arXiv subjects

Biman Bagchi

Publications and source records attributed to Biman Bagchi.

At least 19 recordsLinked to original sources

arXiv2026

Memory Control of Ice Growth During Non-Equilibrium Freezing of Water

Freezing of supercooled water is a classic non-equilibrium problem, yet the influence of thermal history on crystallization remains unclear. Using molecular dynamics simulations with the TIP4P/Ice model, we investigate how the initial temperature $T_i$ shapes freezing following rapid quenching to 250 K. By monitoring the evolution of hydrogen-bonded ring structures, we find a non-monotonic dependence of the freezing time $t_F$ on $T_i$, with the slowest crystallization occurring near 300 K. Remarkably, this means that initially hotter water can freeze faster than cooler water, a molecular-scale analogue of the Mpemba effect. A non-stationary generalized Langevin equation framework shows that two-time memory kernels retain information about the system's thermal past, directly influencing crystallization dynamics. Structural analysis further reveals that five-membered rings act as kinetic traps, while correlations among ring types regulate the accessibility of ice-like motifs. These results uncover a molecular origin of memory-driven freezing and establish structural memory as a key driver of non-equilibrium phase transitions.

cond-mat.mes-hall↗

arXiv2026

Fragility from Enthalpy Fluctuations and Fictive-Temperature Dynamics

Fragility and fictive temperature are two central measures of glass formation, but their connection is usually expressed indirectly through structural relaxation times or cooling-rate dependence. Here we formulate this connection in terms of configurational enthalpy fluctuations. The time evolution of the fictive temperature during cooling or aging is controlled by the enthalpy--enthalpy correlation function that also determines the frequency-dependent configurational heat capacity. Fragility enters through the strong temperature dependence of the structural relaxation time and therefore controls how rapidly the corresponding enthalpy-relaxation spectrum shifts to long times near the glass transition. This leads to a direct time-domain description of the onset and growth of the fictive-temperature lag, including the Debye limit, and connects calorimetric relaxation, fragility, and nonequilibrium structural arrest within a common framework.

cond-mat.stat-mech↗

arXiv2026

From Freezing to Terminal Packing: A Puzzle and a Paradox

A density-functional theory developed for equilibrium freezing also produces a high-density endpoint close to terminal packing. We revisit the nonlinear Ramakrishnan--Yussouff bifurcation framework and distinguish the first crystalline fold, thermodynamic coexistence, and terminal marginality. At the terminal point, the grand-potential curvature vanishes along the principal finite-wavevector density mode, exactly when the nonlinear self-consistency equation loses stiffness. The construction gives exact close packing for one-dimensional hard rods, a terminal hard-disk packing fraction near 0.8407, and a hard-sphere value near 0.629, close to random close packing. These results identify a finite-wavevector thermodynamic marginality of a metastable liquid continuation, rather than equilibrium freezing or mechanical jamming, and expose a persistent puzzle: why should liquid-state correlations encode the approach to terminal disordered packing across different physical dimensions and systems?

cond-mat.soft↗

arXiv2026

Theory of Handedness Selection in Helices of Chiral Polymers and Biopolymers

Helices are among the most common ordered structures in biological and synthetic polymers, but their formation involves more than local conformational preference. A finite helix must nucleate, grow, resist breaking, and maintain a selected handedness against thermal fluctuations. We develop a three-state Ising-like transfer-matrix theory in which each segment is coil-like, right-handed helical, or left-handed helical. This formulation separates ordinary helix--coil cooperativity from the persistence of handedness. The right--left symmetric problem decomposes into symmetric and antisymmetric sectors, giving two characteristic lengths: the helical correlation length $\xi_H$ and the chiral persistence length $\xi_\chi$. In the strongly helical rare-wall limit, $\xi_\chi\simeq (1/2)\exp[\beta(K+J)]$. A local chiral bias, motivated by the Ramachandran landscape, is then amplified over finite helical domains.

cond-mat.soft↗

arXiv2026

Entropic Necks, Dynamic Crossovers, and Fragility in Supercooled Liquids

The dramatic slowdown of dynamics in supercooled liquids is accompanied by a sequence of dynamical crossovers, most notably the transition from high-temperature collision-dominated transport to low-temperature activated structural relaxation. A particularly striking manifestation of this change is the crossover from Rosenfeld excess-entropy scaling to the Adam--Gibbs relation. In this work we develop a theoretical framework based on a configuration-space extension of Zwanzig's entropic-neck picture and combine it with a Mori--Zwanzig memory-function formalism to address anomalies of supercooled liquids. The central idea is that structural relaxation is controlled by the narrowing of configurational pathways connecting metastable basins of the inherent-structure landscape. Starting from coupled slow variables describing intrabasin motion and neck fluctuations, we derive a reduced generalized Langevin description in which elimination of the neck coordinate generates a long-lived memory kernel and naturally leads to entropy-controlled activated dynamics. At high temperatures the neck is broad and readily accessible, yielding Rosenfeld-type transport governed primarily by local structural entropy. Upon cooling, progressive neck constriction produces an increasing entropy deficit, leading to Adam--Gibbs behavior and activated relaxation. Within this picture, fragility acquires a simple geometric interpretation: fragile liquids are characterized by a rapid collapse of the effective configurational neck with decreasing temperature, whereas strong liquids exhibit a much slower evolution of accessible pathways. The framework does not by itself compute the configurational entropy, mismatch penalty, or cooperative length from microscopic interactions; its aim is to provide a dynamical and geometrical interpretation.

cond-mat.stat-mech↗

arXiv2026

Living Helices in Fluctuating Polymer Chains: Cooperative Nucleation, Dynamics, and Lifetime

Helical segments in polymer chains are often transient, finite, and dynamically evolving, yet their origin and stability remain incompletely understood. Here we develop a minimal coarse-grained statistical-mechanical theory that explains how such living helices emerge in fluctuating polymer systems. Using a three-state model with cooperative interactions, we show that helix formation proceeds through a multistep nucleation mechanism. An initial constrained pre-nucleus forms first, followed by cooperative stabilization that promotes the growth of finite helical segments. The resulting free-energy landscape naturally favors marginally stable helices whose size is determined by a competition between cooperative gains and nonlinear penalties arising from stiffness, torsional strain, and solvent fluctuations. By formulating the dynamics as a stochastic process in segment size, we derive analytical expressions for both formation times and lifetimes within a mean first-passage framework. For representative parameters relevant to flexible polymers and peptide segments, the theory predicts characteristic timescales in the nanosecond to sub-microsecond range. The present analysis supports a view of living helices as finite, mobile excitations whose stability is controlled by cooperativity, boundary motion, and solvent-induced fluctuations.

cond-mat.soft↗

arXiv2026

Spatial Correlations Restore Zwanzig's Mean-Field Diffusion Result in Rugged Energy Landscapes

Transport in disordered environments is often controlled not by typical fluctuations but by rare, extreme events that dominate long-time dynamics. In such settings, Zwanzig's classic mean-field theory predicts that energetic roughness reduces the diffusion coefficient by an exponential factor governed solely by the variance of the disorder. However, this prediction breaks down in uncorrelated Gaussian landscapes, where rare but deep multi-site traps dominate transport and lead to a much stronger suppression of diffusion. Here, we present a unified theoretical framework that clarifies both the origin of this breakdown and its resolution. We show that Zwanzig's local averaging can be interpreted as a Gaussian cumulant expansion whose validity is destroyed by uncorrelated disorder through the emergence of extreme trapping events. Introducing Gaussian spatial correlations fundamentally reshapes the landscape: roughness increments become smoother, asymmetric multi-site traps are suppressed, and the statistics of escape pathways are regularized. As a result, Zwanzig's exponential scaling is recovered. We provide an explicit analytical derivation demonstrating how spatial correlations modify trap statistics and restore mean-field diffusion, complemented by illustrative numerical examples showing the dramatic reduction of escape times in correlated landscapes.

cond-mat.stat-mech↗

arXiv2026

Microscopic Pathways to Helix Formation: Packing Stabilization and Sticky Interactions in Chiral Polymer Condensates

Helices are not generic outcomes of polymer collapse. Collapsed conformations of semiflexible polymers with isotropic attractions typically form globules, toroids, or rod-like structures, as seen in simulations and described by coarse-grained necklace and surface-tension models. Helical conformations, in contrast, are generally absent in minimal theories based solely on bending elasticity and isotropic cohesion, since such descriptions lack any mechanism to select torsion, pitch, or periodic packing. Here we identify two minimal and physically distinct routes by which helices can become stable without invoking biochemical specificity. Route (A) is geometric and steric: combining a tube-like packing (thickness) constraint with generic attractions selects an ideal helical packing with finite radius and pitch. Left- and right-handed helices remain exactly degenerate in free energy, so chirality emerges spontaneously even without explicit chiral interactions. Route (B) is energetic and commensurate: periodic "sticker" attractions between monomers separated by a fixed contour distance $m$ enforce a registry between interaction spacing and chain geometry. This commensurability stabilizes helical states by enabling repeated contacts along the backbone, naturally connecting to classical Gibbs-DiMarzio and Zimm-Bragg mechanisms. For both routes, we derive analytical relations for helix radius and pitch, curvature and bending energy, contact-distance constraints, and crossover conditions to toroidal and rod-like morphologies, expressed in terms of persistence length $L_p$, interaction strength, and chain length $N$. This framework explains why helices are non-generic in polymer collapse, identifies the physical ingredients required for their stabilization, and provides testable predictions for when helical and chiral condensates should emerge.

cond-mat.stat-mech↗

arXiv2026

Effects of Dynamic Disorder on Diffusion in Rugged Energy Landscapes

Established theoretical studies of diffusion in rugged (or rough) potential surfaces have largely focused on quenched energy landscapes. Here we study diffusion on a rugged energy landscape in the presence of dynamic disorder, a situation relevant to a wide range of disordered systems, including glasses, disordered solids, and biomolecular transport. For static (quenched) Gaussian disorder, Zwanzig derived a compact mean field expression for the diffusion constant, showing that increasing ruggedness leads to a sharp reduction of diffusive transport. Subsequent work demonstrated that in one-dimensional discrete lattices diffusion is further suppressed by rare but long-lived multi-site traps that lie beyond the mean-field description. In many physical systems, however, the local energy landscape is not frozen but fluctuates in time, there by modifying trap lifetimes and transport properties. In this work we develop a minimal, analytically tractable theory of diffusion on rugged energy landscapes with dynamic disorder by allowing site or barrier energies to fluctuate as dichotomic (telegraph) processes with given amplitude and flipping rate. Using a Kehr type formulation appropriate for discrete hopping processes, we derive an analytic expression for the diffusion constant in terms of mean waiting times. We show that dynamic disorder induces a continuous crossover from quasi-quenched, trap-dominated transport to an annealed, motional narrowing regime as the fluctuation rate increases. Explicit numerical calculations confirm this crossover, interpolating between rare-event-dominated diffusion and Zwanzig mean-field regime.

cond-mat.stat-mech↗

arXiv2026

Stiffness induced structures and morphological transitions in semiflexible polymers

Semiflexible polymers in poor solvents exhibit a rich variety of collapsed morphologies, including globules, toroids, and rodlike bundles, arising from the competition between attractive interactions and chain stiffness. Computer simulations and experiments on stiff and conjugated polymers have revealed complex morphological crossovers, yet a unified theoretical description remains incomplete. Here we develop a coarse-grained, field-theoretic free-energy framework for linear polymers with variable stiffness that captures these morphologies and their transitions within a common description. The theory is built on three key ingredients: a density field describing monomer attraction and excluded-volume effects, a nematic order parameter accounting for orientational ordering in dense regions, and the bending rigidity of a worm-like chain. Using simple variational ansatzes for competing morphologies, we derive analytic expressions for their free energies and identify the boundaries separating coil, globule, toroidal, and rodlike conformational regimes as functions of the reduced attraction strength and the effective persistence length. The resulting phase-diagram topology provides a transparent free-energy-based framework for interpreting morphology diagrams observed in simulations and experiments on semiflexible polymers in poor solvents. We find the possibility of the existence of a triple point involving globules, rods and toroids.

cond-mat.stat-mech↗

arXiv2025

Diffusion in Rugged Energy Landscapes in the Presence of Spatial Correlations : A Surprising Route to Zwanzig's Mean-Field Prediction

Diffusion in rugged free-energy landscapes is central to diverse problems in chemical physics, biomolecular dynamics, polymer transport and numerous disordered systems. Zwanzig's well-known classic mean-field theory predicts that roughness reduces the diffusion coefficient by an exponential factor determined solely by the variance of the disorder. However, the numerical studies of Banerjee, Seki, and Bagchi (BSB) showed that this result fails for uncorrelated Gaussian-distributed site energies because rare but deep three-site traps dominate long-time transport. BSB introduced Gaussian \emph{spatial} correlations - originally developed in astrophysics to model turbulent density fluctuations - and demonstrated that even modest correlations suppress these pathological traps and restore Zwanzig's exponential scaling. Here we present here a unified theoretical framework clarifying (i) why Zwanzig's local averaging, may be viewed as a Gaussian cumulant expansion, could breakdown. In particular, how its validity is destroyed by uncorrelated disorder, and (ii) how Gaussian spatial correlations reshape roughness increments, eliminate asymmetric multi-site traps, and thereby recover mean-field diffusion, and (iii) a derivation showing exactly how Gaussian spatial correlations modify roughness increments, trap statistics, and ultimately the diffusion constant. We also provide explicit numerical triplet examples illustrating the dramatic reduction of escape times produced by spatial correlations.

cond-mat.stat-mech↗

arXiv2025

From Frequency Dependent Specific Heat to Fictive Temperature of a Glassy Liquid

Upon rapid quenching of temperature of a glass forming liquid, the system falls out of equilibrium due its finite relaxation time. Additionally, the relaxation becomes progressively slower with time. The created nonequilibrium state of the glassy system is conveniently described by introducing a fictive temperature which provides the instantaneous state of the nonequilibrium system. The fictive temperature $T_{f} (t)$ is time dependent. During cooling, the fictive temperature is higher than the actual temperature. After the cooling or quenching has ceased, the fictive temperature approaches the final temperature at a rate that depends on the relaxation properties of the liquid. In this work we use linear response theory to connect the time dependence of the fictive temperature to memory function which is shown to be related to the frequency dependent specific heat which itself depends on the fictive temperature $T_{f} (t)$. Thus, one requires { \it a self-consistent calculation} to capture the interdependence of relaxation rate and structural response function. We present a numerical calculation where we apply our relations to silica where the relaxation function that describes the frequency dependent specific heat and is modeled as a stretched exponential William-Watts (WW) function, while the relaxation time is modeled as a Vogel-Fulcher-Tammann (VFT). We calculate the fictive temperature self-consistently. $T_{f}(t)$ exhibits the fall out from actual temperature as time (t) progresses.

cond-mat.stat-mech↗

arXiv2025

Surface Induced Frustration of Inherent Dipolar Order in Nanoconfined Water

Surface effects could play a dominant role in modifying the natural liquid order. In some cases, the effects of the surface interactions can propagate inwards, and even can interfere with a similar propagation from opposite surfaces. This can be particularly evident in liquid water under nano-confinement. The large dipolar cross-correlations among distinct molecules that give rise to the unusually large dielectric constant of water (and in turn owe their origin to the extended hydrogen bond (HB) network) can get perturbed by surfaces. The perturbation can propagate inwards and then interfere with the one from the opposite surface if confinement is only a few layers wide. This can give rise to short-to-intermediate range solvent-mediated interaction between two surfaces. Here we study the effects of such interactions on the dielectric constant of nano-confined liquids, not just water but also ordering at protein surfaces. The surfaces work at two levels: (i) induce orientational realignment, and (ii) alter the cross-correlations between water molecules. Molecular dynamics simulations and statistical analyses are used to address these aspects in confinement of slit pores, nano tube/cylinder, and nano sphere. In addition, we consider the hydration layers of multiple proteins with vastly different structural features. These studies give us a measure of the extent or the length scale of cross-correlations between dipole moments of water molecules. We find an interesting orientational arrangement in the protein hydration layers, giving rise to long-range molecular cross-correlations. To decouple the effect of HB from the effect of geometry, we additionally study acetonitrile under nanoconfinement. Importantly, while a protein's interior is characterized by a small dielectric constant, the dipole moment of a peptide bond is large, and thus susceptible to fluctuations in water.

cond-mat.soft↗

arXiv2025

Diffusion-entropy scaling across dimensions

A quantitative relationship between the diffusion coefficient $D$ of a tagged particle in a liquid and the entropy $S$ of that liquid has long been sought, as it would allow entropy to be inferred directly from diffusion measurements and transport properties to be predicted from thermodynamic information. Here, we employ extensive computer simulations to independently compute both $D$ and $S$ for Lennard-Jones (LJ) liquids and for water across a wide range of thermodynamic state points. Our study covers two and three dimensions for both systems, and additionally explores one-dimensional confinement for water. We find that the ratio of diffusion coefficients between two states follows an almost perfect exponential dependence on their entropy difference. For LJ liquids, the exponential prefactor exhibits a pronounced dependence on dimensionality $d$, consistent in trend but quantitatively distinct from theoretical predictions. In contrast, water shows a strikingly weak dimensionality $d$ dependence, deviating from theory, which we attribute to the dominant role of jump diffusion. Remarkably, the exponential diffusion-entropy relationship persists even when translational and rotational contributions to entropy are separated and considered individually. This robustness suggests that entropy provides a unifying measure governing particle mobility in liquids, largely independent of microscopic mechanisms or dimensional constraints.

cond-mat.stat-mech↗

arXiv2024

Unique Dielectric Behaviour and Anomalies in Nanoconfined Liquids

The dielectric properties of a bulk dipolar liquid have been subjects of intense interest during the past decades. A surprising result was the discovery of a strong wavenumber dependence in the bulk homogeneous state. Such behaviour seems to suggest the possibility of a strong system size dependence of the dielectric constant (DC) of a nanoconfined liquid, although details have been revealed only recently. Dielectric properties of nanoconfined water indeed show marked sensitivity not only to the size and shape (dielectric boundaries) of confinement but also to the nature of surface-water interactions. For geometries widely studied, namely, water confined in a narrow slit, nanocylinder, and nanospherical cavity, the asymptotic approach to the bulk value of the DC with the increase in confinement size, is found to be surprisingly slow. This seems to imply the appearance of a dipolar cross-correlation length, much larger than the molecular length-scale of water. In narrow slit and narrow cylinder, the dielectric function becomes both inhomogeneous and anisotropic, and the longitudinal and transverse components display markedly different system size dependencies. This sensitivity can be traced back to the dependence of the DC on the ratio of the mean square dipole moment fluctuation to the volume of the system. The observed sensitivity of collective dipole moment fluctuations to the length scale of confinement points to the possibility of using DC to estimate orientational correlation length scale which has been an elusive quantity. Furthermore, the determination of volume also requires special consideration when the system size is in nanoscale. We discuss these and several other interesting issues along with several applications that have emerged in recent years.

cond-mat.soft↗

arXiv2024

Dynamics of Nonequilibrium Dimerization of Model Polymer Chains

Dimerization and subsequent aggregation of polymers and biopolymers often occur under nonequilibrium conditions. When the initial state of the polymer is not collapsed or the final folded native state, the dynamics of dimerization can follow a course sensitive to both the initial conditions and the conformational dynamics. Here we study the dimerization process by using computer simulations and analytical theory where both the two monomeric polymer chains are in the elongated state and are initially placed at a separation distance, d0. Subsequent dynamics lead to the concurrent processes of collapse, dimerization and/or escape. We employ Langevin dynamics simulations with a coarse-grained model of the polymer to capture certain aspects of the dimerization process. At separations d0 much shorter than the length of the monomeric polymer, the dimerization could happen fast and irreversibly, from the partly extended polymer state itself. At an initial separation larger than a critical distance, dc, the polymer collapse precedes dimerization and a significant number of single polymers do not dimerize within the time scale of simulations. To quantify these competition, we introduce several time-dependent order parameters, namely, (i) the time-dependent radius of gyration of individual polymers describing the conformational state of the polymer, (ii) a centre-to-centre of mass distance parameter RMM, and (iii) a time dependent overlap function Q(t) between the two monomeric polymers, mimicking contact order parameter popular in protein folding. In order to better quantify the findings, we perform a theoretical analysis to capture the stochastic processes of collapse and dimerization by using dynamical disorder model.

cond-mat.soft↗

arXiv2024

Relation between Entropy, Diffusion and Relaxation Kinetics

Intermolecular correlations lower values of both diffusion and entropy. We present an analysis of the existing relations between long-time diffusion (D) and entropy. S. A recently proposed inequality, a lower bound, by Sorkin et al., expresses the long-time diffusion in terms of diffusion in a reference state and the entropy difference. Such a relationship may provide a measure of intermolecular correlations. We show that for a one-dimensional rugged energy landscape, the lower bound becomes equality only if certain three-site correlations are neglected. When these correlations are included, we can derive an accurate expression that agrees with computer simulations. The strong dimensionality dependence of diffusion of a Brownian particle in a rugged energy landscape also resembles the recently proposed inequality. We show that for interacting colloids, a mode-coupling theory-type calculation of diffusion coefficient can be combined with the new inequality to estimate entropy change from long-range inter-colloid correlations. Interestingly, the rate of barrier crossing in a multidimensional potential energy surface, related to diffusion in a periodic lattice, is shown to admit a relation that depends on the entropy change in a way reminiscent of the relation between D and S.

cond-mat.stat-mech↗

arXiv2024

The Hydrophobic Interaction Induced Strengthening of Hydrogen Bond in Water-DMSO Binary Mixture

The lifetime of a hydrogen bond between water and dimethyl sulfoxide (DMSO) is found to be considerably longer than that between two water molecules in the neat water. This is counter-intuitive because the charge on the oxygen in DMSO is considerably less than that in water. Additionally, the strength of the water-dimethyl sulfoxide (w-D) hydrogen bond is found to be strongly composition dependent; the lifetime of the hydrogen bond is ten times larger at 30% over that at very low concentration. Using computer simulations, we perform microscopic structural and dynamic analysis to find that these anomalies arise at least partly from an action-at-a-distance effect where the attraction between the hydrophobic methyl groups results in self-aggregation of DMSO molecules that cages both rotational and linear motions of molecules involved. This is reflected in the observed strong correlation of the lifetime with the local coordination number of the associated methyl groups. The elongated w-D h-bond lifetime causes a slowdown of collective dynamics and affects the lifetime of the w-w h-bond. This nonlinear feedback mechanism explains the strong composition dependence of viscosity and anticipated to play a dominant role in many self-assemblies. Furthermore, the w-D hydrogen bond breaking mechanism changes from low to high DMSO concentration, a phenomenon not anticipated a priori. We introduce a new order parameter-based free energy surface of the bond breaking pathway. A two-dimensional transition state rate theory (TSRT) calculation is performed for the lifetime of the w-D h-bond that is found to be semi-quantitatively accurate

cond-mat.soft↗