Bram Lefebvre | Searcharxiv

arXiv2023

Frenetic steering: nonequilibrium-enabled navigation

We explain the steering of slow degrees of freedom by coupling them to driven components for which the time-symmetric reactivities are manipulated. We present the strategy and main principle that make that sort of navigation feasible. For illustration, nonlinear limit cycles (as in the van der Pol oscillator) and strange attractors (as in the Lorenz dynamics) are seen to emerge when the driving in the nonequilibrium medium is kept fixed while the frenesy is tuned to produce the required forces. We imagine that such frenetic steering is available in Life as well, allowing selection of the appropriate biological functioning.

cond-mat.stat-mech↗

arXiv2022

Frenetic steering in a nonequilibrium graph

In traditional recognition tasks of neural networks, a potential landscape or cost function guides the system toward patterns using gradient dynamics. That is not how the brain works as its dynamics is far from equilibrium. We present an alternative and proof of principle for pattern recovery in a nonequilibrium model whereby only time-symmetric kinetics are altered. As a mathematical model, a random walker on a randomly-oriented complete graph is subject to finite driving in the direction of the arcs. Some vertices of the graph represent patterns. A first algorithm constructs basins of attraction for these patterns. A second algorithm updates the time-symmetric factors in the transition rates, in order for the walker to quickly reach a pattern and remain there for a sufficiently long time, whenever starting from a vertex in its basin of attraction.

cond-mat.stat-mech↗