Maximum Caliber: a general variational principle for dynamical systems

TL;DR

Maximum Caliber is a versatile variational principle that extends the maximum entropy approach to dynamical systems, enabling inference of path distributions far from equilibrium and applicable across various complex systems.

Contribution

It introduces Max Cal as a general framework for predicting dynamical trajectories, surpassing near-equilibrium limitations of traditional methods.

Findings

Max Cal can derive known non-equilibrium relations.

It effectively infers trajectory distributions from limited data.

Applicable to biological, neural, and non-thermal systems.

Abstract

We review here {\it Maximum Caliber} (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of {\it Maximum Entropy} (Max Ent) is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of Non-Equilibrium Statistical Physics -- such as the Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations, and Prigogine's Minimum Entropy Production -- are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give recent examples of MaxCal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle, and some limitations.