arXiv subjects

Soumyabrata Saha

Publications and source records attributed to Soumyabrata Saha.

9 recordsLinked to original sources

arXiv2026

Steady-state density large deviations in driven diffusive systems

A diffusive system coupled to boundary reservoirs reaches a non-equilibrium steady state whose density fluctuations can exhibit correlations over macroscopic distances. While current fluctuations are well understood for generic systems, exact results for the steady-state density large-deviation functional remain restricted to a few special models. We introduce a field transformation within Macroscopic Fluctuation Theory that, in one dimension, captures two broad exactly solvable classes characterized respectively by local and non-local large-deviation functionals. The transformation also allows us to explicitly determine the optimal fluctuation paths, exposing the dynamical origin of non-locality and time irreversibility. For generic transport coefficients, the same transformation provides a systematic perturbative scheme in the boundary drive. In particular, we show that a finite bulk drive shifts the onset of non-locality from quadratic to linear order in the boundary drive and generically generates long-range connected multipoint correlations of arbitrarily high order. In higher dimensions, this onset depends on the orientation of the bulk drive relative to the boundary-induced density gradient.

cond-mat.stat-mech↗

arXiv2026

An exactly solvable macroscopic fluctuation theory of single-file diffusion

Single-file diffusion is a ubiquitous phenomenon in low-dimensional systems, arising in transport inside narrow channels. Its natural continuum model is a one-dimensional gas of extended Brownian hard rods (BHR). Perhaps owing to the perceived intractability of this problem, much of the literature has traditionally focused on lattice exclusion models, where integrability methods have yielded remarkable, albeit limited, exact results. A major recent advance comes from a formal solution of macroscopic fluctuation theory (MFT) for the exclusion process. Yet, despite the formal solution, only a handful of properties have been made explicit. We show that the corresponding MFT of the extended BHR gas is in fact exactly solvable through a canonical transformation. We demonstrate this by explicit computation of the large-deviation statistics of the tracer-position and integrated-current in both annealed and quenched ensembles. We further show that an analogous canonical transformation applies to the MFT of lattice gases with finite-volume exclusion, yielding corresponding tracer and current statistics. We validate our results using rare-event simulations for both the continuum and the lattice models.

cond-mat.stat-mech↗

arXiv2026

Effect of slow bonds on current fluctuations in the symmetric simple exclusion process

The symmetric simple exclusion process (SSEP) is a paradigmatic model of classical non-equilibrium dynamics. Exact results for large deviations of particle current in the SSEP have been obtained in various settings using integrability-based methods. In this Article, we discuss how these results are modified in the presence of localized slow bonds. We consider three conventional geometries: (a) a finite one-dimensional lattice weakly coupled to unequal reservoirs at its boundaries, (b) a semi-infinite one-dimensional lattice weakly coupled to a boundary reservoir, and (c) an infinite one-dimensional lattice with localized slow bonds near the origin. For each case, we present exact expressions for the large deviation function of current and validate them through rare-event simulations based on the cloning algorithm. In connection with our results, we present an elementary derivation of the exact large deviation function for the current in the semi-infinite SSEP, complementing recent results obtained through more elaborate techniques.

cond-mat.stat-mech↗

arXiv2026

Universal tracer statistics in single-file transport

We uncover an emergent universality in the large-scale, long-time statistics of a one-dimensional hard-rod gas evolving under two fundamentally different classes of microscopic dynamics: stochastic (diffusive) and unitary (ballistic). Remarkably, despite the difference of the two systems, the one-time joint distribution of the positions of multiple tracers exhibits identical non-Gaussian fluctuations, up to a simple dynamical scaling. This universality holds in both annealed and quenched ensembles, demonstrating a persistent memory of the initial state. Differences between the dynamics manifest at large scales only in multi-time statistics. Our conclusions are based on explicit large-deviation results for the one-time statistics of tracer pairs and the two-time statistics of a single tracer. Similar physics extends to current fluctuations, demonstrated explicitly in the quenched ensemble. We obtain these results from exact microscopic solutions for both dynamics and, independently, from fluctuating hydrodynamics in the ballistic case in the annealed ensemble. Our rare-event simulations further corroborate these findings and provide a novel demonstration of sampling atypical fluctuations in both types of hard-rod gas.

cond-mat.stat-mech↗

arXiv2026

A bottom-up approach to fluctuating hydrodynamics: Coarse-graining of stochastic lattice gases and the Dean-Kawasaki equation

Fluctuating hydrodynamics provides a quantitative, large-scale description of many-body systems in terms of smooth variables, with microscopic details entering only through a small set of transport coefficients. Although this framework has been highly successful in characterizing macroscopic fluctuations and correlations, a systematic derivation of fluctuating hydrodynamics from underlying stochastic microscopic dynamics remains obscure for broad classes of interacting systems. For stochastic lattice gas models with gradient dynamics and a single conserved density, we develop a path-integral based coarse-graining procedure that recovers fluctuating hydrodynamics in a controlled manner. Our analysis highlights the essential role of local-equilibrium averages, which go beyond naïve mean-field-type gradient expansions. We further extend this approach to interacting Brownian particles by coarse-graining the Dean-Kawasaki equation, revealing a mobility proportional to the density and a diffusivity determined by the thermodynamic pressure.

cond-mat.stat-mech↗

arXiv2025

Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond

Two influential exact results in classical one-dimensional diffusive transport are about current statistics for the symmetric simple exclusion process: one in the stationary state on a finite line coupled with two unequal reservoirs at the boundaries, and the other in the non-stationary state on an infinite line. We present the corresponding result for the intermediate geometry of a semi-infinite line coupled with a single reservoir. This result is obtained using the fluctuating hydrodynamics approach of macroscopic fluctuation theory and confirmed by rare event simulations using a cloning algorithm. We apply our exact result for solving several related challenging problems, namely, the full counting statistics in presence of a defect bond, exclusion process with localized injection, survival of a tagged particle in presence of an absorbing boundary, and the stretched exponential decay in a kinetically constrained model.

cond-mat.stat-mech↗

arXiv2025

Hydrodynamics of a hard-core active lattice gas

We present a fluctuating hydrodynamic description of an active lattice gas model with excluded volume interactions that exhibits motility-induced phase separation under appropriate conditions. For quasi-one dimension and higher, stability analysis of the noiseless hydrodynamics gives quantitative bounds on the phase boundary of the motility-induced phase separation in terms of spinodal and binodal. Inclusion of the multiplicative noise in the fluctuating hydrodynamics describes the exponentially decaying two-point correlations in the stationary-state homogeneous phase. Our hydrodynamic description and theoretical predictions based on it are in excellent agreement with our Monte Carlo simulations and pseudospectral iteration of the hydrodynamics equations. Our construction of hydrodynamics for this model is not suitable in strictly one-dimension with single-file constraints, and we argue that this breakdown is associated with micro-phase separation.

cond-mat.stat-mech↗

arXiv2024

Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries: A Hydrodynamic Perspective

We revisit the one-dimensional model of the symmetric simple exclusion process slowly coupled with two unequal reservoirs at the boundaries. In its non-equilibrium stationary state, the large deviations functions of density and current have been recently derived using exact microscopic analysis by Derrida, Hirschberg and Sadhu in J. Stat. Phys. 182, 15 (2021). We present an independent derivation using the hydrodynamic approach of the macroscopic fluctuation theory (MFT). The slow coupling introduces additional boundary terms in the MFT-action, which modifies the spatial boundary conditions for the associated variational problem. For the density large deviations, we explicitly solve the corresponding Euler-Lagrange equations using a simple local transformation of the optimal fields. For the current large deviations, our solution is obtained using the additivity principle. In addition to recovering the expression of the large deviations functions, our solution describes the most probable path for these rare fluctuations.

cond-mat.stat-mech↗

arXiv2023

Current fluctuations in a semi-infinite line

We present the application of a fluctuating hydrodynamic theory to study current fluctuations in diffusive systems on a semi-infinite line in contact with a reservoir with slow coupling. We show that the distribution of the time-integrated current across the boundary at large times follows a large deviation principle with a rate function that depends on the coupling strength with the reservoir. The system exhibits a long-term memory of its initial state, which was earlier reported on an infinite line and can be described using quenched and annealed averages of the initial state. We present an explicit expression of the rate function for independent particles, which we verify using an exact solution of the microscopic dynamics. For the symmetric simple exclusion process, we present expressions for the first three cumulants of both quenched and annealed averages.

cond-mat.stat-mech↗