Geometric methods are indispensable for analyzing, predicting, and mitigating the complex behaviors inherent in nonlinear systems. In this regime, the most probable transition path minimizes the Onsager-Machlup action functional, marking the likeliest route across an energy barrier. Lifting the analysis from individual sample paths to the infinite-dimensional space of probability densities, the book recasts these transitions as Schr\"odinger bridges - optimal paths between boundary distributions defined by minimizing relative entropy - and shows that the Onsager-Machlup path emerges as a special case when metastable states are idealized as Dirac masses. Generalizing further through {\alpha}-divergences, which connect to entropies and the thermodynamic cost of nonequilibrium transitions, it introduces information geodesics as the resulting optimal density paths, offering a unified geometric account of how complex systems move between metastable regimes under uncertainty.
Active systems navigate complex environments through non-equilibrium fluctuations, rendering standard equilibrium transition-rate theories inadequate. Moreover, transition rates provide only partial information on how stochastic dynamics explore metastable states, whereas knowledge of the optimal paths offers deeper ph...
We investigate a discontinuous route from integrability to chaos using a confined stochastic random walk and a deterministic stadium-like billiard. In both systems, the stationary diffusive observable exhibits a finite jump at the transition: it vanishes at the unperturbed limit but approaches a finite, geometry-contro...
A. K. P. da Fonseca, Marcelo de Almeida Presotto, D. M. Oliveira et al.· 0 citations
This paper develops a generalization of Zubarev's nonequilibrium statistical operator method for the case of simultaneous inclusion of additive and nonlocal boundary functionals of trajectories. Using a unified thermodynamic approach, a three-parameter model of nonequilibrium systems is constructed, including the first...
A chemical transition state is a phase-space bottleneck: trajectories approach along stable directions and leave along unstable directions. Lagrangian betweenness (LB), introduced in finite-time transport theory for fluid flows, combines backward and forward deformation in a way suggestive of this gather-and-disperse g...
We derive a new set of bounds controlling the speed-up of the survival rate of trajectory-dependent observables induced by the application of a perturbation. Via the study of survival probabilities in two different contexts, continuous-time Markov jump processes and overdamped diffusions, we obtain different fashions o...
Davide Santolin, G. Falasco· 0 citations
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