Enzo Orlandini

Large-deviation theory describes the statistics of rare fluctuations, while self-similarity captures scale-invariant behavior. Both are central pillars of statistical physics, yet the extent of their overlap is not well understood. Here, we ask whether a stochastic process can simultaneously satisfy both. We show that, under a precise set of conditions—exact self-similarity governed by one Hurst exponent and a scaled cumulant-generating function that is analytic around the origin—compatibility holds only if the scaling distribution is Gaussian. We illustrate this result with a broad class of subordinated stochastic processes, including continuous-time random walks, diffusing-diffusivity models, and polymers in the grand-canonical ensemble. In non-Gaussian cases, a characteristic timescale separates regular large-deviation and self-similar regimes. At criticality, the divergence of the correlation time and the emergence of a singular cumulant generating function make a regular large-deviation description inappropriate and lead to a strong enhancement of extreme dynamical fluctuations.

Active agents are likely to accumulate near confining obstacles due to collective motion. Here we investigate how the nature of the microscopic drive—self-propulsion or velocity alignment—selects distinct accumulation patterns, leading to either delocalized or compact clustered states. We first characterize the dynamical regimes emerging from the interplay of these two driving mechanisms under perfectly reflective or smooth boundary conditions. We then introduce boundary friction and observe a drastic change in the accumulation patterns, with dynamical phases that are absent in the previous case. By connecting emergent macroscopic structures to their underlying interactions, this work provides a practical route to infer the dominant microscopic mechanism ruling boundary-mediated collective behavior, with potential applications ranging from single-cell migration to bioinspired robotics.

A ring polymer in a confining space may exhibit at least two phases, namely, an expanded (or solvent-rich phase) if its concentration is small, or a collapsed (or polymer-rich phase) when it is concentrated and compressed. These phases are discussed in [P.-G. de Gennes (Cornell, Ithaca, New York, 1979)] and have been modeled, traditionally, in the mean field using Flory-Huggins theory [P. J. Flory, J. Chem. Phys. 10, 51 (1942); M. Huggins, J. Am. Chem. Soc. 64, 2716 (1942)]. In three dimensions, the ring polymer may also be knotted, or linked, and have its conformational degrees of freedom constrained by its topology. In a lattice model of confined knotted ring polymers, there are indications that the thermodynamic properties of the ring polymer (for example, the osmotic pressure [F. Gassoumov and E. J. Janse van Rensburg, J. Phys. A: Math. Theor. 52, 025004 (2019); E. J. Janse van Rensburg, Phys. Rev. E 100, 012501 (2019)]) are a function of its topology. In this paper, we explore a lattice knot model of a confined ring polymer as a function of its chemical potential. We show that a well-defined phase transition occurs between solvent-rich and polymer-rich phases when the lattice knot exhibits either the unknot topology or any other fixed knot type. Furthermore, we observe small yet significant variations in the free energy near the critical point when comparing trefoil knots with other nontrivial knot types. These findings indicate that the thermodynamic properties of confined ring polymers depend on their topological entanglement characteristics (namely, their knot type).

We study the equilibrium properties of a model of magnetic diblock copolymer where each monomer is decorated with an Ising-like spin. Spins interact ferromagnetically within each block and antiferromagnetically across blocks, generating frustration between magnetic ordering and spatial organization. By employing a mean-field approach and Monte Carlo simulations for self-avoiding walks on the cubic lattice, we investigate the system’s response to an external magnetic field. We discover a rich phase diagram that includes: a swollen phase with both filaments magnetically disordered and spatially extended; a mixed compact phase characterized by a single globule in which the two filaments are strongly intertwined; a segregated compact phase composed of two globular, magnetically ordered, and spatially separated blocks. Furthermore, if the magnitude of the intra-block ferromagnetic interaction differs between the two blocks, we observe a hybrid segregated (“tadpole”) phase where one extended block coexists with a collapsed one. Mean-field predictions of the location of the phase boundaries are in quantitative agreement with Monte Carlo results. These findings provide a minimal statistical–mechanical framework for field-controlled self-assembly of tunable patterns by magnetically heterogeneous polymers, which may also serve as a simple platform for future investigations of the coupling between internal epigenetic-like states and chromatin folding.

We show that Clifford algebras provide a natural language to describe the physics of liquid crystal defects in 3D. This framework shows that most of these defects have fermionic nature, as the director field profile on a 2D cross section can algebraically be represented by a spinor. Defects in uniaxial, biaxial nematics, and cholesterics are represented by elements belonging to different Clifford algebras, suggesting that there are fundamental distinctions between topological defects in each of these phases. Our theory allows nematic defects to be interpreted as Majorana-like spinors, as defects and antidefects are topologically equivalent, while some cholesteric defects, such as screw dislocations, are better viewed as Weyl-like spinors of well-defined chirality. Defects can be described by a “defect bivector,” an algebraic element that quantifies the rototranslation associated with them. In cholesterics, fermionic defects of different types can combine to yield composite quasiparticles with either fermionic or bosonic nature. Under cylindrical confinement, these quasiparticles provide the way to understand the structure of screw dislocations. In the bulk, they may condensate to form topological phases, such as blue phases or skyrmion lattices. Our results provide a surprising link between liquid crystals, particle physics, and topological quantum matter.

Supervised machine learning methods are emerging as valid alternatives to standard mathematical methods for identifying knots in long, collapsed polymers. Here, we introduce a hybrid supervised/unsupervised machine learning approach for knot classification based on a variational autoencoder enhanced with a knot type classifier (VAEC). The neat organization of knots in its latent representation suggests that the VAEC, only based on an arbitrary labeling of three-dimensional configurations, has grasped complex topological concepts such as chirality, unknotting number, braid index, and the grouping in families such as achiral, torus, and twist knots. The understanding of topological concepts is confirmed by the ability of the VAEC to distinguish the chirality of knots 9_{42} and 10_{71} not used for its training and with a notoriously undetected chirality to standard tools. The well-organized latent space is also key for generating configurations with the decoder that reliably preserve the topology of the input ones. Our findings demonstrate the ability of a hybrid supervised-generative machine learning algorithm to capture different topological features of entangled filaments and to exploit this knowledge to faithfully reconstruct or produce knotted configurations without simulations.

Complex fluids subjected to localized microscopic energy inputs, typical of active microrheology setups, exhibit poorly understood nonequilibrium behaviors because of the intricate self-organization of their mesoscopic constituents. In this work, we show how to identify changes in the microstructural conformation of the fluid by monitoring the variance of the probe position, based on a general method grounded in the breakdown of the equipartition theorem. To illustrate our method, we perform large-scale Brownian dynamics simulations of an effective model of micellar solution and we link the different scaling regimes in the variance of the probe’s position to the transitions from diffusive to jump dynamics, where the fluid intermittently relaxes the accumulated stress. This suggests that stored elastic stress may be the physical mechanism behind the nonlinear friction curves recently measured in micellar solutions, pointing at a mechanism for the observed multi-step rheology. Our approach overcomes the limitations of continuum macroscopic descriptions and introduces an empirical method, applicable in experiments, to detect nonequilibrium transitions in the structure of complex fluids.

In this paper we examine the relative knotting probabilities in a lattice model of ring polymers confined in a cavity. The model is of a lattice knot of size n in the cubic lattice, confined to a cube of side length L and with volume V=(L+1)^{3} sites. We use Monte Carlo algorithms to estimate approximately the number of conformations of lattice knots in the confining cube. If p_{n,L}(K) is the number of conformations of a lattice polygon of length n and knot type K in a cube of volume L^{3}, then the relative knotting probability of a lattice polygon to have knot type K, relative to the probability that the polygon is the unknot (the trivial knot, denoted by 0_{1}), is ρ_{n,L}(K/0_{1})=p_{n,L}(K)/p_{n,L}(0_{1}). We determine ρ_{n,L}(K/0_{1}) for various knot types K up to six crossing knots. Our data show that these relative knotting probabilities are small over a wide range of the concentration φ=n/V of monomers for values of L≤12 so that the model is dominated by unknotted lattice polygons. Moreover, the relative knot probability increases with φ along a curve that flattens as the Hamiltonian state is approached.

Phase diagram for a magnetic polymer with Blume–Emery–Griffith spins, with snapshots (phases: swollen disordered, SD; compact ordered, CO; compact disordered, CD). These results may be relevant to understand epigenetic memory in chromatin.

We study a spherically confined mixture of polymers and colloidal rings. Unlike in standard colloid-polymer mixtures, the polymers interact topologically with the rings by threading them. We find that, above a critical value of the ring radius, threading yields a topological transition from a fluid to a gel-like phase characterized by a space-spanning network of interlocked polymers and rings, which we refer to as a bicomponent gel, or bigel. By exploiting the mixture dual character (rings and polymers), we predict analytically the value of the critical radius. We also show that the mobility of entanglements in the mixture slows down upon entering the gel phase, due to topological hindrance arising from threadings, while the transition rates between topological states of the colloidal probes provide another strong dynamical signature of the gel phase. Published by the American Physical Society 2025