An equivalence between a Maximum Caliber analysis of two-state kinetics and the Ising model

TL;DR

This paper demonstrates that analyzing two-state kinetics via Maximum Caliber can be mapped onto the 1-D Ising model, providing a new perspective and predictive relations for dynamical quantities.

Contribution

It introduces a novel mapping of Maximum Caliber analysis of two-state systems onto the Ising model, revealing new relationships and predictive capabilities.

Findings

Maximum Caliber results agree with simulations and experiments.

New relationships between occupancy, transitions, and transition probabilities.

Maxwell-like relations enable predictions across different potential landscapes.

Abstract

Application of the information-theoretic Maximum Caliber principle to the microtrajectories of a two-state system shows that the determination of key dynamical quantities can be mapped onto the evaluation of properties of the 1-D Ising model. The strategy described here is equivalent to an earlier Maximum Caliber formulation of the two-state problem, but reveals a different way of imposing the constraints which determine the probability distribution of allowed microtrajectories. The theoretical calculations of second moments, covariances, and correlation times that are obtained from Maximum Caliber agree well with simulated data of a particle diffusing on a double Gaussian surface, as well as with recent experiments on a particle trapped by a dual-well optical trap. The formalism reveals a new relationship between the average occupancy of the two states of the system, the average number of transitions between the two states that the system undergoes, Markov transition probabilities, and the discretization time step. In addition, Maxwell-like relations imply how measurements on one potential landscape can be used to make predictions about the dynamics on a different potential landscape, independent of further experiment.