arXiv subjects

Francesco Coghi

Publications and source records attributed to Francesco Coghi.

At least 19 recordsLinked to original sources

arXiv2026

Rare events of small-noise Doob conditioned processes

Doob fixed-time conditioning enables the sampling of rare trajectories of Markov processes by modifying the drift so that reaching a prescribed target at a given time is guaranteed. We study the statistics of this conditioned path ensemble through the moment generating function in the weak-noise large deviation regime. Since the Doob drift is rarely available in closed form, we reinterpret the conditioned ensemble as the original process post-selected on the terminal constraint, thereby avoiding explicit construction of the Doob transform. This viewpoint then yields an optimal-control representation for the leading exponential contribution to the generating function, expressed as a variational principle with terminal boundary conditions set by the Doob end-point constraint. We illustrate the framework with two analytical examples and with an application to heat dissipation of a minimal model of biomolecular folding.

cond-mat.stat-mech↗

arXiv2026

Level 2.5 large deviations and uncertainty relations for self-interacting jump processes: tilting constructions and the emergence of time-scale separation

Self-interacting jump processes (SIJPs) describe systems with non-Markovian stochastic dynamics in which transition rates depend on empirical observables of the process, which gives rise to long-range memory and feedback. We derive the ``level-2.5'' large deviation (LD) principle governing the joint fluctuations of empirical occupation measure and the flux matrix for a broad class of SIJPs with general functional dependence on an empirical observable. The derivation is based on an exponential tilting construction and reveals a separation between a faster timescale of the microscopic dynamics and a slower timescale of the memory-driven evolution of transition rates, which is expressed through an exponentially discounted LD rate functional. Using this variational framework, we derive kinetic and thermodynamic uncertainty relations that extend classical Markovian bounds to non-Markovian systems, and illustrate their performance with simple examples.

cond-mat.stat-mech↗

arXiv2026

Level 2.5 large deviations and uncertainty relations for non-Markov self-interacting dynamics

We address the general problem of formulating the dynamical large deviations of non-Markovian systems in a closed form. Specifically, we consider a broad class of ``self-interacting'' jump processes whose dynamics depends on the past through a functional of a state-dependent empirical observable. Exploiting a natural separation of timescales, we obtain the exact (so-called ``level 2.5'') large deviation joint statistics of the empirical measure over configurations and of the empirical flux of transitions. As an application of this general framework, we derive explicit general bounds on the fluctuations of trajectory observables, generalising to the non-Markovian case both thermodynamic and kinetic uncertainty relations. We illustrate our theory with simple examples, and discuss potential applications of these results.

cond-mat.stat-mech↗

arXiv2025

Jump Processes with Self-Interactions: Large Deviation Asymptotics

We consider a pure jump process $\{X_t\}_{t\ge 0}$ with values in a finite state space $S= \{1, \ldots, d\}$ for which the jump rates at time instant $t$ depend on the occupation measure $L_t \doteq t^{-1} \int_0^t \delta_{X_s}\,ds$. Such self-interacting chains arise in many contexts within statistical physics and applied probability. Under appropriate conditions, a large deviation principle is established for the pair $(L_t, R_t)$, as $t \to \infty$, where $R_t$ is the empirical flux process associated with the jump process. We show that the rate function takes a simple form that can be viewed as a dynamical generalization of the classical Donsker and Varadhan rate function for the analogous quantities in the setting of Markov processes, in particular, unlike the Markovian case, the rate function is not convex. Since the state process is non-Markovian, different techniques are needed than in the setting of Donsker and Varadhan and our proofs rely on variational representations for functionals of Poisson random measures and stochastic control methods.

math.PR↗

arXiv2025

Accelerated first-passage dynamics in a non-Markovian feedback Ornstein--Uhlenbeck process

We study the first-passage dynamics of a non-Markovian stochastic process with time-averaged feedback, which we model as a one-dimensional Ornstein--Uhlenbeck process wherein the particle drift is modified by the empirical mean of its trajectory. This process maps onto a class of self-interacting diffusions. Using weak-noise large deviation theory, we calculate the leading order asymptotics of the time-dependent distribution of the particle position, derive the most probable paths that reach the specified position at a given time and quantify their likelihood via the action functional. We compute the feedback-modified Kramers rate and its inverse, which approximates the mean first-passage time, and show that the feedback accelerates dynamics by storing finite-time fluctuations, thereby lowering the effective energy barrier and shifting the optimal first-passage time from infinite to finite. Although we identify alternative mechanisms, such as slingshot and ballistic trajectories, we find that they remain sub-optimal and hence do not accelerate the dynamics. These results show how memory feedback reshapes rare event statistics, thereby offering a mechanism to potentially control first-passage dynamics.

cond-mat.stat-mech↗

arXiv2025

Self-interacting processes via Doob conditioning

We connect self-interacting processes, that is, stochastic processes where transitions depend on the time spent by a trajectory in each configuration, to Doob conditioning. In this way we demonstrate that Markov processes with constrained occupation measures are realised optimally by self-interacting dynamics. We use a tensor network framework to guide our derivations. We illustrate our general results with new perspectives on well-known examples of self-interacting processes, such as random walk bridges, excursions, and forced excursions.

cond-mat.stat-mech↗

arXiv2024

Density-dependent stochastic resetting: a large deviations framework for achieving target distributions over networks

We develop a framework for designing density-dependent stochastic resetting protocols to regulate distributions of random walkers on networks. Resetting mechanisms that depend on local densities induce correlations in otherwise non-interacting walkers. Our framework allows for the study of both transient trajectories and stationary properties and identifies resetting protocols that maximise the likelihood of homogeneous and, more generally, rare configurations of random walkers.

cond-mat.stat-mech↗

arXiv2024

Current fluctuations of a self-interacting diffusion on a ring

We investigate fluctuations in the average speed or current of a self-interacting diffusion (SID) on a ring, mimicking the non-Markovian behaviour of an agent influenced by its own path. We derive the SID's phase diagram, showing a delocalisation-localisation phase transition from self-repelling to self-attracting. Current fluctuations are analysed using: (i) an adiabatic approximation, where the system reaches its stationary distribution before developing current fluctuations, and (ii) an original extension of level 2.5 large deviations for Markov processes combined with perturbation theory. Both methods provide lower bounds to current fluctuations, with the former tighter than the latter in all localised regimes, and both equally tight in the self-repelling region. Both methods accurately estimate the asymptotic variance and suggests a phase transition at the onset of the localised regime.

cond-mat.stat-mech↗

arXiv2024

Dynamical fluctuations of random walks in higher-order networks

Although higher-order interactions are known to affect the typical state of dynamical processes giving rise to new collective behavior, how they drive the emergence of rare events and fluctuations is still an open problem. We investigate how fluctuations of a dynamical quantity of a random walk exploring a higher-order network arise over time. \newtext{In the quenched case, where the hypergraph structure is fixed, through large deviation theory we show that the appearance of rare events is hampered in nodes with many higher-order interactions, and promoted elsewhere. Dynamical fluctuations are further boosted in an annealed scenario, where both the diffusion process and higher-order interactions evolve in time. Here, extreme fluctuations generated by optimal higher-order configurations can be predicted in the limit of a saddle-point approximation.} Our study lays the groundwork for a wide and general theory of fluctuations and rare events in higher-order networks.

cond-mat.dis-nn↗

arXiv2024

Thermodynamic cost for precision of general counting observables

We analytically derive universal bounds that describe the trade-off between thermodynamic cost and precision in a sequence of events related to some internal changes of an otherwise hidden physical system. The precision is quantified by the fluctuations in either the number of events counted over time or the times between successive events. Our results are valid for the same broad class of nonequilibrium driven systems considered by the thermodynamic uncertainty relation, but they extend to both time-symmetric and asymmetric observables. We show how optimal precision saturating the bounds can be achieved. For waiting time fluctuations of asymmetric observables, a phase transition in the optimal configuration arises, where higher precision can be achieved by combining several signals.

cond-mat.stat-mech↗

arXiv2024

Generalized Landauer bound from absolute irreversibility

In this work, we introduce a generalization of the Landauer bound for erasure processes that stems from absolutely irreversible dynamics. Assuming that the erasure process is carried out in an absolutely irreversible way so that the probability of observing some trajectories is zero in the forward process but finite in the reverse process, we derive a generalized form of the bound for the average erasure work, which is valid also for imperfect erasure and asymmetric bits. The generalized bound obtained is tighter or, at worst, as tight as existing ones. Our theoretical predictions are supported by numerical experiments and the comparison with data from previous works.

cond-mat.stat-mech↗

arXiv2023

Understanding random-walk dynamical phase coexistence through waiting times

We study the appearance of first-order dynamical phase transitions (DPTs) as `intermittent' co-existing phases in the fluctuations of random walks on graphs. We show that the diverging time scale leading to critical behaviour is the waiting time to jump from one phase to another. This time scale is crucial for observing the system's relaxation to stationarity and demonstrates ergodicity of the system at criticality. We illustrate these results through three analytical examples which provide insights into random walks exploring random graphs.

cond-mat.stat-mech↗

arXiv2023

Adaptive power method for estimating large deviations in Markov chains

We study the performance of a stochastic algorithm based on the power method that adaptively learns the large deviation functions characterizing the fluctuations of additive functionals of Markov processes, used in physics to model nonequilibrium systems. This algorithm was introduced in the context of risk-sensitive control of Markov chains and was recently adapted to diffusions evolving continuously in time. Here we provide an in-depth study of the convergence of this algorithm close to dynamical phase transitions, exploring the speed of convergence as a function of the learning rate and the effect of including transfer learning. We use as a test example the mean degree of a random walk on an Erdös-Rényi random graph, which shows a transition between high-degree trajectories of the random walk evolving in the bulk of the graph and low-degree trajectories evolving in dangling edges of the graph. The results show that the adaptive power method is efficient close to dynamical phase transitions, while having many advantages in terms of performance and complexity compared to other algorithms used to compute large deviation functions.

cond-mat.stat-mech↗

arXiv2023

Convergence of the Integral Fluctuation Theorem estimator for nonequilibrium Markov systems

The Integral Fluctuation Theorem for entropy production (IFT) is among the few equalities that are known to be valid for physical systems arbitrarily driven far from equilibrium. Microscopically, it can be understood as an inherent symmetry for the fluctuating entropy production rate implying the second law of thermodynamics. Here, we examine an IFT statistical estimator based on regular sampling and discuss its limitations for nonequilibrium systems, when sampling rare events becomes pivotal. Furthermore, via a large deviation study, we discuss a method to carefully setup an experiment in the parameter region where the IFT estimator safely converges and also show how to improve the convergence region for Markov chains with finite correlation time. We corroborate our arguments with two illustrative examples.

cond-mat.stat-mech↗

arXiv2023

Maximal dispersion of adaptive random walks

Maximum entropy random walks (MERWs) are maximally dispersing and play a key role in optimizing information spreading in various contexts. However, building MERWs comes at the cost of knowing beforehand the global structure of the network, a requirement that makes them totally inadequate in real case scenarios. Here, we propose an adaptive random walk (ARW), which instead maximizes dispersion by updating its transition rule on the local information collected while exploring the network. We show how to derive ARW via a large-deviation representation of MERW and study its dynamics on synthetic and real world networks.

cond-mat.stat-mech↗

arXiv2022

Delocalization-localization dynamical phase transition of random walks on graphs

We consider random walks evolving on two models of connected and undirected graphs and study the exact large deviations of a local dynamical observable. We prove, in the thermodynamic limit, that this observable undergoes a first-order dynamical phase transition (DPT). This is interpreted as a `co-existence' of paths in the fluctuations that visit the highly connected bulk of the graph (delocalization) and paths that visit the boundary (localization). The methods we used also allow us to characterize analytically the scaling function that describes the finite size crossover between the localized and delocalized regimes. Remarkably, we also show that the DPT is robust with respect to a change in the graph topology, which only plays a role in the crossover regime. All results support the view that a first-order DPT may also appear in random walks on infinite-size random graphs.

cond-mat.stat-mech↗

arXiv2022

Graph-combinatorial approach for large deviations of Markov chains

We consider discrete-time Markov chains and study large deviations of the pair empirical occupation measure, which is useful to compute fluctuations of pure-additive and jump-type observables. We provide an exact expression for the finite-time moment generating function, which is split in cycles and paths contributions, and scaled cumulant generating function of the pair empirical occupation measure via a graph-combinatorial approach. The expression obtained allows us to give a physical interpretation of interaction and entropic terms, and of the Lagrange multipliers, and may serve as a starting point for sub-leading asymptotics. We illustrate the use of the method for a simple two-state Markov chain.

cond-mat.stat-mech↗

arXiv2021

Role of current fluctuations in nonreversible samplers

It is known that the distribution of nonreversible Markov processes breaking the detailed balance condition converges faster to the stationary distribution compared to reversible processes having the same stationary distribution. This is used in practice to accelerate Markov chain Monte Carlo algorithms that sample the Gibbs distribution by adding nonreversible transitions or non-gradient drift terms. The breaking of detailed balance also accelerates the convergence of empirical estimators to their ergodic expectation in the long-time limit. Here, we give a physical interpretation of this second form of acceleration in terms of currents associated with the fluctuations of empirical estimators using the level 2.5 of large deviations, which characterises the likelihood of density and current fluctuations in Markov processes. Focusing on diffusion processes, we show that there is accelerated convergence because estimator fluctuations arise in general with current fluctuations, leading to an added large deviation cost compared to the reversible case, which shows no current. We study the current fluctuation most likely to arise in conjunction with a given estimator fluctuation and provide bounds on the acceleration, based on approximations of this current. We illustrate these results for the Ornstein-Uhlenbeck process in two dimensions and the Brownian motion on the circle.

cond-mat.stat-mech↗