arXiv subjects

Manuel Santos Gutierrez

Publications and source records attributed to Manuel Santos Gutierrez.

3 recordsLinked to original sources

arXiv2026

Markov matrix perturbations to optimize dynamical and entropy functionals

An important problem in applied dynamical systems is to compute the external forcing that provokes the largest response of a desired observable quantity. For this, we investigate the perturbation theory of Markov matrices in connection with linear response theory in statistical physics. We use perturbative expansions to derive linear algorithms to optimize physically relevant quantities such as: entropy, Kullback-Liebler-divergence and entropy production of Markov matrices and their related probability vectors. These optimization algorithms are applied to Markov chain representations of discrete and continuous flows in and out of equilibrium. We consider Markov matrix representations originating from Ulam-type approximations of transfer operators and a reduced order model of a turbulent flow based on unstable periodic orbits theory. We also propose a numerical protocol to recast matrix perturbations into vector field perturbations. The results allow to physically interpret the obtained optimizing perturbations without knowledge of the underlying equations, in a data-driven way.

math.DS↗

arXiv2026

Data-driven analysis of metastability in a stochastic bistable system

We present a methodology to analyze metastable properties of a simple prototypical stochastic bistable system by identifying slow inter-well and fast saddle escape processes using the formalism of the Koopman operator. Instead of studying noise-induced transitions by following the trajectories of the system, we track them by studying the time evolution and the decay rate of the subdominant mode of the Koopman operator, thus in a geometry-agnostic framework. The obtained escape time statistics together with the decay rate are in good agreement with the predictions - both the exponential and subexponential ones - of large deviation theory in the weak-noise limit, both in equilibrium and nonequilibrium conditions. The subdominant Koopman mode also allows for an accurate reconstruction of the competing basins of attraction. Furthermore, going deeper in the Koopman spectrum, we are able to recognise modes that are associated with intra-well variability as well as with the escape of trajectories from the saddle towards the attractor, both in the equilibrium and nonequilibrium case. Our methodology, being grounded in purely data-driven techniques, could provide a comprehensive, multi-scale framework for studying high-dimensional metastable systems.

cond-mat.stat-mech↗

arXiv2025

A General Framework for Linking Free and Forced Fluctuations via Koopmanism

The link between forced and free fluctuations for nonequilibrium systems can be described via a generalized version of the celebrated fluctuation-dissipation theorem. The use of the formalism of the Koopman operator makes it possible to deliver an intepretable form of the response operators written as a sum of exponentially decaying terms, each associated one-to-one with a mode of natural variability of the system. Here we showcase on a stochastically forced version of the celebrated Lorenz '63 model the feasibility and skill of such an approach by considering different Koopman dictionaries, which allows us to treat also seamlessly coarse-graining approaches like the Ulam method. Our findings provide support for the development of response theory-based investigation methods also in an equation-agnostic, data-driven environment.

cond-mat.stat-mech↗