arXiv subjects

Costantino Di Bello

Publications and source records attributed to Costantino Di Bello.

5 recordsLinked to original sources

arXiv2026

Poisson-shot-noise hybrid machines: efficiency and quasistatic divergence

We study stochastic models of a microscopic active heat engine, comprised of an overdamped Brownian particle trapped in a harmonic potential, and in simultaneous contact with thermal (passive) and athermal (active) baths. The interaction with the active bath is modeled as a stochastic force described by Poisson shot-noise (PSN) having a specified amplitude distribution. With analytical calculations and numerical simulations, we study the thermodynamic performance of the machine to quasistatic cyclic protocols analogous to those running two-stroke and Stirling-like engines. For specific parameter ranges, the thermodynamic behavior is that of a $\textit{hybrid machine}$, simultaneously operating as a heat engine with respect to the passive/active baths and as a refrigerator with respect to the passive/active baths. Focusing on the parameter region where the overall performance is such of an engine, we show that the average total extracted work per cycle divided by average total heat intake from the cold baths per cycle may surpass the Carnot efficiency associated with the temperature of the passive baths. Applying the second law for active heat engines, we focus on a bona fide efficiency (bounded by Carnot's efficiency) that incorporates an information-theoretic metric $\mathcal{I}-$ which we call $\textit{quasistatic divergence}-$ quantifying how distinguishable are the engine's statistics in the quasistatic limit with respect to a continually changing equilibrium distribution. We analyze, with theory and numerical simulations, how the PSN shot rate and the degree of non-Gaussianity in the particle position distribution influence the efficiency of the engine, and explore the correlation between non-Gaussianity and efficiency. Our findings reveal optimal PSN shot rates maximizing the engine's efficiency and an intriguing non-bijective relation between efficiency and kurtosis

cond-mat.stat-mech↗

arXiv2025

Exactly solvable diffusions from space-time transformations

We consider a general one-dimensional overdamped diffusion model described by the Itô stochastic differential equation (SDE) ${dX_t=μ(X_t,t)dt+σ(X_t,t)dW_t}$, where $W_t$ is the standard Wiener process. We obtain a specific condition that $μ$ and $σ$ must fulfil in order to be able to solve the SDE via mapping the generic process, using a suitable space-time transformation, onto the simpler Wiener process. By taking advantage of this transformation, we obtain the propagator in the case of open, reflecting, and absorbing \emph{time-dependent\/} boundary conditions for a large class of diffusion processes. In particular, this allows us to derive the first-passage time statistics of such a large class of models, some of which were so far unknown. While our results are valid for a wide range of non-autonomous, non-linear and non-homogeneous processes, we illustrate applications in stochastic thermodynamics by focusing on the propagator and first-passage-time statistics of isoentropic processes that were previously realized in the laboratory with Brownian particles trapped with optical tweezers.

cond-mat.stat-mech↗

arXiv2025

Partial versus total resetting for Lévy flights in d dimensions: similarities and discrepancies

While stochastic resetting (or total resetting) is less young and more established concept in stochastic processes, partial stochastic resetting (PSR) is a relatively new field. PSR means that, at random moments in time, a stochastic process gets multiplied by a factor between 0 and 1, thus approaching but not reaching the resetting position. In this paper, we present new results on PSR highlighting the main similarities and discrepancies with total resetting. Specifically, we consider both symmetric $α$-stable Lévy processes (Lévy flights) and Brownian motion with PSR in arbitrary d dimensions. We derive explicit expressions for the propagator and its stationary measure, and discuss in detail their asymptotic behavior. Interestingly, while approaching to stationarity, a dynamical phase transition occurs for the Brownian motion, but not for Lévy flights. We also analyze the behavior of the process around the resetting position and find significant differences between PSR and total resetting.

cond-mat.stat-mech↗

arXiv2023

Brownian particle in a Poisson-shot-noise active bath: exact statistics, effective temperature, and inference

We study the dynamics of an overdamped Brownian particle in a thermal bath that contains a dilute solution of active particles. The particle moves in a harmonic potential and experiences Poisson shot-noise kicks with specified amplitude distribution due to moving active particles in the bath. From the Fokker-Planck equation for the particle dynamics we derive the stationary solution for the displacement distribution along with the moments characterizing mean, variance, skewness, and kurtosis, as well as finite time first and second moments. We also compute an effective temperature through the fluctuation-dissipation theorem and show that equipartition theorem holds for all zero-mean kick distributions, including those leading to non-Gaussian stationary statistics. For the case of Gaussian-distributed active kicks we find a re-entrant behaviour from non-Gaussian to Gaussian stationary states and a heavy-tailed leptokurtic distribution across a wide range of parameters as seen in recent experimental studies. Further analysis reveals statistical signatures of the irreversible dynamics of the particle displacement in terms of the time asymmetry of cross-correlation functions. Fruits of our work is the development of a compact inference scheme that may allow experimentalists to extract the rate and moments of underlying shot-noise solely from the statistics of the particle position.

cond-mat.stat-mech↗

arXiv2023

Current fluctuations in stochastically resetting particle systems

We consider a system of non-interacting particles on a line with initial positions distributed uniformly with density $ρ$ on the negative half-line. We consider two different models: (i) each particle performs independent Brownian motion with stochastic resetting to its initial position with rate $r$ and (ii) each particle performs run and tumble motion, and with rate $r$ its position gets reset to its initial value and simultaneously its velocity gets randomised. We study the effects of resetting on the distribution $P(Q,t)$ of the integrated particle current $Q$ up to time $t$ through the origin (from left to right). We study both the annealed and the quenched current distributions and in both cases, we find that resetting induces a stationary limiting distribution of the current at long times. However, we show that the approach to the stationary state of the current distribution in the annealed and the quenched cases are drastically different for both models. In the annealed case, the whole distribution $P_{\rm an}(Q,t)$ approaches its stationary limit uniformly for all $Q$. In contrast, the quenched distribution $P_{\rm qu}(Q,t)$ attains its stationary form for $Q Q_{\rm crit}(t)$. We show that $Q_{\rm crit}(t)$ increases linearly with $t$ for large $t$. On the scale where $Q \sim Q_{\rm crit}(t)$, we show that $P_{\rm qu}(Q,t)$ has an unusual large deviation form with a rate function that has a third-order phase transition at the critical point. We have computed the associated rate functions analytically for both models. Using an importance sampling method that allows to probe probabilities as tiny as $10^{-14000}$, we were able to compute numerically this non-analytic rate function for the resetting Brownian dynamics and found excellent agreement with our analytical prediction.

cond-mat.stat-mech↗