Maximum Caliber: a general variational principle for dynamical 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.

References in corpus (8)

• Work and information processing in a solvable model of Maxwell's demon
• Nonuniversal power law scaling in the probability distribution of scientific citations
• A maximum entropy framework for non-exponential distributions
• Non-equilibrium steady states : maximization of the Shannon entropy associated to the distribution of dynamical trajectories in the presence of constraints
• A derivation of the master equation from path entropy maximization
• Beyond the Boltzmann factor for corrections to scaling in ferromagnetic materials and critical fluids
• Fluctuation-theory constraint for extensive entropy in Monte-Carlo simulations
• Mini-grand canonical ensemble: chemical potential in the solvation shell