arXiv subjects

Noah Ziethen

Publications and source records attributed to Noah Ziethen.

7 recordsLinked to original sources

arXiv2026

Nucleation and time-reversal symmetry breaking in nonconserved scalar field theories

Classical nucleation theory (CNT) describes the formation of a stable phase from a metastable one in terms of a single reaction coordinate that corresponds to the radius of a nucleating droplet. In this work, we provide a full account of nonequilibrium nucleation theory (NNT), which generalizes CNT to non-equilibrium field theories with non-conserved order parameter. We present two equivalent derivations of the dynamics of the droplet radius: a stochastic route, based on a direct projection of the stochastic field equation onto the radial reaction coordinate, and a route based on the minimization of the Freidlin-Wentzell action. Crucially, the quasipotential barrier predicted by NNT differs from the one found when assuming the instanton to be the time-reversal of the relaxation dynamics. Whereas the interfacial density profile differs from that on the relaxation path, an analytical derivation of NNT remains possible using a careful definition of the reaction coordinate. This leverages the perturbative structure that (in common with CNT) emerges in the limit of large critical radius. We further derive with similar techniques the dynamics of capillary waves, whose stability is required for the CNT/NNT precept of a near-spherical droplet to prevail. After deriving our theory for generic non-conserved field-theories, we address two explicit examples: a non-equilibrium generalization of Model A (Active Model A), and a population dynamics model (with two choices of noise that each break time-reversal symmetry). In both cases, we validate our analytical NNT against numerical results obtained by action minimization, with excellent agreement. NNT provide a systematic framework for constructing nucleation theories in a broad class of non-equilibrium systems from active matter, reaction-diffusion systems and population dynamics.

cond-mat.stat-mech↗

arXiv2026

Nonequilibrium nucleation theory for nonconserved fields: from active matter to population dynamics

Classical nucleation theory (CNT) describes the formation of a stable phase from a metastable one. In equilibrium systems, it quantifies the free-energy competition between a favorable bulk gain and an unfavorable interfacial cost. For systems without detailed balance, the corresponding nonequilibrium nucleation theory (NNT) was so far developed only for cases with a conserved order parameter, such as active fluid-fluid phase separation. Here we construct the NNT for systems with a (single, scalar) nonconserved order parameter. Unlike in the conserved case, the nucleation barrier controlling (noise-driven) droplet growth is profoundly altered by deviations in the interfacial density profile from the one arising during (deterministic) droplet relaxation. The barrier can nonetheless be analysed by carefully defining the reaction coordinate (droplet radius) to project out those deviations. We give explicit NNT predictions for models drawn from population dynamics and active matter, finding excellent agreement with numerical studies.

cond-mat.stat-mech↗

arXiv2025

Chemically Active Liquid Bridges Generate Repulsive Forces

Droplets help organize cells by compartmentalizing biomolecules and by mediating mechanical interactions. When bridging two structures, such droplets generate capillary forces, which depend on surface properties and distance. While the forces exerted by passive liquid bridges are well understood, the role of active chemical reactions, which are often present in biological droplets, remains unclear. To elucidate this case, we study a single liquid bridge with continuous chemical turnover. These reactions control the bridge radius and lead to purely repulsive forces-contrasting with the typically attractive forces in passive systems. Our results reveal how chemical activity can fundamentally alter forces generated by liquid bridges, which could be exploited by cells.

cond-mat.soft↗

arXiv2024

Heterogeneous Nucleation and Growth of Sessile Chemically Active Droplets

Droplets are essential for spatially controlling biomolecules in cells. To work properly, cells need to control the emergence and morphology of droplets. On the one hand, driven chemical reactions can affect droplets profoundly. For instance, reactions can control how droplets nucleate and how large they grow. On the other hand, droplets coexist with various organelles and other structures inside cells, which could affect their nucleation and morphology. To understand the interplay of these two aspects, we study a continuous field theory of active phase separation. Our numerical simulations reveal that reactions suppress nucleation while attractive walls enhance it. Intriguingly, these two effects are coupled, leading to shapes that deviate substantially from the spherical caps predicted for passive systems. These distortions result from anisotropic fluxes responding to the boundary conditions dictated by the Young-Dupré equation. Interestingly, an electrostatic analogy of chemical reactions confirms these effects. We thus demonstrate how driven chemical reactions affect the emergence and morphology of droplets, which could be crucial for understanding biological cells and improving technical applications, e.g., in chemical engineering.

cond-mat.soft↗

arXiv2023

Vascular adaptation model from force balance: Physarum polycephalum as a case study

Understanding vascular adaptation, namely what drives veins to shrink or grow, is key for the self-organization of flow networks and their optimization. From the top-down principle of minimizing flow dissipation at a fixed metabolic cost within flow networks, flow shear rate resulting from the flows pervading veins is hypothesized to drive vein adaptation. Yet, there is no bottom-up derivation of how flow forces impact vein dynamics. From the physical principle of force balance, shear rate acts parallel to vein walls, and hence, naively shear rate could only stretch veins and not dilate or shrink them. We, here, resolve this paradox by theoretically investigating force balance on a vein wall in the context of the vascular network of the model organism Physarum polycephalum. We propose, based on previous mechanical studies of cross-linked gels, that shear induces a nonlinear, anisotropic response of the actomyosin gel, making up vein walls that can indeed drive vein dilatation. Furthermore, our force balance approach allows us to identify that shear feedback occurs with a typical timescale and with a typical target shear rate that are not universal properties of the material but instead depend smoothly on the location of the vein within the network. In particular, the target shear rate is related to the vein's hydrostatic pressure, which highlights the role of pressure in vascular adaptation. Finally, since our derivation is based on force balance and fluid mechanics, we believe our approach can be extended to vascular adaptation in other organisms.

cond-mat.soft↗

arXiv2023

Thermodynamically Consistent Phase-Field Theory Including Nearest-Neighbor Pair Correlations Explains Failure of Mean-Field Reasoning

Most of our current understanding of phase separation is based on ideas that disregard correlaions. Here we illuminate unexpected effects of correlations on the structure and thermodynamics of interfaces and in turn phase separation, which are decisive in systems with strong interactions. Evaluating the continuum limit of the Ising model on the Bethe-Guggenheim level, we derive a Cahn-Hilliard free energy that takes into account pair correlations. For a one-dimensional interface in a strip geometry these are shown to give rise to an effective interface broadening at interaction strengths near and above the thermal energy, which is verified in the Ising model. Interface broadening is the result of an entropy-driven interface delocalization, which is not accounted for in the widely adopted mean field theory. Pair correlations are required for thermodynamic consistency as they enforce a thermodynamically optimal local configuration of defects and profoundly affect nucleation and spinodal decomposition at strong coupling.

cond-mat.stat-mech↗

arXiv2022

Nucleation of chemically active droplets

Driven chemical reactions can control the macroscopic properties of droplets, like their size. Such active droplets are critical in structuring the interior of biological cells. Cells also need to control where and when droplets appear, so they need to control droplet nucleation. Our numerical simulations demonstrate that reactions generally suppress nucleation if they stabilize the homogeneous state. An equilibrium surrogate model reveals that reactions increase the effective energy barrier of nucleation, enabling quantitative predictions of the increased nucleation times. Moreover, the surrogate model allows us to construct a phase diagram, which summarizes how reactions affect the stability of the homogeneous phase and the droplet state. This simple picture provides accurate predictions of how driven reactions delay nucleation, which is relevant for understanding droplets in biological cells and chemical engineering.

cond-mat.soft↗