The Maximum Caliber Variational Principle for Nonequilibria

Abstract

Ever since Clausius in 1865 and Boltzmann in 1877, the concepts of entropy and of its maximization have been the foundations for predicting how material equilibria derive from microscopic properties. But, despite much work, there has been no equally satisfactory general variational principle for nonequilibrium situations. However, in 1980, a new avenue was opened by E.T. Jaynes and by Shore and Johnson. We review here maximum caliber, which is a maximum-entropy-like principle that can infer distributions of flows over pathways, given dynamical constraints. This approach is providing new insights, particularly into few-particle complex systems, such as gene circuits, protein conformational reaction coordinates, network traffic, bird flocking, cell motility, and neuronal firing.

Inferring a network from dynamical signals at its nodes

“…We describe here a way to infer how the dynamics on multi-node networks evolves over time. We use an inference principle for dynamics and networks called Maximum Caliber [12][13][14]. Unlike previous methods, this approach utilizes only the available experimental data and requires minimal assumptions [1][2][3][4][5][6]58].…”

“…Instead, we are given limited information and seek to infer the model directly from the data itself. The method of choice for inferring dynamical processes from limited information is the Principle of Maximum Caliber (Max Cal) [8][9][10][11][12][13][14]. Max Cal is a procedure that predicts full stochastic distributions by maximizing the route entropy subject to the constraint of a few known average rates.…”

“…Like Max Ent, Max Cal requires minimal model assumptions that are not warranted by the data itself. For example, Max Cal has proven capable of reproducing many known results from non-equilibrium physics, such as Fick's law and the master equation [14][15][16]. In addition, Max Cal has been show to accurately predict single-cell dynamics [17,18], such as in gene circuits [19][20][21] and and stochastic cycles [22,23], directly from noisy experimental data.…”

Use and Abuse of Entropy in Biology: A Case for Caliber

“…Thus, generalizable stochastic models utilizing caliber may be the best approach to model biological processes, such as evolution and succession, based on thermodynamic principles. For more on caliber methods and their use in biology, see the review by Ghosh et al [48] 5. Discussion…”

Confronting pitfalls of AI-augmented molecular dynamics using statistical physics

“…Here this is made feasible through the use of the "Spectral Gap Optimization of Order Parameters (SGOOP)" framework. 54 This builds a maximum caliber or path entropy 55 based model of the unbiased dynamics along different AI based representations even when the underlying observables arise from biased simulations, which then yields spectral gaps along dif-ferent slow modes obtained from AI trials. We demonstrate this path entropy based screening procedure in the context of our recent iterative AI-MD scheme "Reweighted Auotencoded Variational Bayes for enhanced sampling (RAVE)".…”