arXiv subjects

Andrea Auconi

Publications and source records attributed to Andrea Auconi.

13 recordsLinked to original sources

arXiv2026

Thermodynamic Bounds from Otto--Villani Functional Inequalities

The dissipation in the relaxation of an ensemble of conservative stochastic systems towards the equilibrium steady state is quantified by the free energy difference. Functional inequalities within the framework of [F. Otto and C. Villani, J. Funct. Anal. 173, 361 (2000)] are here revisited which connect the free energy dynamics and optimal transport, offering a geometric perspective on the instantaneous speed of relaxation in the presence of potential barriers. These are illustrated with numerical relaxation experiments on Landau-Ginzburg potentials. The same inequalities hold for relaxation toward nonequilibrium steady states once the potential is replaced by the pseudo-potential defined by the stationary density.

cond-mat.stat-mech↗

arXiv2026

Field Theory of Bayesian Rate Estimation

We address the statistical inference of a time-dependent rate of events in the framework of Bayesian field theory. This maps the problem to a Langevin equation which, beyond the local linear regime taken as reference, involves nonlinearities and an explicit dependence on the shape of the maximum \textit{a posteriori} estimator curve. We study the corresponding impacts in a perturbative expansion, based on an analytically derived scaling relation for the order of shape corrections. We find that the pure nonlinearities dominate the mean and skewness. Crucially, we uncover that the leading correction to the variance is driven by noise propagation from the signal's effective curvature. We test the derived expansion and universal kernels against computationally expensive Monte Carlo simulations, and illustrate their applicability on real neural spike data.

stat.ME↗

arXiv2026

Information-Geometric Signatures of Nonconservative Driving

We propose an information-geometric signature of nonconservative driving that detects violations of detailed balance using the Kullback--Leibler divergence and the Fisher information. For Markov jump processes satisfying detailed balance, we show that, near equilibrium, the acceleration of the Kullback--Leibler divergence relative to the equilibrium state is given by twice the Fisher information with respect to time. In contrast, for relaxation toward a nonequilibrium steady state, this relation is generally violated even near the steady state. We refer to the resulting discrepancy as the relaxation gap and derive a lower bound on the steady-state entropy production rate in terms of this gap. We demonstrate that this bound is particularly tight for networks with simple cyclic topologies. Finally, we show that analogous relations and bounds hold for Fokker--Planck dynamics.

cond-mat.stat-mech↗

arXiv2024

Nonequilibrium relaxation inequality on short timescales

An integral relation is derived from the Fokker-Planck equation which connects the steady-state probability currents with the dynamics of relaxation on short timescales in the limit of small perturbation fields. As a consequence of this integral relation, a lower bound on the steady-state entropy production is obtained. For the particular case of an ensemble of random perturbation fields of weak spatial gradient, a simpler bound is derived from the integral relation which provides a feasible method to estimate entropy production from relaxation experiments.

cond-mat.stat-mech↗

arXiv2023

Interaction uncertainty in financial networks

A minimal stochastic dynamical model of the interbank network is introduced, with linear interactions mediated by an integral of recent variations. Defining stress as the variance over the banks' states, the interaction correction to the stress expectation is derived and studied on the short-medium timescale in an expansion. It is shown that, while different interaction matrices can amplify or absorb fluctuations, on average interactions increase the stress expectation. More in general, this analytical framework enables to estimate the impact of uncertainty about financial exposures, and to draw conclusions about the importance of disclosure.

q-fin.MF↗

arXiv2023

Conjecture of an information-response inequality

The invariant response was defined from a formulation of the fluctuation-response theorem in the space of probability distributions. An inequality is here conjectured which sets the mutual information as an upper bound to the invariant response, and its large information limit is proven. Applications to the thermodynamics of feedback control and to estimation theory are discussed.

physics.bio-ph↗

arXiv2022

Learning stochastic filtering

We quantify the performance of approximations to stochastic filtering by the Kullback-Leibler divergence to the optimal Bayesian filter. Using a two-state Markov process that drives a Brownian measurement process as prototypical test case, we compare two stochastic filtering approximations: a static low-pass filter as baseline, and machine learning of Voltera expansions using nonlinear Vector Auto Regression (nVAR). We highlight the crucial role of the chosen performance metric, and present two solutions to the specific challenge of predicting a likelihood bounded between $0$ and $1$.

cond-mat.stat-mech↗

arXiv2021

Research Notes: Gradient sensing in Bayesian chemotaxis

Bayesian chemotaxis is an information-based target search problem inspired by biological chemotaxis. It is defined by a decision strategy coupled to the dynamic estimation of target position from detections of signaling molecules. We extend the case of a point-like agent previously introduced in [Vergassola et al., Nature 2007], which establishes concentration sensing as the dominant contribution to information processing, to the case of a circular agent of small finite size. We identify gradient sensing and a Laplacian correction to concentration sensing as the two leading-order expansion terms in the expected entropy variation. Numerically, we find that the impact of gradient sensing is most relevant because it provides direct directional information to break symmetry in likelihood distributions, which are generally circle-shaped by concentration sensing.

physics.bio-ph↗

arXiv2021

Composite search of active particles in three-dimensional space based on non-directional cues

We theoretically address minimal search strategies of active, self-propelled particles towards hidden targets in three-dimensional space. The particles can sense if a target is close, e.g., by detecting signaling molecules released by a target, but they cannot deduce any directional cues. We focus on composite search strategies, where particles switch between extensive outer search and intensive inner search; inner search is started when the proximity of a target is detected and ends again when a certain inner search time has elapsed. In the simplest strategy, active particles move ballistically during outer search, and transiently reduce their directional persistence during inner search. In a second, adaptive strategy, particles exploit a dynamic scattering effect by reducing directional persistence only outside a well-defined target zone. These two search strategies require only minimal information processing capabilities and a single binary or tertiary internal state, respectively, yet increases the rate of target encounter substantially. The optimal inner search time scales as a power-law with exponent -2/3 with target density, reflecting a trade-off between exploration and exploitation.

cond-mat.soft↗

arXiv2021

Fluctuation-response theorem for Kullback-Leibler divergences to quantify causation

We define a new measure of causation from a fluctuation-response theorem for Kullback-Leibler divergences, based on the information-theoretic cost of perturbations. This information response has both the invariance properties required for an information-theoretic measure and the physical interpretation of a propagation of perturbations. In linear systems, the information response reduces to the transfer entropy, providing a connection between Fisher and mutual information.

cs.IT↗

arXiv2019

Influence of photic perturbations on circadian rhythms

The circadian clock is the molecular mechanism responsible for the adaptation to daily rhythms in living organisms. Oscillations and fluctuations in environmental conditions regulate the circadian clock through signaling pathways. We study the response to continuous photic perturbations in a minimal molecular network model of the circadian clock, composed of 5 nonlinear delay differential equations with multiple feedbacks. We model the perturbation as a stationary stochastic process, and we consider the resulting irreversibility of trajectories as a key effect of the interaction. In particular we adopt a measure of mutual mapping irreversibility in the time series thermodynamics framework, and we find 12 hours harmonics.

physics.bio-ph↗

arXiv2018

A fluctuation theorem for time-series of signal-response models with the backward transfer entropy

The irreversibility of trajectories in stochastic dynamical systems is linked to the structure of their causal representation in terms of Bayesian networks. We consider stochastic maps resulting from a time discretization with interval τof signal-response models, and we find an integral fluctuation theorem that sets the backward transfer entropy as a lower bound to the conditional entropy production. We apply this to a linear signal-response model providing analytical solutions, and to a nonlinear model of receptor-ligand systems. We show that the observational time τhas to be fine-tuned for an efficient detection of the irreversibility in time-series.

physics.data-an↗

arXiv2016

Causal influence in linear response models

The intuition of causation is so fundamental that almost every research study in life sciences refers to this concept. However a widely accepted formal definition of causal influence between observables is still missing. In the framework of linear Langevin networks without feedbacks (linear response models) we developed a measure of causal influence based on a decomposition of information flows over time. We discuss its main properties and compare it with other information measures like the Transfer Entropy. Finally we outline some difficulties of the extension to a general definition of causal influence for complex systems.

stat.OT↗