydrodynamic interface over substantially wider temporal and spatial ranges than previously accessible. Beyond the previously identified scaling behavior, we find four successive self-similar regimes characterized by the $R_{\beta}$-scaling with $\beta=1/6$, 1/2, 1, and 2, connected by three distinct crossovers. All four regimes exhibit robust collapse near the interface tip, while geometrical dependence becomes detectable farther from the singular region. This systematic variation across space and scaling regimes is consistent with scale separation and enhanced universality closer to the breakup singularity. The characteristic scales associated with the different $R_{\beta}$-scalings become comparable at the common geometric scale $z_m \simeq R$. These findings demonstrate that self-similar dynamics can undergo multiple successive crossovers among distinct scaling regimes rather than directly approaching a single asymptotic self-similar state.

Origami structures typically have a multiplicity of folded states that are connected to a flat sheet, making the folding protocol for specific end shapes challenging to design and deploy. Here, we introduce reprogrammable origami hinges that use bistable buckled shims to reversibly control their preferred folding direction. A shim embedded across a hinge produces an asymmetric torque-angle response that favors either mountain or valley folding. Switching the shim between its two stable states reverses this response, allowing the folding direction of each hinge to be reprogrammed after fabrication. By independently controlling the states and geometries of the shims, we enable a single origami sheet to access multiple folding branches and transform into prescribed three-dimensional shapes. We further introduce self-switching hinges in which folding causes the shims to snap between their stable states. These elements allow the sheet to reprogram its folding pathway under global mechanical inputs applied to the boundaries. Our approach embeds both shape selection and transition rules directly within the mechanics of the hinges, providing a versatile framework for creating multifunctional, deployable, and reconfigurable structures.

Active matter, i.e., nonequilibrium systems that transform non-thermal energy from the environment into self-propulsion or other functional mechanisms, has attracted the attention of the statistical physics community in recent decades. Flocking, as shown by the aerial displays of starling flocks, is perhaps one of the most intriguing collective behaviors exhibited by active matter. While the bulk behavior of free collective motion is now fairly well understood, at least when the surrounding fluid can be neglected (the so-called dry approximation), much less is known when collective motion explicitly breaks a continuous rotational symmetry, either globally or locally. This thesis explores the effects of such explicit symmetry breaking on the dynamics of collective motion. Global symmetry breaking may arise from an anisotropic environment, where a favored direction sets the mean flocking direction. A key question addressed here is how to detect small anisotropies without prior knowledge of the underlying environmental asymmetry. The thesis then examines boundary-induced symmetry breaking. In confined flocking systems, local anisotropies arise at the boundaries and significantly affect both bulk and boundary behavior, especially in finite-sized setups. We focus in particular on a polar active fluid confined between two parallel repelling walls, showing that the influence of the boundaries extends far into the bulk. Finally, we consider a more subtle confinement inspired by the phototactic behavior of certain cyanobacteria, showing that key features of active matter, such as accumulation at boundaries, can arise even without mechanical confinement. The results shed light on how symmetry-breaking perturbations, whether imposed globally or locally, alter the dynamics of active matter systems and offer new insights into the control of collective motion.

The axisymmetric profile \(\sin\psi(\rho)=c_0\rho\log(\rho/\rho_B)\) introduced by Naito, Okuda, and Ouyang is an exact solution of the unconstrained Helfrich shape equation for every \(\rho>0\), but its mean curvature diverges logarithmically at the dimple center. A covariant local analysis shows that in Cartesian graph coordinates the immersion is nondegenerate and belongs to \(W^{2,p}\) for every finite \(p\); it is \(C^{1,\alpha}\) for every \(\alpha<1\), but neither \(C^{1,1}\) nor \(C^2\). The conformal factor has a finite nonzero limit, so the point has branch multiplicity one and is not a branch point in the sense used in weak-immersion compactness theory. The Helfrich energy is finite, whereas the complete Euler–Lagrange operator carries the distributional residue \(\E_{\CH}=4\pi c_0\delta_p\) under the convention specified below. Hence the profile is a classical solution on the punctured surface and a finite-energy weak immersion, but it is not a free weak critical point of the unforced Canham–Helfrich functional. Stationarity is restored after adding the corresponding point-force potential or under a pinned-point constraint. Area and volume multipliers cannot cancel the Dirac residue. The apparent sign discrepancy between the shape equation used in the original papers and the modern convention is explained by the opposite definition of mean curvature. These results delimit precisely what can and cannot be inferred from modern existence and regularity theorems for Canham–Helfrich minimizers.

Understanding the interfacial structure of multi-site polymer adsorption is critical for the rational design of functional nanomaterials. However, the distribution of chains attached via one, two, or more anchor points has remained inaccessible to experiments and conventional simulations. Experiments typically measure ensemble averages such as total adsorbed mass, while molecular dynamics simulations are limited to timescales far shorter than the relevant adsorption processes. To address this challenge, we introduce the State-Resolved Integral of First-Passage Times (SR-IFS) method. This approach decouples fast intra-layer conformational adjustments from the slow kinetics of external chain exchange, enabling quantitative prediction of the time-dependent distribution of attachment states ($p_1$, $p_2$, $p_3$) within a multi-site adsorbed layer. Using 3-arm star-like polymers as a model system, we show that the interfacial state distribution evolves from an initial prevalence of three-point attachments to a more heterogeneous mixture over long time scales, and that the equilibrium distribution can be systematically tuned by adjusting the monomer binding energy. The SR-IFS method provides access to this state-resolved information, offering a connection between microscopic kinetics and macroscopic interfacial properties.

We investigate nonequilibrium phase transitions and thermodynamic properties of driven Potts models coupled to two thermal reservoirs at different temperatures. The interplay with the multi-state structure of the Potts model leads to distinct phase-transition scenarios. The proposed driving scheme breaks the symmetry between the Potts states and gives rise to multiple transitions within the ordered phases, where the phases are characterized by different numbers of stable fixed points. This number can vary from $q$ fixed points to $1$ fixed point, corresponding to $q-1$ distinct transitions. The driving scheme strongly affects the thermodynamic operation regimes, allowing the system to operate as a heat engine. We demonstrate that these phenomena persist for both a mean-field (MF) model and a two-dimensional model, confirming the robustness of the results with respect to dimensionality. For the MF case, we also develop a phenomenological description in the strongly ordered regime that yields analytical expressions for the power, heat currents, and efficiency. Our results show how multi-state collective interactions, nonequilibrium driving, and thermal bias jointly generate a rich phase structure and the emergence of a collective heat engine.

We develop an active self-consistent field theory (ASCFT) for studying the steady-state behavior of active Ornstein–Uhlenbeck polymers. Starting from the stochastic equations of motion under the unified colored noise approximation, we derive an effective Hamiltonian that extends the classical polymer field theory to non-equilibrium systems. The resulting free energy functional incorporates both the Flory–Huggins interaction parameter $\chi N$ and the persistence time $\tau$ of the active noise, enabling a unified description of thermodynamic and activity-driven effects. To solve the governing equations, we implement a stable implicit-explicit numerical scheme that handles the fourth-order term induced by activity. Our simulations reveal that increasing activity suppresses microphase separation, with the density modulation amplitude decaying as $\Delta\phi \propto \tau^{-1/2}$ for large $\tau$. This scaling is independent of copolymer composition and is confirmed by an asymptotic analysis of the free energy functional in the large-$\tau$ limit. The ASCFT framework provides a new theoretical tool for predicting and designing the non-equilibrium morphologies of active polymer systems, bridging the gap between traditional self-consistent field theory and active matter physics.

The Generalized Langevin Equation (GLE) is an integro-differential equation of motion for a general observable of a many-body system and is rigorously derived using the projection operator formalism. In the standard derivation, a stationary canonical phase space distribution is used for the projection. Here, we derive a novel class of GLEs using a non-stationary projection distribution that constrains the initial ensemble to a hypersurface in phase space on which the observable has a fixed value $A_0$. As a result, all GLE parameters, and in particular the memory friction kernel, depend on $A_0$ and can be extracted from short simulations that do not sample the entire phase space. Applying this non-stationary GLE to protein folding trajectories, we find for villin and an $\alpha$-helical poly-alanine segment that the total friction is higher in the folded state. These results demonstrate that observable-dependent friction effects are non-negligible and can be accounted for using non-stationary GLEs derived by constrained projection schemes.