Table of contents

A series of international conferences on Statistical Physics, going by the name Statphys-Kolkata, have been organized in Kolkata (erstwhile Calcutta) at regular intervals of two-three years, the first one being held in 1992-93. The eighth of this series, Statphys-Kolkata VIII (http://newweb.bose.res.in/Conferences/STATPHYSKOLKATAVIII/) was held during December 1-5, 2014, at the Satyendra Nath Bose National Centre for Basic Sciences, Kolkata. This volume contains selected papers by the speakers and participants of the Conference.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

We present examples of how time-symmetric kinetic factors contribute to the response either in nonlinear order around equilibrium or in linear order around nonequilibrium. The phenomenology we associate to that so called frenetic contribution are negative differential conductivity, changes in the Einstein relation between friction and noise, and population inversion.

We have introduced an approach to nonequilibrium thermodynamics of an open chemical reaction network in terms of the propensities of the individual elementary reactions and the corresponding reverse reactions. The method is a microscopic formulation of the dissipation function in terms of the relative entropy or Kullback-Leibler distance which is based on the analogy of phase space trajectory with the path of elementary reactions in a network of chemical process. We have introduced here a fluctuation theorem valid for each opposite pair of elementary reactions which is useful in determining the contribution of each sub-reaction on the nonequilibrium thermodynamics of overall reaction. The methodology is applied to an oligomeric enzyme kinetics at a chemiostatic condition that leads the reaction to a nonequilibrium steady state for which we have estimated how each step of the reaction is energy driven or entropy driven to contribute to the overall reaction.

We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined distribution such as the Gibbs- Boltzmann one is performed under the detailed balance condition. In the present study, we propose a modified Langevin dynamics violating the detailed balance condition on the transition- probability formulation. We confirm that the numerical implementation of the proposed method actually demonstrates two major beneficial improvements: acceleration of the relaxation to the predetermined distribution and reduction of the correlation time between two different realizations in the steady state.

Many existing studies on pattern formation in the reaction-diffusion systems rely on deterministic models. However, environmental noise is often a major factor which leads to significant changes in the spatiotemporal dynamics. In this paper, we focus on the spatiotemporal patterns produced by the predator-prey model with ratio-dependent functional response and density dependent death rate of predator. We get the reaction-diffusion equations incorporating the self-diffusion terms, corresponding to random movement of the individuals within two dimensional habitats, into the growth equations for the prey and predator population. In order to have the noise added model, small amplitude heterogeneous perturbations to the linear intrinsic growth rates are introduced using uncorrelated Gaussian white noise terms. For the noise added system, we then observe spatial patterns for the parameter values lying outside the Turing instability region. With thorough numerical simulations we characterize the patterns corresponding to Turing and Turing-Hopf domain and study their dependence on different system parameters like noise-intensity, etc.

We present results for a finite variant of the one-dimensional Toom model with closed boundaries. We show that the steady state distribution is not of product form, but is nonetheless simple. In particular, we give explicit formulas for the densities and some nearest neighbour correlation functions. We also give exact results for eigenvalues and multiplicities of the transition matrix using the theory of R-trivial monoids in joint work with A. Schilling, B. Steinberg and N. M. Thiéry.

In their seminal work, Brunet and Derrida made predictions on the random point configurations associated with branching random walks. We shall discuss the limiting behavior of such point configurations when the displacement random variables come from a power law. In particular, we establish that two prediction of remains valid in this setup and investigate various other issues mentioned in their paper.

During spontaneous imbibition, a wetting liquid is drawn into a porous medium by capillary forces. Recently, anomalous scaling properties of front broadening during spontaneous imbibition of water in Vycor glass, a nanoporous medium, were reported. The mean height and the width of the propagating front increase with time t both proportional to t^1/2. We argue that this anomalously large roughening exponent of β = 1/2 is due to long-lasting meniscus arrests, when at pore junctions the meniscus propagation in one or more branches comes to a halt when the Laplace pressure of the meniscus exceeds the hydrostatic pressure within the junction. From this hypothesis we derive the scaling relations for the emerging arrest time distribution in random pore networks and show that the average front width is proportional to the height yielding a roughness exponent of exactly β = 1/2 as measured in the Vycor glass imbibition experiments. Extensive simulations of a random pore network model confirm these predictions. Finally, using a microfluidic setup as well as molecular dynamics simulations on the nanoscale, the basic hypothesis of the scaling theory is confirmed by demonstrating the existence of arrest events in Y-shaped junctions, analyzing them quantitatively and comparing them with the theoretical predictions.

The nonequilibrium behaviours of kinetic Ising ferromagnet driven by a propagating magnetic field wave have been studied by Monte Carlo simulation. Two types of propagating magnetic field waves are used here. Namely, the plane wave and the spherical wave. For plane propagating wave passing through the Ising ferromagnet, system undergoes a phase transition from a pinned phase to a propagating phase, as the temperature increases. The transition temperature is found to depend on the amplitude of the propagating magnetic field. A phase boundary is drawn in the plane described by the temperature of the system and amplitude of the propagating field. On the other hand, the nonequilibrium behaviours shown by the Ising ferromagnet driven by spherical magnetic field wave, are different. Here, the system exists in three different dynamical phases. The low temperature pinned phase, the intermediate temperature centrally localised breathing phase and the high temperature extended spreading phase. Here also, the transition temperatures are observed to depend upon the amplitude of the propagating magnetic field wave. The phase boundaries are drawn in the plane represented by temperature of the system and the amplitude of the propagating magnetic field wave. The two boundaries merge at the Onsager value of equilibrium critical temperature in the limit of vanishingly small amplitude of the propagating magnetic field. This article is mainly a review of earlier works and is based on the invited lecture delivered in the conference STATPHYSKOLKATAVIII, held at SNBNCBS, Kolkata, India in December 1-5, 2014. This article is dedicated to Prof. H. Nishimori on the occasion of his 60th birthday.

Magneto-optical imaging studies on a high-quality Bi₂Sr₂CaCu₂O₈ single crystal partially patterned with a triangular array of holes reveal enhanced flux shielding in the patterned region of the sample. By mapping local magnetic field and shielding current density distributions at different applied magnetic fields and temperatures we determine the regime where pinning from the patterned holes dominates over the intrinsic pinning in the sample. In this regime, the flux density near the center of the patterned region is observed to increase when the applied field is varied from below the matching field to just above it, while significant magnetic field gradients are sustained in the patterned region. Our measurements indicate heterogeneous pinning properties of the vortex population, exhibiting signatures of both weak and strong pinning, in the nanopatterned region of the superconductor.

Many complex systems can be represented as networks of dynamical elements whose states evolve in response to interactions with neighboring elements, noise and external stimuli. The collective behavior of such systems can exhibit remarkable ordering phenomena such as chimera order corresponding to coexistence of ordered and disordered regions. Often, the interactions in such systems can also evolve over time responding to changes in the dynamical states of the elements. Link adaptation inspired by Hebbian learning, the dominant paradigm for neuronal plasticity, has been earlier shown to result in structural balance by removing any initial frustration in a system that arises through conflicting interactions. Here we show that the rate of the adaptive dynamics for the interactions is crucial in deciding the emergence of different ordering behavior (including chimera) and frustration in networks of Ising spins. In particular, we observe that small changes in the link adaptation rate about a critical value result in the system exhibiting radically different energy landscapes, viz., smooth landscape corresponding to balanced systems seen for fast learning, and rugged landscapes corresponding to frustrated systems seen for slow learning.

We present and compare different versions of a simple particle pump-model that describes average directed current of repulsively interacting particles in a narrow channel, due to time-varying local potentials. We analyze the model on discrete lattice with particle exclusion, using three choices of potential-dependent hopping rates that obey microscopic reversibility. Treating the strength of the external potential as a small parameter with respect to thermal energy, we present a perturbative calculation to obtain the expression for average directed current. This depends on driving frequency, phase, and particle density. The directed current vanishes as density goes to zero or close packing. For two choices of hopping rates, it reaches maximum at intermediate densities, while for a third choice, it shows a curious current reversal with increasing density. This can be interpreted in terms of a particle-hole symmetry. Stochastic simulations of the model show good agreement with our analytic predictions.

We report here recent findings that multiple cytoskeletal filaments (assumed rigid) pushing an obstacle typically generate more force than just the sum of the forces due to individual ones. This interesting phenomenon, due to the hydrolysis process being out of equilibrium, escaped attention in previous experimental and theoretical literature. We first demonstrate this numerically within a constant force ensemble, for a well known model of cytoskeletal filament dynamics with random mechanism of hydrolysis. Two methods of detecting the departure from additivity of the collective stall force, namely from the force-velocity curve in the growing phase, and from the average collapse time versus force curve in the bounded phase, is discussed. Since experiments have already been done for a similar system of multiple microtubules in a harmonic optical trap, we study the problem theoretically under harmonic force. We show that within the varying harmonic force ensemble too, the mean collective stall force of N filaments is greater than N times the mean stall force due to a single filament; the actual extent of departure is a function of the monomer concentration.

Conformational changes in biomacromolecules govern majority of biological processes. Complete characterization of conformational contributions to thermodynamics of complexation of biomacromolecules has been challenging. Although, advances in NMR relaxation experiments and several computational studies have revealed important aspects of conformational entropy changes, efficient and large-scale estimations still remain an intriguing facet. Recent histogram-based method (HBM) offers a simple yet rigorous route to estimate both conformational entropy and free energy changes from same set of histograms in an efficient manner. The HBM utilizes the power of histograms which can be generated as accurately as desired from an arbitrarily large sample space from atomistic simulation trajectories. Here we discuss some recent applications of the HBM, using dihedral angles of amino acid residues as conformational variables, which provide good measure of conformational thermodynamics of several protein-peptide complexes, obtained from NMR, metal-ion binding to an important metalloprotein, interfacial changes in protein-protein complex and insight to protein function, coupled with conformational changes. We conclude the paper with a few future directions worth pursuing.

Social inequality is a topic of interest since ages, and has attracted researchers across disciplines to ponder over it origin, manifestation, characteristics, consequences, and finally, the question of how to cope with it. It is manifested across different strata of human existence, and is quantified in several ways. In this review we discuss the origins of social inequality, the historical and commonly used non-entropic measures such as Lorenz curve, Gini index and the recently introduced k index. We also discuss some analytical tools that aid in understanding and characterizing them. Finally, we argue how statistical physics modeling helps in reproducing the results and interpreting them.

We present a minimal model to address the issue of how the interaction between foragers influence their encounter rates with resources. We consider a two-dimensional lattice model to study the optimal strategy for a group of foragers (walkers) searching for targets distributed heterogeneously. A forager who has not detected any target has the choice of, either joining other foragers in the neighbourhood, who have detected targets, or continue searching independently. The optimal strategy appears to be a mixture of these choices. Remarkably, we observe that scale-free walks appear for strategies far from optimality. In general, we investigate the behaviour of the model with a parameter characterizing the propensity of the foragers to aggregate and the radius of interaction characterizing the neighbourhood of a forager.

Non-equilibrium dynamics of the Ising model is a classical stochastic process whereas quantum mechanics has no stochastic elements in the classical sense. Nevertheless, it has been known that there exists a close formal relationship between these two processes. We reformulate this relationship and use it to compare the efficiency of simulated annealing that uses classical stochastic processes and quantum annealing to solve combinatorial optimization problems. It is shown that classical dynamics can be efficiently simulated by quantum- mechanical processes whereas the converse is not necessarily true. This may imply that quantum annealing may be regarded as a more powerful tool than simulated annealing for optimization problems.

Phase transitions in random k-SAT problems are connected to their computational complexity. While polynomical time algorithms are known to solve the problem for k = 2, for k ≥ 3 the problem is known to be NP-complete. Recently we have studied random k-SAT and many of its variants on regular infinite trees. We find that the solvability threshold for k = 2 matches the exact value of the threshold on regular random graphs. For higher k, the values are very close to those predicted using other techniques like cavity method.

The maximum entropy principle (MEP) is a very useful working hypothesis in a wide variety of inference problems, ranging from biological to engineering tasks. To better understand the reasons of the success of MEP, we propose a statistical-mechanical formulation to treat the space of probability distributions constrained by the measures of (experimental) observables. In this paper we first review the results of a detailed analysis of the simplest case of randomly chosen observables. In addition, we investigate by numerical and analytical means the case of smooth observables, which is of practical relevance. Our preliminary results are presented and discussed with respect to the efficiency of the MEP.