Papers

Crystallisation of calcium carbonate (CaCO$_3$) in aqueous solutions is essential for carbon dioxide sequestration and the sustainable production of calcium carbonate materials, which are widely used in industry and increasingly explored for novel applications. While crystallisation is often analysed within the framework of classical nucleation theory, CaCO$_3$ and other ionic crystals often form through amorphous precursor phases, motivating the need for alternative descriptions. In this work, we investigate the relationship between the formation of the first CaCO$_3$ coordination sphere, a fundamental unit of local ordering, and ionic aggregation using two complementary simulation approaches: on-the-fly probability-enhanced sampling (OPES) and asynchronous and infinite-swap replica exchange transition interface sampling ($\infty$RETIS). OPES was used to explore free-energy landscapes, whereas $\infty$RETIS was used to determine reaction kinetics. We studied systems at two levels of supersaturation, between which the formation of the first coordination sphere exhibited distinct kinetic behaviour. These differences were found to be linked to concentration-dependent ionic aggregation. At lower concentration, aggregation remains limited, whereas higher concentration promotes extensive spinodal-like aggregation. For both concentrations, the first coordination sphere forms within the pre-formed clusters through one of two distinct pathways: either within a cluster close to the minimum size required for its formation, or within larger amorphous aggregates whose size and structure depend on concentration. The coexistence of these pathways at both levels of supersaturation reveals the multifaceted nature of early-stage CaCO$_3$ crystallisation and highlights the importance of differentiating ionic aggregation and organisation.

We study the contributions of half-BPS surface defects to supersymmetric Casimir energy and the universal logarithmic term of supersymmetric Rényi entropy in four- and six-dimensional SCFTs. Using equivariant integration of defect anomaly polynomials and its extension to supersymmetric Rényi backgrounds, we obtain closed expressions for these observables in terms of defect 't Hooft anomalies. For Gukov–Witten defects preserving transverse rotations in four-dimensional $\mathcal{N} = 4$ super Yang–Mills theories, both observables depend on a single R-symmetry anomaly. For $\mathcal{N} = (0, 4)$ defects in six-dimensional $\mathcal{N} = (1, 0)$ theories, additional terms arise from the gravitational anomaly. We provide complementary checks using chiral algebras, five-dimensional localization, and holographic probe branes at large $N$, while localized chiral fermions reproduce the gravitational-anomaly contributions. The framework also recovers Wilson-surface results in six-dimensional $\mathcal{N} = (2, 0)$ theories.

Microscopic simulations resolve spatial patterns but are feasible only over small domains and short timescales, whereas bulk descriptions erase those patterns through spatial averaging. Mesoscopic fields preserve this spatial organisation, but their effective equations are known only for selected microscopic systems and scaling limits. We introduce Deep Mesoscopic Dynamics (DeepMesoD), which uses neural networks to learn an effective mesoscopic field equation from microscopic trajectories at a prescribed coarse-graining scale. For the nonconserved dissipative dynamics studied here, DeepMesoD learns the free-energy functional with a spatial interaction kernel and a state-dependent dissipation operator constrained by the fluctuation-dissipation relation. We first validate the construction in the Ising-Kac model, where the learned mesoscopic equation recovers the known hydrodynamic limit and rollouts remain stable far beyond the training horizon. We then treat two systems without closed-form mesoscopic descriptions. For a two-dimensional Heisenberg ferromagnet governed by atomistic spin dynamics, DeepMesoD learns a mesoscopic model whose predictions match atomistic references up to 1 ns, and a rollout with an unseen initial condition remains bounded up to 25 ns. For layered CrBr$_3$, the learned kernel captures the suppression and sign reversal of interlayer coupling at a stacking fault whose location and strength are not supplied as inputs. Controlled changes to the learned interaction show how fault number and placement shape multistep magnetic responses, complementing our magneto-photoluminescence measurements. Across the two atomistic systems, DeepMesoD achieves a three-to-four-order-of-magnitude reduction in wall-clock time compared with atomistic spin dynamics.

Based on our previous results regarding critical exponent estimates for the 3D Ising model and scaling relations [1], we have proven that the exact value of the correlation-length exponent is $\frac{\sqrt[3]{2}}{2}$. This is in very close agreement with the most precise numerical estimates currently available. Using a group theoretical approach and some propositions of constructive geometry, we derived an exact construction of algebraic expressions for the critical exponents $\gamma$ and $\beta$. We proved that these expressions depend solely on the exact value of $\nu\,$.

We revisit the statistical mechanics of Transformer attention via modern Hopfield models. We present a free-energy formalism to characterize parameter regimes and critical thresholds for robust attention inference. The resulting free-energy landscape incorporates randomness in query states and attention weights. Attention then emerges as the equation of motion of the corresponding statistical-mechanical system (i.e., modern Hopfield model) through the standard free-energy minimization principle. This allows us to identify first-order phase transitions in attention between glassy and robust-inference phases. We further extend to attentions with stochastic queries and keys. Together, our results provide a rigorous statistical-mechanics framework for characterizing phase structure and inference reliability across a family of Transformer attention mechanisms.

Feynman's ratchet illustrates how work can be extracted from thermal fluctuations in the presence of two heat baths at different temperatures. While some experimental realizations of the ratchet effect have been studied, most lack miniaturization, which is important for some applications. Here, we propose a physical implementation of Feynman's ratchet based on Josephson junctions exhibiting the superconducting diode effect. This setup functions as a heat engine that generates work solely from a temperature gradient via thermal fluctuations. We analyze its output power and efficiency, and, through the Seebeck coefficient, identify the conditions under which the device operates in reverse, functioning instead as a Peltier cooler.

Spatial sudden death of entanglement refers to the disappearance of quantum correlations between subsystems after a certain distance called the entanglement length. Specifically, given a density matrix $\rho_{ABC}$ on a tripartite system $ABC$ with $B$ spatially separating $A$ and $C$, the entanglement length is the distance $\ell(A,C)$ after which the reduced density matrix $\rho_{AC}$, given by tracing out the $B$ subsystem, is separable. We show in the case of gapped ground states in any dimension that the entanglement length is finite on finite subsystems. Restricting to one-dimensional systems, we prove that normal matrix product states have a finite entanglement length independent of $A$ and $C$, and that a finite pure state with such uniform entanglement length has a matrix product state representation with bond dimension independent of $A$ and $C$. Consequently, in one dimension, entanglement length distinguishes matrix product states from all other pure states.

Nitrite photochemistry in atmospheric aerosols and natural waters is a major source of hydroxyl radicals and reactive nitrogen oxides. Contrary to the prevailing view that in the environment aqueous nitrite photochemistry proceeds exclusively through photoexcitation followed by homolytic bond cleavage, we show that visible light directly ionizes aqueous nitrite in individual micron-sized droplets. Although the photoionization cross section is exceptionally small, this pathway is observable at the high photon flux densities accessible in single-droplet experiments. Molecular simulations reveal that this is because photoionization absorption has an exceptionally long wavelength tail due to the large solvent reorganization energy in aqueous solutions. Kinetic modeling of an aqueous-phase reaction mechanism quantitatively accounts for the observed chemistry and predicts the formation of nitrate, hydroxyl radicals, and solvated electrons. The overlap of the predicted broad photoionization continuum with the visible solar spectrum further suggests that visible-light photoionization is an overlooked source of nitrogen oxides, solvated electrons, and oxidants in atmospheric aerosols, snowpack, and natural waters. Under dilute conditions, where dissolved oxygen is the main sink for solvated electrons, photoionization is expected to be the dominant photochemical loss pathway for nitrite.

We unify known mutual-linearity relations for Markov jump processes and chemical reaction networks within a common framework based on classical finite-response theory. In a Markov jump process, an exact finite-response identity shows that all stationary probability changes share a common factor when the rates of one edge change. Eliminating this factor gives the relations between probabilities, observables, and currents, even far from equilibrium. We also explain how the same argument applies when one coefficient of a linear system changes and recovers the known relations in Laplace space and between stationary complex activities in chemical reaction networks.

Hydrodynamics as an effective field theory (EFT) has been immensely successful for predicting the behaviour of time-ordered correlation functions in the long-time, large-distance regime. In this paper, we analyse the predictions of hydrodynamics for scrambling as probed by out-of-time order correlators (OTOCs). To do so, we consider an all-derivative order generalisation of the Schwinger-Keldysh EFT of hydrodynamics extended to a four-fold time contour required to capture OTOCs. A crucial ingredient of the construction is a local SL(2,R) symmetry, which has previously been suggested as a mechanism for scrambling. We also derive this exact EFT from the microscopic formulation of the maximally chaotic low-temperature limit of the SYK lattice, thereby determining all transport coefficients for this model. As a novel application, we compute the OTOC of energy currents, find that its exponential growth saturates the chaos bound, and match it to expectations based on a shockwave (or scramblon) effective description. Our work shows that the universality of hydrodynamics degrees of freedom extends beyond traditional time-ordered correlators to more complex observables such as OTOCs.

Can the Alexander-Orbach conjecture hold on hierarchical lattices? We construct Gromov-Hausdorff-Prokhorov scaling limits of critical percolation clusters on hierarchical lattices in the chemical metric and determine the typical spectral dimensions of the associated diffusions. These dimensions are dense in $(1,2)$; however, outside a narrow region in dimension space, we prove that the Alexander-Orbach conjecture fails on every hierarchical lattice under consideration.

We study the spontaneous motion and collective dynamics of self-phoretic particles on a one-dimensional periodic domain. The particles act as localized chemical sources (of a particle-dependent strength) of a field and the particles themselves respond to the gradients of the field they generate (with a particle-dependent phoretic mobility). The chemical field itself diffuses and evaporates. For a single particle, we derive the exact threshold for spontaneous propulsion and establish the emergence of stable constant-velocity states near onset through a supercritical pitchfork bifurcation. We then consider an active source coupled to a non-emitting tracer and determine the conditions for slipping and stable phase-locked motion. For two mutually coupled sources, the stationary antipodal configuration can lose stability through either a pitchfork or a Hopf bifurcation, depending on the relative source strengths and phoretic mobilities. We determine the competing instability thresholds and compare them with direct numerical simulations of the coupled particle-field equations. Beyond onset, the resulting translating and oscillatory states provide qualitative counterparts to modes of motion observed experimentally for camphor disks in annular water channels. These results connect the onset of individual propulsion, tracer entrainment, and collective motion within a common analytically tractable framework.

Within the framework of non-extensive statistical mechanics, $q$-Gaussian distributions arise as maximum-entropy solutions of Tsallis entropy under suitable escort moment constraints. Although widely used in physics, biology, geology, finance, and related fields, standard $q$-Gaussians are intrinsically symmetric and cannot capture asymmetric fluctuations often observed in empirical data. We ask whether asymmetry can arise from the Tsallis maximum-entropy principle without externally skewing or joining distributions. We show that this is achieved by retaining the Tsallis entropy and imposing a global escort mean together with distinct downside and upside escort semi-variances. The key step is to reformulate the problem of maximum Tsallis entropy in terms of the escort density. The nonlinear escort constraints then become affine, while maximizing Tsallis entropy becomes equivalent to maximizing a strictly concave functional over a convex feasible set. Consequently, any admissible stationary solution is the unique global maximizer of the corresponding variational problem. The finite-sample approximation properties of the proposed asymmetric $q$-Gaussian are studied through Monte Carlo experiments using synthetic data generated from Azzalini skew-Student distributions. Compared with the classical symmetric $q$-Gaussian, the asymmetric specification systematically provides a closer approximation to synthetic asymmetric heavy-tailed distributions. Finally, we fit the model to return series from major equity indices, a commodity, and cryptocurrencies, and compare its in-sample goodness of fit with that of a symmetric $q$-Gaussian. The results show that the asymmetric model offers a closer in-sample description of unconditional return distributions, most clearly in the tails.

Poorly soluble species can have mean populations below one in small systems such as nanopores. In this regime, the grand-potential minimum, which identifies the most probable particle number, differs from the ensemble-averaged solute loading. We use grand-canonical Wang-Landau sampling (GCWLS) to calculate the density of states $\Omega(N_\mathrm{A}, N_\mathrm{B})$ for a binary Lennard-Jones mixture of solute B in solvent A, both in bulk and in slit pores. One set of GCWLS simulations gives ensemble averages over a range of chemical potentials, whereas conventional grand-canonical Monte Carlo (GCMC) simulation requires a separate simulation at each state point. Independent GCMC simulations confirm the GCWLS ensemble averages. The solvent number distribution is nearly Gaussian, whereas the dilute solute distribution is skewed and Poisson-like. The most probable solute number therefore lies below the ensemble-averaged loading $\langle N_\mathrm{B}\rangle$ and is zero whenever $\langle N_\mathrm{B}\rangle<1$. Reading the solute loading from the grand-potential minimum underestimates it and can falsely indicate that no solute is present. Defining the oversolubility as $\mathcal{O}_\mathrm{B}=x_\mathrm{B}^{\mathrm{conf}}/x_\mathrm{B}^{\mathrm{bulk}}$, where $x_\mathrm{B}$ is the solute mole fraction, we find $\mathcal{O}_\mathrm{B}\approx12$ in a pore of 3.5 particle diameters width when both wall interactions are repulsive. Adding wall-solute attraction moderately raises it to $\approx13$, whereas wall-solvent attraction lowers it to $\approx3.4$. This comparison shows that the wall-solvent interaction controls most of the enhancement. As the pore widens, $\mathcal{O}_\mathrm{B}$ decreases toward unity. In bulk and in nanopores alike, the solubility of poorly soluble species should be obtained from ensemble averages rather than from grand-potential minima.

Active gels are intrinsically non-equilibrium materials whose structural and dynamical heterogeneity emerges from the interplay of attractive interactions, thermal fluctuations, and self-propulsion. We investigate a model active gel, simulated using large-scale Brownian dynamics simulations, to explore the effects of temperature $T$, active force strength $f_0$, persistence timescale $\tau_p$, and active particle concentration $\rho_a$. We characterize the structure of the evolving gel network through morphological analysis, while dynamical changes are quantified by the relaxation timescale and dynamical heterogeneity (DH). We show that an optimal choice of activity parameters yields a percolating gel network with faster gelation and larger voids and clusters, enhancing mechanical stability. Conversely, the structural relaxation timescale and DH decrease with increasing activity, indicating enhanced particle rearrangements and reduced spatial correlations of mobile and immobile regions. An effective temperature ($T_\text{eff}$) framework for colloidal gels maps structural quantities and relaxation timescales in an active gel onto those of a passive gel. More interestingly, the growth of DH with increasing swim force can also be described by the same effective-temperature framework, in stark contrast to observations in active glasses. Our findings show that, in colloidal gels, temperature and active force compete, giving rise to similar structural ordering and, consequently, similar DH at the same $T_\text{eff}$. These findings highlight the crucial role of structural ordering in governing DH in active colloidal gels, as compared to active glasses.

The Shannon-Rényi (SR) entropy characterizes the probability distribution of many-body wave functions in a chosen basis and is directly accessible from single-shot measurement snapshots in cold-atom experiments, yet its theoretical evaluation in interacting systems carries exponential cost. Here we construct a field-theoretic spacetime manifold for the SR entropy in which $q$ replicas are glued at the imaginary-time boundaries, recasting it as a ratio of generalized partition functions amenable to large-scale quantum Monte Carlo simulation. On this basis we develop a reweight-annealing framework with two complementary strategies: a virtual-parameter scheme interpolating between unglued and fully glued limits via binomial-weighted partial gluing, and a real-parameter scheme using a physical coupling constant as the annealing variable within stochastic series expansion. Both reduce the computational cost from exponential to polynomial. Most importantly, we establish for the first time a finite-size scaling theory for the SR entropy near a quantum critical point, $S_q=a(g)L^2+S_q^0\left((g-g_c)L^{1/\nu}\right)$; data collapse of its first derivative yields the correlation-length exponent $\nu$ for both the O(3) and Ising universality classes, realized in the spin-$\frac{1}{2}$ columnar dimerized Heisenberg model and the bilayer Heisenberg-Ising model. The same simulations extract the Goldstone-mode count $N_G=2$ and the $Z_2$ ground-state degeneracy $\ln 2$ from subleading terms. These results elevate the SR entropy to a standalone, order-parameter-free diagnostic of quantum criticality with the same scaling status as the entanglement entropy, and close the loop between theory and quantum simulation by enabling quantitative benchmarking of experimental snapshots from state-of-the-art quantum simulators.

The yielding of amorphous solids has been extensively studied in the athermal limit, but the influence of thermal fluctuations is much less understood, in particular for glasses of different stability. Using molecular dynamics simulations of a model glass where the swap Monte Carlo algorithm can be employed, we study the yield stress at finite temperature and shear rate, both in steady flow and at shear start-up, over a broad range of glass stability. Thermal fluctuations soften both the dynamic yield stress in steady state and the start-up yield stress. In all cases, the temperature dependence is compatible with the $T^{2/3}$ law expected for thermally activated yielding near a saddle-node instability, with no systematic dependence of the exponent on stability or shear rate. Extrapolations to zero temperature recover the athermal yield stresses. The amplitude of the softening at start-up, by contrast, depends strongly on stability: highly stable glasses are much less sensitive to temperature than poorly annealed ones. A description of yielding at finite temperature must therefore account explicitly for the stability of the glass.

We formulate a Derjaguin-corrected Kelvin equation for phase transitions in finite open slits. In such pores, capillary condensation is modified by the finite wall length because the condensed phase is bounded by two terminal menisci pinned at the slit ends. Starting from the macroscopic generalized Kelvin equation, we introduce a scaling approximation which replaces the implicit edge-contact-angle condition by a closed analytic expression while preserving the exact limiting behaviours. We then incorporate mesoscopic wetting-layer contributions into the finite-slit free-energy balance. The single-wall contribution naturally separates into a planar Derjaguin term and a residual finite-length correction controlled by the competition between the wall length $H$ and the parallel correlation length $\xi_\parallel$. The resulting equation reduces to the standard Derjaguin-Kelvin equation for infinitely long slits and to the macroscopic finite-slit Kelvin equation when adsorbed layers are absent. Explicit forms are derived for long-ranged dispersion forces and for short-ranged forces. The theory is tested using classical density functional theory for finite slits with attractive Lennard-Jones walls and hard walls, corresponding respectively to capillary condensation and its drying analogue, capillary evaporation. The Derjaguin-corrected theory substantially improves on the purely macroscopic prediction, capturing both the correct infinite-slit limit and the observed dependence on wall length. For the short-ranged hard-wall system, the agreement with DFT remains nearly quantitative even for very narrow slits.

An isolated quantum system evolves reversibly, yet a small subsystem can lose nearly all information about its initial state. Conserved quantities may retain some of this information, depending on how strongly they overlap with local observables. Here we consider a subsystem in an arbitrary initial state coupled to a maximally mixed bath. We show that the worst-input mean-square equilibration error, maximised over window origins, is bounded from above and below by the mean square of a complete local autocorrelation, with the stationary part subtracted. A correlation record over a finite interval therefore controls the equilibration error in every interval of the same length. The result allows arbitrary degeneracies of energies and gaps. We apply it to two static Hamiltonian families. For fixed spin subsystems in the one-particle sector of a bounded-range periodic clock, fixed-accuracy thermalisation is guaranteed on windows that grow only slightly faster than linearly with system size, despite exponentially small positive energies. A random commuting model with logarithmic interaction range retains an extensive set of conserved observables. Its expected mean-square error is bounded by a finite-size term and an inverse-time term. The inverse-time dependence is unavoidable because of the initial transient. These examples show how local relaxation can coexist with exact conservation laws and a finely spaced spectrum.

We investigate the computational capabilities of a one-dimensional lattice of negatively coupled circle maps in its traveling wave regime. We interpret propagating waves as information carriers and exploit their interactions to implement Boolean logic. The logical states are encoded by the propagation direction of the traveling waves, while the presence or absence of a wave at a designated output location represents the logical output. Using controlled wave collisions, we demonstrate the realization of NAND and NOR gates along with other basic gates. Since NAND and NOR operations are functionally complete, the results establish that the traveling wave regime of the negatively coupled circle-map lattice supports universal Boolean computation in principle. The demonstrated logical operations remain valid over a finite range of the coupling strength \epsilon and map parameter \omega, indicating robustness of the computational scheme to parameter variations. Our results therefore demonstrate that computational functionality can emerge from the collective nonlinear dynamics of a coupled map lattice, providing a con- nection between the dynamical properties of traveling wave states and collision based information processing.

Swap Monte Carlo dramatically accelerates the equilibration of deeply supercooled liquids while preserving the equilibrium Boltzmann distribution. Recent work has argued that swap and other accelerated algorithms act by reparameterizing time: different dynamics follow the same slow relaxation process, but with different clocks. Here we test this idea in a continuously polydisperse glass former. We confirm that mean collective overlaps satisfy an approximate time reparameterization, in agreement with earlier results. However, the associated clock depends systematically on the collective probe length and on the relaxation stage. Thus the observed collective collapse does not define a unique, observable-independent material time. Over the numerically accessible $\alpha$-relaxation regime, swap changes not only the rate of relaxation, but also its length-scale dependence. The resulting collective reparameterization is therefore only approximate and does not establish an exact dynamical equivalence between swap and reference relaxation.

We show that a common quantum-jump feedback protocol can permanently reverse the nonequilibrium free-energy ordering of two prescribed initial states while preserving their Gibbs equilibrium. The construction exploits collective compensation between monitored channels: their feedback corrections cancel at equilibrium but remain active during relaxation. This balance preserves free-energy monotonicity while allowing the relaxation modes to be reshaped. We prove that eliminating the complete slow-sector contribution of the initially higher-free-energy state, while retaining it for the comparison state, produces distinct asymptotic decay exponents. Their free-energy ratio then vanishes at long times, guaranteeing a permanent thermodynamic quantum Mpemba inversion under the same controlled dynamics. A thermal qutrit realizes the mechanism through coherence interference and exhibits distinct detection thresholds for spectral selection and exact slow-sector cancellation under feedback retuning.

Local out-of-time-order correlators (OTOCs) measure the growth of initially small commutators. For bounded local operators, this growth ends when the local commutator becomes of order one, but in an extended system the region over which it is large can continue to expand. We study this spatial proliferation using three related observables: the local squared commutator $C_r(t)$, its spatial sum $\bar C(t) = \sum_r C_r(t)$, and the symmetrically regularised connected dOTOC $D(t)$ of two extensive observables. We show that Lieb–Robinson locality gives $\bar C(t) \lesssim t^d$. We then prove that, in a Gibbs state with uniform exponential clustering, the full dOTOC obeys the same bound, $D(t) \lesssim t^d$, improving our earlier suboptimal $t^{3d}$ bound. We illustrate these results in two quantum many-body systems: a Brownian coupled-cluster model and a finite-temperature SYK chain. In both cases, an exact disorder symmetry relates $D(t)$ to $\bar C(t)$ and allows us to follow the same extensive observable from the pre-scrambling Lyapunov regime into the post-scrambling growth associated with an expanding saturated region. This late-time power-law growth is the concrete realisation of the weak quantum chaos introduced in our earlier work.

We numerically study spectral and wave-function properties, as well as time evolution, in finite-size commensurate approximations of the 3D Aubry-André model. We explicitly show, through scaling analysis, the existence of two critical points. One of the critical points is a localization-delocalization transition in real-space, similar to the critical point in the 3D Anderson model. The other is a localization-delocalization transition in a dual momentum space, which does not have any analog in the 3D Anderson model. We estimate their values from spectral measures, such as the gap ratio and the spectral form factor, as well as from wave-function measures, such as the inverse participation ratio and the participation entropy. Additionally, we demonstrate that both critical points exhibit hallmarks of critical points between quantum ergodicity and localization. First, the eigenstates and the eigenspectrum at the critical point fulfill the mutual universal relation between the eigenspectrum compressibility $\chi$ and the eigenstate fractal dimension $d^{(1)}$ [S. Jiricek et al., Proc. Nat. Acad. Sci. 123, e2518027123 (2026)]. Second, the dynamics of the wave packet at the critical point is governed by the critical dynamical exponent $z$, characterized by the spectral fractal dimension and the dimensionality of the lattice [M. Hopjan and L. Vidmar, Phys. Rev. Lett. 135, 060401 (2025)]. Thus, similarly to the 3D Anderson model, the critical dynamical exponent is sub-diffusive with the value of $z=3$.

A gap exists in connecting biological evolution within the framework of statistical mechanics. It has been hoped that statistical mechanics would provide us with a general predictive principle for the emergence of novelty and complexity. However, the emergence of novel functional features initiated by stochastic processes remains difficult to describe, because these processes commonly arise outside near-equilibrium or linear-response regimes. To understand how environmental influences generate diverse, open-ended, complex objects by driving physical systems to specific regions of phase space over long spatial and temporal scales, a new approach to non-equilibrium thermodynamics is necessary. Here, we present the coupling of assembly theory (AT) with statistical mechanics as a framework that works within the laws of thermodynamics, but can contextualise the processes of novelty, complexity, and evolution within these laws. We map construction processes from physical space to assembly space (AS) and introduce the concept of an assembler, a machine that constructs objects contingent on previous states and is represented by bitwise operations. Using this approach, we apply principles from stochastic thermodynamics with AT to define selection within large combinatorial spaces1 and estimate the work required to create novel and complex objects. This approach allows us to represent complex processes, such as selection, within large combinatorial spaces as a set of rules for a memory-feedback loop followed by the assembler. This framework concretely defines the relationships between thermodynamics and information theory by introducing a novel aspect of physics that uses history and causal contingency to influence the probabilistic time evolution of complex systems.

The local Hilbert space dimension is a fundamental parameter in quantum many-body systems, but its role in controlling the ergodicity-breaking transition remains less explored. We systematically study this question by introducing toy models of qudits in zero dimensions that exhibit an ergodicity-breaking transition. Using the hybridization condition, we analytically obtain the dependence of the critical value of the interactions on the local Hilbert space dimension. Numerical studies of spectral correlation measures show agreement with the theoretical predictions, hence confirming the existence of the ergodicity-breaking transition in these models. We further introduce a distinct higher spin version of the model and numerically obtain the same critical behavior, demonstrating that the observed critical point is independent of the microscopic structure of interactions considered.

We formulate the Generalized Constraint-Controlled Rheological Model (GCCRM) for entangled linear and long-arm-branched polymer melts under sinusoidal periodic shear deformation (SPSD), spanning the linear and strongly nonlinear regimes. Molecular architecture, conformation, chain stretch, flow-active constraints, convective constraint release, dynamic tube dilation, and activated arm retraction define a common upstream molecular state. This state feeds two time-domain constitutive pathways (a configurational stress and a dissipative internal-variable stress) which are recombined before Fourier analysis. For branched polymers, the architecture is described by an entire backbone of molecular weight $M_{bb}$ and $N_a$ long arms of molecular weight $M_a$, with a compliance-weighted representative-constitutive-cell partition. The linear limit is normalized so that the configurational moduli sum to the entanglement modulus, while dynamic tube dilation and stretch drive distinct contributions to dissipative activation. Under reduced closures, GCCRM generates a smooth nonlinear elastic response with an onset of nonlinearity, an approximately logarithmic growth regime, an architecture-dependent maximum, and distinct high-deformation asymptotes. Fourier harmonics, ELR, VLR, and Lissajous curves are treated as post-processing observables of the total stress. The framework establishes a consistent constitutive architecture whose quantitative validation requires one parameter set per material across SPSD and, prospectively, transient shear histories.

Quantum thermalization of closed systems – i.e. the relaxation of local properties to their thermodynamic value along the Hamiltonian evolution – is generically expected in non-integrable systems at finite energy density. In this work we show that quantum spin systems with at least one spin component coupled through long-range ferromagnetic interactions, and a second spin component coupled to a field, cannot in general thermalize to a paramagnetic state whenever they have a finite, negative energy per spin. The long-range interactions we consider decay as a power law of the distance, $\sim r^{-\alpha}$ with $\alpha < d$, where $d$ is the number of spatial dimensions of the system. The lack of thermalization is generic to an infinite family of Hamiltonians, and it is not associated to any form of integrability. It can instead be understood by the anomalous features of the thermodynamics of the system in the paramagnetic phase, which cannot be reflected in the properties of the eigenstates. This leads to a breakdown of eigenstate typicality and of the eigenstate thermalization hypothesis. Interestingly, the non-thermal states emerging at long times in the dynamics display long-range multipartite entanglement, elevating the breakdown of thermalization to a resource.

Using MC simulations based on an efficient single-cluster growth algorithm, we investigate two types of three-dimensional extended-range percolation models, namely cubic and complex (non-compact) neighborhoods. We obtain high-precision percolation thresholds $p_c$ for approximately 100 distinct structures and further explore the relationship between these thresholds and the topology of the lattices, which includes the total coordination number $z$, the number of sites $z_i$ and these sites' distance to the central site $r_i$ of the given neighborhood in the $i$th coordination zone. Both bond and site percolation are analyzed for cubic neighborhoods on the SC lattice. For bond percolation, the asymptotic value of $zp_c$ tends to Bethe-lattice behavior ($zp_c\sim1$), and finite-$z$ correction is found to be consistent with $zp_{c}-1\sim a_{1}z^{-x}$, where $x=(d-1)/d$. For site percolation, the value of $zp_c$ varies non-monotonically, exhibiting an initial increase followed by a decrease with the coordination number $z$. Linear fitting leads to $zp_c\sim2.5987(1)$ for large $z$, predicting a value of continuum percolation threshold of aligned cubes $\eta_c=0.324838(12)$ using $zp_c=2^{d}\eta_c$. We then examine site percolation for non-compact neighborhoods extending to the fifth coordination zone on SC, FCC, and BCC lattices. Through a comparison of the three indices of $z$, $\xi=\sum_iz_ir_i^2/i$, and $\zeta=\sum_iz_ir_i$, we find that $\zeta$ is effective in removing the degeneracy. The results obtained show power-law dependence $p_c\propto(\zeta/K)^{-\gamma}$ with $\gamma_{\mathrm{SC}}^{\zeta}=0.703(12)$, $\gamma_{\mathrm{FCC}}^{\zeta}=0.728(10)$, and $\gamma_{\mathrm{BCC}}^{\zeta}=0.699(12)$ for SC, FCC, and BCC lattices, and $p_c\propto\zeta^{-\gamma}$ with $\gamma^{\zeta}=0.719(9)$ independent of the underlying lattice. The number $K$ indicates lattice connectivity.

Area laws express the expectation that entanglement in gapped quantum ground states scales with a boundary rather than a volume. In one dimension this holds for every Rényi entropy, and the Rényi area-law conjecture asserts the same in higher dimensions for each fixed $0<\alpha<1$. Here we disprove this conjecture in every spatial dimension two and higher. We construct finite-range Hamiltonians with fixed local dimension, bounded interaction strength, unique ground states and a uniform spectral gap, whose ground states exhibit volume-law Rényi entanglement while obeying a von Neumann area law and remaining connected to product states through uniformly gapped local paths. The mechanism is error-space complexity: locally identifiable components of arbitrarily small weight can encode states with high entanglement complexity. We also establish the worst-case rank-error trade-off for approximate ground-state projectors, a key tool in one-dimensional area-law proofs. At fixed gap, the optimal Schmidt rank at projection error $\epsilon$ across a planar cut of cross-section $A$ scales as $\exp[\tilde{\Theta}((A\log\epsilon^{-1})^{2/3})]$ when $\log\epsilon^{-1}\gtrsim A$. Thus $\alpha=1$ is the sharp threshold for a universal Rényi area law within this adiabatically connected class.