arXiv subjects

Farhad H. Jafarpour

Publications and source records attributed to Farhad H. Jafarpour.

At least 19 recordsLinked to original sources

arXiv2026

Thermodynamic Uncertainty Relation For a Multi-Phase Alternating Renewal Random Walk

Thermodynamic Uncertainty Relations (TURs) impose universal bounds linking current precision to entropy production in nonequilibrium systems. While general bounds like the Proesmans--Van den Broeck (PV) relation provide a broad framework, they often remain loose for processes characterized by renewal events. In this work, we derive a generalized entropic bound for current fluctuations in renewal-reward processes. By utilizing a rigorous variance decomposition within the framework of renewal-reward theory, we obtain a model-independent bound that is not only rigorous but tighter than the standard PV relation. Notably, in the linear-response regime, our bound correctly scales with the renewal rate and identifies a precision penalty arising from cycle-length fluctuations. These results provide a physically informative constraint on the precision of run-and-tumble-type dynamics and highlight the universal limits of transport in complex stochastic walkers.

cond-mat.stat-mech↗

arXiv2026

Giant Fluctuations in Self-Propelled Particles with Age-Dependent Switching

We investigate the transport and fluctuation properties of self-propelled particles whose motion is governed by an age-dependent phase-switching mechanism. The dynamics alternate between a Markovian downstream phase with a constant switching probability $r$ and a semi-Markovian upstream phase in which the age-dependent hazard probability $a/(b+c)$ decays with the internal clock $c$, representing persistent orientation. The time-averaged velocity, as an order parameter, shows a continuous transition at $a=1$ which separates an upstream-dominated ballistic regime ($a<1$) from an ergodic diffusive regime ($a>1$). Through generating-function methods and discrete-time moment recurrences, we derive exact expressions for the propagator and determine the long-time asymptotics of the mean displacement and variance. At the critical point $a=1$, the system exhibits giant fluctuations, with the variance scaling ballistically up to a logarithmic correction, $\mathrm{Var}(x_T) \propto T^2 / \log T$. These results demonstrate how slowly decaying reorientation probabilities lead to a marginal breakdown of the Central Limit Theorem, enabling unusually high-variance exploratory dynamics in biased environments.

cond-mat.stat-mech↗

arXiv2026

Semi-Markovian Dynamics of a Self-Propelled Particle in a Confined Environment: A Large-Deviation Study

We study the large deviations of the time-integrated current for a self-propelled particle moving within a confined environment. The dynamics is modeled as a semi-Markovian process, where the transitions between a \textit{normal running phase} (Phase $0$) and a \textit{wall-attached phase} (Phase $1$) are governed by time-dependent reset probabilities. We study two different examples: In the first case, the particle undergoes a biased random walk in Phase $0$, while it intermittently resets and interacts with the container boundaries, remaining stationary in Phase $1$. In this scenario, the reset probabilities for transitions between the two phases follow an ``aging'' logic. In the second case, the particle alternates between two active phases: a Markovian Phase $0$ characterized by memoryless, downstream-biased motion, and a semi-Markovian Phase $1$ with a reversed, upstream bias representing boundary-attached navigation. Here, we assume a time-independent survival probability in Phase $0$ and a time-dependent one in Phase $1$. By analyzing the Scaled Cumulant Generating Function (SCGF) in the long-time limit, we derive the conditions for Dynamical Phase Transition (DPT)s in the fluctuations of the particle velocity. We demonstrate that, depending on the aging strength, the system exhibits either discontinuous (first-order) or continuous (second-order) DPTs. Analytical predictions are validated via computer simulations.

cond-mat.stat-mech↗

arXiv2019

Current fluctuations in a stochastic system of classical particles with next-nearest-neighbor interactions

A totally asymmetric exclusion process consisting of classical particles with next-nearest-neighbor interactions has been considered on a 1D discrete lattice with a ring geometry. Using large deviation techniques, we have investigated fluctuations of particle current in two and three-particle sectors. In two-particle sector, we have obtained exact large deviation function for the probability distribution of particle current. In this sector, we have also calculated the the propensity of each configuration to exhibit atypical particle current. Analytical results for both scaled cumulant generating function of particle current and average particle current are compared with those obtained from cloning Monte Carlo simulations. Numerical results in three-particle sector have also been presented.

cond-mat.stat-mech↗

arXiv2019

Stochastic modeling of gene expression: application of ensembles of trajectories

It is well established that gene expression can be modeled as a Markovian stochastic process and hence proper observables might be subjected to large fluctuations and rare events. Since dynamics is often more than statics, one can work with ensembles of trajectories for long but fixed times, instead of states or configurations, to study dynamics of these Markovian stochastic processes and glean more information. In this paper we aim to show that the concept of ensemble of trajectories can be applied to a variety of stochastic models of gene expression ranging from a simple birth-death process to a more sophisticate model containing burst and switch. By considering the protein numbers as a relevant dynamical observable, apart from asymptotic behavior of remote tails of probability distribution, generating function for the cumulants of this observable can also be obtained. We discuss the unconditional stochastic Markov processes which generate the statistics of rare events in these models.

physics.bio-ph↗

arXiv2019

Effective dynamics in an asymmetric death-branching process

In this paper we study activity fluctuations in an asymmetric death-branching process in one-dimension. The model, which is a variant of the asymmetric Glauber model, has already been studied in [12]. It is known that in the low-activity region i.e. below the typical activity in the steady-state, the dynamical free energy of the system can be calculated exactly. However, the behavior of the system in the high-activity region is different and more interesting. The system undergoes a series of dynamical phase transitions. In present work we justify the hierarchy of dynamical phase transitions in terms of effective interactions in the system. It turns out that the effective interactions are long-range and that they can be described in terms of interactions between repelling shock fronts.

cond-mat.stat-mech↗

arXiv2019

Effective dynamics of a conditioned generalized linear Glauber model

In order to study the stochastic Markov processes conditioned on a specific value of a time-integrated observable, the concept of ensembles of trajectories has been recently used extensively. In this paper, we consider a generic reaction-diffusion process consisting of classical particles with nearest-neighbor interactions on a one-dimensional lattice with periodic boundary conditions. By introducing a time-integrated current as a physical observable, we have found certain constraints on the microscopic transition rates of the process under which the effective process contains local interactions; however, with rescaled transition rates comparing to the original process. A generalization of the linear Glauber model is then introduced and studied in detail as an example. Associated effective dynamics of this model is investigated and constants of motion are obtained.

cond-mat.stat-mech↗

arXiv2017

Effective Stochastic Generator with Site-dependent Interactions

It is known that the stochastic generators of effective processes associated with the unconditioned dynamics of rare events might consist of non-local interactions; however, it can be shown that there are special cases for which these generators can include local interactions. In this paper we investigate this possibility by considering systems of classical particles moving on a one-dimensional lattice with open boundaries. The particles might have hard-core interactions similar to the particles in an exclusion process or there can be arbitrary many particles at single site as in a zero-range process. Assuming that the interactions in the original process are local and site-independent, we will show that under certain constraints on the microscopic reaction rules, the stochastic generator of unconditioned process can be local but site-dependent. As two examples, the asymmetric zero-temperature Glauber model and the A-model with diffusion are presented and studied under the above mentioned constraints.

cond-mat.stat-mech↗

arXiv2015

On Effective Stochastic Generators for Conditioned Dynamics at an Atypical Reaction-Diffusion Current

We consider the fluctuations of a time-integrated particle current around an atypical value in a generic stochastic Markov process involving classical particles with two-site interaction and hardcore repulsion on a finite one-dimensional lattice with open boundaries. We address the question of which interactions one has to impose on such process to make the atypical value of the current typical. It is known that a corresponding effective stochastic Markov process might exist whose typical value of the current is equal to the atypical value of the current in the original process within a time-translational invariant regime. This effective process has, in principle, non-local transition rates. Nevertheless, it turns out that under some conditions the stochastic generator of the effective process has the same dynamical rules as the stochastic generator of the original process. We find these conditions and show that our approach can be generalized to any time-integrated observable.

cond-mat.stat-mech↗

arXiv2014

Rare-event trajectory ensemble approach to study dynamical phase transitions in the zero temperature Glauber model

The dynamics of a one-dimensional stochastic system of classical particles consisting of asymmetric death and branching processes is studied. The dynamical activity, defined as the number of configuration changes in a dynamical trajectory, is considered as a proper dynamical order parameter. By considering an ensemble of dynamical trajectories and applying the large deviation method, we have found that the system might undergo both continuous and discontinuous dynamical phase transitions at critical values of the counting field. Exact analytical results are obtained for an infinite system. Numerical investigations confirm our analytical calculations.

cond-mat.stat-mech↗

arXiv2013

A new family of exactly solvable disordered reaction-diffusion systems

Using a matrix product method the steady-state of a family of disordered reaction-diffusion systems consisting of different species of interacting classical particles moving on a lattice with periodic boundary conditions is studied. A new generalized quadratic algebra and its matrix representations is introduced. The steady-states of two members of this exactly solvable family of systems are studied in detail.

cond-mat.stat-mech↗

arXiv2013

Phase transition in an exactly solvable reaction-diffusion process

We study a non-conserved one-dimensional stochastic process which involves two species of particles $A$ and $B$. The particles diffuse asymmetrically and react in pairs as $A\emptyset\leftrightarrow AA\leftrightarrow BA \leftrightarrow A\emptyset$ and $B\emptyset \leftrightarrow BB \leftrightarrow AB \leftrightarrow B\emptyset$. We show that the stationary state of the model can be calculated exactly by using matrix product techniques. The model exhibits a phase transition at a particular point in the phase diagram which can be related to a condensation transition in a particular zero-range process. We determine the corresponding critical exponents and provide a heuristic explanation for the unusually strong corrections to scaling seen in the vicinity of the critical point.

cond-mat.stat-mech↗

arXiv2013

Particle current fluctuations in a particle-nonconserving process

We have considered a one-dimensional coagulation-decoagulation system of classical particles on a finite lattice with reflecting boundaries. It is known that the system undergoes a phase transition from a high-density to a low-density phase. Using a matrix product approach we have obtained an exact expression for the average entropy production rate of the system in the thermodynamic limit. We have also performed a large deviation analysis for fluctuations of entropy production rate and particle current. It turns out that the characteristics of the kink in the large deviation function can be used to spot the phase transition point. We have found that for very weak driving field (when the system approaches to its equilibrium) and also for very strong driving field (when the system is in the low-density phase) the large deviation function for fluctuations of entropy production rate is almost parabolic while in the high-density phase it prominently deviates from Gaussian behavior. The validity of the Gallavotti-Cohen fluctuation relation for the large deviation function for particle current is also verified.

cond-mat.stat-mech↗

arXiv2012

Entropy Production of Nonequilibrium Steady States with Irreversible Transitions

In nature stationary nonequilibrium systems cannot exist on their own, rather they need to be driven from outside in order to keep them away from equilibrium. While the internal mean entropy of such stationary systems is constant, the external drive will on average increase the entropy in the environment. This external entropy production is usually quantified by a simple formula, stating that each microscopic transition of the system between two configurations $c \to c'$ with rate $w_{c\to c'}$ changes the entropy in the environment by $ΔS_{\rm env} = {\ln w_{c \to c'}}-{\ln w_{c' \to c}}$. According to this formula irreversible transitions $c \to c'$ with a vanishing backward rate $w_{c'\to c}=0$ would produce an infinite amount of entropy. However, in experiments designed to mimic such processes, a divergent entropy production, that would cause an infinite increase of heat in the environment, is not seen. The reason is that in an experimental realization the backward process can be suppressed but its rate always remains slightly positive, resulting in a finite entropy production. The paper discusses how this entropy production can be estimated and specifies a lower bound depending on the observation time.

cond-mat.stat-mech↗

arXiv2011

One-transit paths and steady-state of a non-equilibrium process in a discrete-time update

We have shown that the partition function of the Asymmetric Simple Exclusion Process with open boundaries in a sublattice-parallel updating scheme is equal to that of a two-dimensional one-transit walk model defined on a diagonally rotated square lattice. It has been also shown that the physical quantities defined in these systems are related through a similarity transformation.

cond-mat.stat-mech↗

arXiv2011

Bose-Einstein condensation and a two-dimensional walk model

We introduce a two-dimensional walk model in which a random walker can only move on the first quarter of a two-dimensional plane. We calculate the partition function of this walk model using a transfer matrix method and show that the model undergoes a phase-transition. Surprisingly the partition function of this two-dimensional walk model is exactly equal to that of a driven-diffusive system defined on a discrete lattice with periodic boundary conditions in which a phase transition occurs from a high-density to a low-density phase. The driven-diffusive system can be mapped to a zero-range process where the particles can accumulate in a single lattice site in the low-density phase. This is very reminiscent of real-space Bose-Einstein condensation.

cond-mat.stat-mech↗

arXiv2010

Multiple-transit paths and density correlation functions in PASEP

We consider the partially asymmetric simple exclusion process (PASEP) when its steady-state probability distribution function can be written in terms of a linear superposition of product measures with a finite number of shocks. In this case the PASEP can be mapped into an equilibrium walk model, defined on a diagonally rotated square lattice, in which each path of the walk model has several transits with the horizontal axis. We particularly show that the multiple-point density correlation function in the PASEP is related to the probability that a path has multiple contacts with the horizontal axis from the above or below.

cond-mat.stat-mech↗

arXiv2009

Equivalence of a one-dimensional driven-diffusive system and an equilibrium two-dimensional walk model

It is known that a single product shock measure in some of one-dimensional driven-diffusive systems with nearest-neighbor interactions might evolve in time quite similar to a random walker moving on a one-dimensional lattice with reflecting boundaries. The non-equilibrium steady-state of the system in this case can be written in terms of a linear superposition of such uncorrelated shocks. Equivalently, one can write the steady-state of this system using a matrix-product approach with two-dimensional matrices. In this paper we introduce an equilibrium two-dimensional one-transit walk model and find its partition function using a transfer matrix method. We will show that there is a direct connection between the partition functions of these two systems. We will explicitly show that in the steady-state the transfer matrix of the one-transit walk model is related to the matrix representation of the algebra of the driven-diffusive model through a similarity transformation. The physical quantities are also related through the same transformation.

cond-mat.stat-mech↗