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Near equilibrium, thermodynamic intuition suggests that fast, irreversible processes will dissipate more energy and entropy than slow, quasistatic processes connecting the same initial and final states. Here, we test the hypothesis that…

Statistical Mechanics · Physics 2022-12-07 Rebecca A. Bone , Daniel J. Sharpe , David J. Wales , Jason R. Green

We consider the ferromagnetic q-state Potts model on a finite grid graph with non-zero external field and periodic boundary conditions. The system evolves according to Glauber-type dynamics described by the Metropolis algorithm, and we…

Probability · Mathematics 2022-12-21 Gianmarco Bet , Anna Gallo , Francesca R. Nardi

We consider the exit event from a metastable state for the overdamped Langevin dynamics $dX_t = -\nabla f(X_t) dt + \sqrt{h} dB_t$. Using tools from semiclassical analysis, we prove that, starting from the quasi stationary distribution…

Analysis of PDEs · Mathematics 2019-01-17 Giacomo Di Gesù , Tony Lelièvre , Dorian Le Peutrec , Boris Nectoux

A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition…

Probability · Mathematics 2011-06-17 Amarjit Budhiraja , Pierre Del Moral , Sylvain Rubenthaler

Studying the subexponential convergence towards equilibrium of a strong Markov process, we exhibit an intermediate Lyapunov condition equivalent to the control of some moment of a hitting time. This provides a link, similar (although more…

Probability · Mathematics 2021-08-03 Armand Bernou

We prove that for a sequence of finite vertex-transitive graphs of increasing sizes, the cover times are asymptotically concentrated if and only if the product of the spectral-gap and the expected cover time diverges. In fact, we prove this…

Probability · Mathematics 2019-12-24 Jonathan Hermon

Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates a class of random dynamical systems, arising from perturbing a one-dimensional piecewise…

Dynamical Systems · Mathematics 2025-10-27 Cecilia González-Tokman , Joshua Peters

The subject of this paper is a fragmentation equation with nonconservative solutions, some mass being lost to a dust of zero-mass particles as a consequence of an intensive splitting. Under some assumptions of regular variation on the…

Probability · Mathematics 2016-08-14 Bénédicte Haas

This paper analyzes the asymptotic behavior of inter-event times in planar linear systems, under event-triggered control with a general class of scale-invariant event triggering rules. In this setting, the inter-event time is a function of…

Systems and Control · Electrical Eng. & Systems 2024-04-02 Anusree Rajan , Pavankumar Tallapragada

We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a…

Systems and Control · Electrical Eng. & Systems 2022-07-13 Kush Grover , Jan Křetínský , Tobias Meggendorfer , Maximilian Weininger

We introduce estimators for the entropy production of a Gibbsian process based on the observation of a single or two typical trajectories. These estimators are built with adequate hitting and return times. We then study their convergence…

Mathematical Physics · Physics 2009-11-11 J. -R. Chazottes , F. Redig

The time at which a one-dimensional continuous strong Markov process attains a boundary point of its state space is a discontinuous path functional and it is, therefore, unclear whether the exit time can be approximated by hitting times of…

Probability · Mathematics 2019-11-11 Thomas Kruse , Mikhail Urusov

Stochastic systems often exhibit multiple viable metastable states that are long-lived. Over very long timescales, fluctuations may push the system to transition between them, drastically changing its macroscopic configuration. In realistic…

Statistical Mechanics · Physics 2023-04-14 Tobias Grafke , Alessandro Laio

We analyze hitting times of simple random walk on realizations of the stochastic block model. We show that under some natural assumptions the hitting time averaged over the target vertex asymptotically almost surely given by $N(1+o(1))$. On…

Probability · Mathematics 2025-04-24 Matthias Löwe , Sara Terveer

Backward reachability analysis computes the set of states that reach a target set under the competing influence of control input and disturbances. Depending on their interplay, the backward reachable set either represents all states that…

Numerical Analysis · Mathematics 2025-09-19 Mark Wetzlinger , Matthias Althoff

The sedimentation of a heavy Stokes particle in a laminar plane or axisymmetric flow is investigated by means of asymptotic methods. We focus on the occurrence of Stommel's retention zones, and on the splitting of their separatrices. The…

Fluid Dynamics · Physics 2010-03-23 J. R. Angilella

In this numerical study, recurrence quantification analysis of chaotic trajectories is explored to detect atypical dynamical behaviour in non-linear Hamiltonian systems. An ensemble of initial conditions is evolved up to a maximum iteration…

Chaotic Dynamics · Physics 2025-07-11 Matheus S. Palmero , Flavio H. Graciano , Edson D. Leonel , Juliano A. de Oliveira

A constant-rate multi-mode system is a hybrid system that can switch freely among a finite set of modes, and whose dynamics is specified by a finite number of real-valued variables with mode-dependent constant rates. We introduce and study…

Optimization and Control · Mathematics 2016-10-19 Fabio Somenzi , Behrouz Touri , Ashutosh Trivedi

We define the hitting time for a Markov decision process (MDP). We do not use the hitting time of the Markov process induced by the MDP because the induced chain may not have a stationary distribution. Even it has a stationary distribution,…

Machine Learning · Computer Science 2022-05-12 Ruichao Jiang , Javad Tavakoli , Yiqinag Zhao

We consider a large family of discrete and continuous time controlled Markov processes and study an ergodic risk-sensitive minimization problem. Under a blanket stability assumption, we provide a complete analysis to this problem. In…

Optimization and Control · Mathematics 2022-07-18 Anup Biswas , Somnath Pradhan