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Ion Santra

Publications and source records attributed to Ion Santra.

At least 19 recordsLinked to original sources
arXiv2026

Heat capacity as a marker for shape and jamming transitions in active systems

Persistence influences the stationary states of active particles, producing boundary accumulation at the single-particle level, and clustering or jamming in interacting systems. These features disappear as the persistence decreases and the system approaches a more passive-like stationary state. We show that these transitions have a distinct calorimetric signature. Using a lattice run-and-tumble dynamics, consistent with local detailed balance, we compute the nonequilibrium heat capacity from the excess heat released following a small temperature perturbation. For a single particle confined between reflecting boundaries, the heat capacity develops a maximum in the persistence regime corresponding to shape transition. Adding an exclusion interaction to the active particles on a periodic lattice, the reorganization of jammed clusters produces a corresponding peak in the thermal response. We also discuss the impact of the time-symmetric part of the transition rates, and show the possibility of seeing the same signatures of heat response in experiments by AC calorimetry. Our results show that nonequilibrium heat capacities can serve as calorimetric probes of nonequilibrium phase transitions.

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arXiv2026

An agitated oscillator chain

We study how the stationary dynamics of an oscillator chain is modified when coupled to a bath of run-and-tumble particles. First, assuming time-scale separation, we derive the induced Langevin chain dynamics with explicit expressions for the streaming term, friction coefficient, and noise amplitude. At high persistence of the run-and-tumble particle bath, the linear friction turns negative, creating an instability. Second, we find that this anti-damping is arrested at long times due to nonlinear effects, reminiscent of a Rayleigh oscillator. We conclude that a passive harmonic chain can be transformed by its coupling to active matter into a self-sustained fluctuating medium with many-body Rayleigh-like dynamics. That transfer of activity results in pulsations of the displacements, spatial oscillations, and the emergence of persistence in velocities along the chain.

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arXiv2026

Negative Differential Heat Conductivity in a Harmonic Chain Coupled to a Particle Reservoir

When coupling thermal baths at different temperatures, negative differential thermal conductivity is typically attributed to nonlinear interactions in the connecting medium. In this work, we demonstrate that such an effect can arise purely from the nature of the thermal baths and their coupling with the medium. Specifically, we construct a bath composed of overdamped thermal particles, which is coupled to one end of a harmonic chain, while the other end is connected to a standard Langevin heat bath. By analyzing the steady-state heat current, we observe significant negative differential thermal conductivity. In particular, as the temperature difference between the two baths diverges, the steady-state heat current through the chain vanishes. The effect is thermokinetic: we compute the effective dissipative coefficient and we find that it scales inversely with the square of the temperature of the particle bath in the high-temperature limit, resulting in an asymptotic decoupling between the bath and the chain. Our results highlight that nonequilibrium transport properties can be strongly influenced by the structure of the environment and its coupling to the system, even in otherwise linear systems.

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arXiv2026

Specific heat of thermally driven chains

We investigate the thermal responses of a harmonic oscillator chain coupled at its boundaries to heat baths held at different temperatures. This setup sustains a steady energy flux, continuously dissipating heat into both reservoirs. By introducing slow variations in the bath temperatures, we quantify the resulting excess heat currents and thereby obtain the nonequilibrium heat capacity matrix at fixed but arbitrary temperature differences. We demonstrate the existence of a well-defined thermodynamic limit for long chains. The specific heat associated with energy exchanges with a single bath depends on the difference in friction coefficients governing the system-bath couplings. That thermokinetic effect is typical for nonequilibrium response. When the couplings with the thermal baths acquire temperature dependence, the specific heat correspondingly inherits a nontrivial temperature dependence, in sharp contrast with equilibrium. Our results provide the first explicit determination of specific heat(s) in a locally interacting, spatially extended driven system. Beyond its exact solvability, the model may offer a natural nonequilibrium extension of the Dulong-Petit law, capturing the high-temperature behavior of driven molecules.

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arXiv2026

Resetting in a viscoelastic bath: the bath remembers

We study stochastic resetting of a probe particle in a viscoelastic environment where only the probe is reset while the medium retains memory of its past dynamics. Using a minimal model with finite correlation time, we analyze the competition between the resetting timescale and the viscoelastic relaxation timescale. This interplay leads to nonequilibrium steady states that differ qualitatively from those of Markovian Brownian motion with resetting. In particular, strong memory effects produce stationary position distributions with non-exponential tails. For instantaneous resets, we derive the limiting steady-state distributions analytically and compute exactly the time dependent leading non-vanishing moments. We also investigate non-instantaneous resetting via constant-velocity return protocols. In contrast to overdamped Brownian motion, where steady-state fluctuations are independent of the return dynamics, we find that in a viscoelastic medium the fluctuations depend on the reset velocity. This protocol dependence arises from the finite memory of the environment and highlights the role of environmental correlations in resetting-induced steady states.

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arXiv2026

Exact Volterra series for mean field dynamics

We derive an exact Volterra series expansion for a mean field of an interacting particle system subject to a potential perturbation, expressing the Volterra expansion kernels in terms of the field's response functions, to any order. Applying this formalism to the mean particle density of a simple fluid, we identify a form reminiscent of dynamical density functional theory, with, however, fundamental differences: A nonlocal mobility kernel appears, and forces derive from a functional of the {\it history} of mean density. The equilibrium density functional is shown to be recovered in the limit of slowly varying perturbation. We identify a freedom in deriving this expansion, which allows different forms of mobility kernels. These developments allow for a systematic improvement of established mean field formalisms.

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arXiv2025

Universal winding properties of chiral active motion

We propose the area swept $A(t)$ and the winding angle $Ω(t)$ as the key observables to characterize chiral active motion. We find that the distributions of the scaled area and the scaled winding angle are described by universal scaling functions across all well-known models of active particles, parametrized by the chirality $ω$, along with a self-propulsion speed $v_0$, and the persistence time $τ$. In particular, we show that, at late times, the average winding angle grows logarithmically with time $\laΩ\ra\sim(ωτ/2)\,\ln t$, while the average area swept has a linear temporal growth $\la A(t)\ra\simeq(ωτD_{\text{eff}})\,t$, where $D_{\text{eff}}=v_0^2 τ/[2(1+ ω^2 τ^2)]$ is the effective diffusion coefficient. Moreover, we find that the distribution of the scaled area $z=[A-\la A\ra]/(2D_{\text{eff}}t)$ is described by the universal scaling function $F_{\text{ch}}(z)=\text{sech}(πz)$. From extensive numerical evidence, we conjecture the emergence of a new universal scaling function $G_{\text{ch}}(z)=\mathcal {N}/[e^{αz} + e^{-βz}]$ for the distribution of the scaled winding angle $z=Ω/[\ln t]$, where the parameters $α$ and $β$ are model-dependent and $\mathcal{N}$ is the normalization constant. In the absence of chirality, i.e., $ω=0$, the scaling function becomes $G_{\text{ch}}(z)=(α/π)\,\mathrm{sech}(αz)$.

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arXiv2025

Tracer dynamics in an interacting active bath: fluctuations and energy partition

We investigate the dynamics of a massive tracer particle coupled to an interacting active bath, modeled as a harmonic chain of overdamped active particles analytically, with an aim to understand the impact of bath interactions and activity on the nonequilibrium fluctuations of the tracer. From the microscopic equations, we derive the tracer particle's effective Langevin equation, obtaining the dissipative and stochastic forces from the bath. We analyze the friction kernel, revealing power-law tails in the weak coupling limit and exponential decay in the strong coupling regime. Due to the interplay between bath interactions, probe-bath coupling, and activity, the mean squared displacement, velocity, and stationary velocity correlations exhibit different dynamical regimes, which we characterize analytically. Under harmonic confinement, we find that energy equipartition holds at low activity but breaks down at higher activity, with the kinetic energy exhibiting a non-monotonic dependence on the activity of the bath.

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arXiv2025

Brownian motion with stochastic energy renewals

We investigate the impact of intermittent energy injections on a Brownian particle, modeled as stochastic renewals of its kinetic energy to a fixed value. Between renewals, the particle follows standard underdamped Langevin dynamics. For energy renewals occurring at a constant rate, we find non-Boltzmannian energy distributions that undergo a shape transition driven by the competition between the velocity relaxation timescale and the renewal timescale. In the limit of rapid renewals, the dynamics mimics one-dimensional run-and-tumble motion, while at finite renewal rates, the effective diffusion coefficient exhibits non-monotonic behavior. To quantify the system's departure from equilibrium, we derive a modified fluctuation-response relation and demonstrate the absence of a consistent effective temperature. The dissipation is characterized by deviations from equilibrium-like response, captured via the Harada-Sasa relation. Finally, we extend the analysis to non-Poissonian renewal processes and introduce a dimensionless conversion coefficient that quantifies the thermodynamic cost of diffusion.

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arXiv2024

Forces from coarse-graining nonequilibrium degrees of freedom: exact results

We explore the relaxation dynamics of a tracer in a harmonic trap coupled to a non-equilibrium bath particle in stationary state, finding qualitative differences compared to the well known equilibrium case. These can be attributed to an additional position and time dependent force acting on the tracer, emerging when averaging the bath degree in the non-equilibrium stationary state conditioned to a certain tracer position. Specifically, we provide analytical results for an overdamped tracer coupled linearly to a bath particle in different nonequilibrium scenarios, namely, subjected to a different temperature than the tracer, or to active noise with Gaussian or non-Gaussian fluctuations. For the case of different temperatures, the conditioned tracer-bath force can be as large in magnitude as the force from the trapping potential. For an active bath particle with memory, even the bath noise takes a finite average under conditioning of the tracer. Further, if the noise of the bath particle is non-Gaussian, the relaxation function of the tracer can be non-monotonic as a function of time. We also compute the \emph{pinned relaxation}, proposing that measurement and comparison of conditioned and pinned relaxation allows determination of the non-equilibrium forces in experiments.

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arXiv2024

Dynamics of switching processes: general results and applications to intermittent active motion

Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a switching mechanism. Specifically, we obtain an exact expression of the Laplace-transformed characteristic function of the particle's position. Then, the characteristic function is used to compute the effective diffusion coefficient of a system performing intermittent dynamics. Further, we employ two examples: 1) Generalized run-and-tumble active particle, and 2) an active particle switching its dynamics between generalized active run-and-tumble motion and passive Brownian motion. In each case, explicit computations of the spatial cumulants are presented. Our findings reveal that the particle's position probability density function exhibit rich behaviours due to intermittent activity. Numerical simulations confirm our findings.

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arXiv2024

Harmonic chain driven by active Rubin bath: transport properties and steady-state correlations

Characterizing the properties of an extended system driven by active reservoirs is a question of increasing importance. Here we address this question in two steps. We start by investigating the dynamics of a probe particle connected to an `active Rubin bath' -- a linear chain of overdamped run-and-tumble particles. We derive exact analytical expressions for the effective noise and dissipation kernels, acting on the probe, and show that the active nature of the bath leads to a modified fluctuation-dissipation relation. In the next step, we study the properties of an activity-driven system, modeled by a chain of harmonic oscillators connected to two such active reservoirs at the two ends. We show that the system reaches a nonequilibrium stationary state (NESS), remarkably different from that generated due to a thermal gradient. We characterize this NESS by computing the kinetic temperature profile, spatial and temporal velocity correlations of the oscillators, and the average energy current flowing through the system. It turns out that, the activity drive leads to the emergence of two characteristic length scales, proportional to the activities of the reservoirs. Strong signatures of activity are also manifest in the anomalous short-time decay of the velocity autocorrelations. Finally, we find that the energy current shows a non-monotonic dependence on the activity drive and reversal in direction, corroborating previous findings.

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arXiv2023

Target search by active particles

Active particles, which are self-propelled nonequilibrium systems, are modelled by overdamped Langevin equations with colored noise, emulating the self-propulsion. In this chapter, we present a review of the theoretical results for the target search problem of these particles. We focus on three most well-known models, namely, run-and-tumble particles, active Brownian particles, and direction reversing active Brownian particles, which differ in their self-propulsion dynamics. For each of these models, we discuss the first-passage and survival probabilities in the presence of an absorbing target. We also discuss how resetting helps the active particles find targets in a finite time.

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arXiv2023

Dynamical fluctuations of a tracer coupled to active and passive particles

We study the induced dynamics of an inertial tracer particle elastically coupled to passive or active Brownian particles. We integrate out the environment degrees of freedom to obtain generalized Langevin equation for the tracer dynamics in both cases. In particular, we find the exact form of the dissipation kernel and effective noise experienced by the tracer and compare it with the phenomenological modeling of active baths used in previous studies. We show that the second fluctuation-dissipation relation (FDR) does not hold at early times for both cases. However, at finite times, the tracer dynamics violate (obeys) the FDR for the active (passive) environment. We calculate the linear response formulas in this regime for both cases and show that the passive medium satisfies an equilibrium fluctuation response relation (FRR), while the active medium does not -- we quantify the extent of this violation explicitly. We show that though the active medium generally renders a nonequilibrium description of the tracer, an effective equilibrium picture emerges asymptotically in the small activity limit of the medium. We also calculate the mean squared velocity and mean squared displacement of the tracer and report how they vary with time.

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arXiv2023

Dichotomous acceleration process in one dimension: Position fluctuations

We study the motion of a one-dimensional particle which reverses its direction of acceleration stochastically. We focus on two contrasting scenarios, where the waiting-times between two consecutive acceleration reversals are drawn from (i) an exponential distribution and (ii) a power-law distribution $ρ(τ)\sim τ^{-(1+α)}$. We compute the mean, variance and short-time distribution of the position $x(t)$ using a trajectory-based approach. We show that, while for the exponential waiting-time, $\langle x^2(t)\rangle\sim t^3$ at long times, for the power-law case, a non-trivial algebraic growth $\langle x^2(t)\rangle \sim t^{2ϕ(α)}$ emerges, where $ϕ(α)=2$, $(5-α)/2,$ and $3/2$ for $α<1,~1<α\leq 2$ and $α>2$, respectively. Interestingly, we find that the long-time position distribution in case (ii) is a function of the scaled variable $x/t^{ϕ(α)}$ with an $α$-dependent scaling function, which has qualitatively very different shapes for $α<1$ and $α>1$. In contrast, for case (i), the typical long-time fluctuations of position are Gaussian.

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arXiv2023

Long time behavior of run-and-tumble particles in two dimensions

We study the long-time asymptotic behavior of the position distribution of a run-and-tumble particle (RTP) in two dimensions and show that the distribution at a time $t$ can be expressed as a perturbative series in $(γt)^{-1}$, where $γ^{-1}$ is the persistence time of the RTP. We show that the higher order corrections to the leading order Gaussian distribution generically satisfy an inhomogeneous diffusion equation where the source term depends on the previous order solutions. The explicit solution of the inhomogeneous equation requires the position moments, and we develop a recursive formalism to compute the same.

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arXiv2023

Stationary states of activity-driven harmonic chains

We study the stationary state of a chain of harmonic oscillators driven by two active reservoirs at the two ends. These reservoirs exert correlated stochastic forces on the boundary oscillators which eventually leads to a nonequilibrium stationary state of the system. We consider three most well-known dynamics for the active force, namely, active Ornstein-Uhlenbeck process, run-and-tumble process and active Brownian process, all of which have exponentially decaying two-point temporal correlations but very different higher order fluctuations. We show that irrespective of the specific dynamics of the drive, the stationary velocity fluctuations are Gaussian in nature with a kinetic temperature which remains uniform in the bulk. Moreover, we find the emergence of an `equipartition of energy' in the bulk of the system -- the bulk kinetic temperature equals the bulk potential temperature in the thermodynamic limit. We also calculate the stationary distribution of the instantaneous energy current in the bulk which always shows a logarithmic divergence near the origin and asymmetric exponential tails. The signatures of specific active driving become visible in the behavior of the oscillators near the boundary. This is most prominent for the RTP and ABP driven chains where the boundary velocity distributions become non-Gaussian and current distribution has a finite cutoff.

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arXiv2022

Direction reversing active Brownian particle in a harmonic potential

We study the two-dimensional motion of an active Brownian particle of speed $v_0$, with intermittent directional reversals in the presence of a harmonic trap of strength $μ$. The presence of the trap ensures that the position of the particle eventually reaches a steady state where it is bounded within a circular region of radius $v_0/μ$, centered at the minimum of the trap. Due to the interplay between the rotational diffusion constant $D_R$, reversal rate $γ$, and the trap strength $μ$, the steady state distribution shows four different types of shapes, which we refer to as active-I & II, and passive-I & II phases. In the active-I phase, the weight of the distribution is concentrated along an annular region close to the circular boundary, whereas in active-II, an additional central diverging peak appears giving rise to a Mexican hat-like shape of the distribution. The passive-I is marked by a single Boltzmann-like centrally peaked distribution in the large $D_R$ limit. On the other hand, while the passive-II phase also shows a single central peak, it is distinguished from passive-I by a non-Boltzmann like divergence near the origin. We characterize these phases by calculating the exact analytical forms of the distributions in various limiting cases. In particular, we show that for $D_R\llγ$, the shape transition of the two-dimensional position distribution from active-II to passive-II occurs at $μ=γ$. We compliment these analytical results with numerical simulations beyond the limiting cases and obtain a qualitative phase diagram in the $(D_R,γ,μ^{-1})$ space.

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