A Projected Entropy Controller for Transition Matrix Calculations

TL;DR

This paper introduces a novel projected entropy controller for transition matrix calculations in Ising models, enabling accurate and simple state sampling by adjusting temperature based on the entropy of Markov chain realizations.

Contribution

It presents a new entropy-based control method for transition matrix calculations that improves sampling uniformity and simplicity over previous approaches.

Findings

Achieves highly accurate state sampling in Ising models.

Simplifies transition matrix calculations compared to existing methods.

Demonstrates effective uniform sampling in physical entropy.

Abstract

We define the projected entropy S(T) at a given temperature T in the context of an Ising model transition matrix calculation as the entropy associated with the distribution of Markov chain realizations in energy-magnetization, E-H, space. An even sampling of states is achieved by accumulating the results from multiple Markov chains while decrementing 1/T at a rate proportional to the inverse of the effective number, exp(S(T)), of accessible projected states. Such a procedure is both highly accurate and far simpler to implement than a previously suggested method based on monitoring the evolution of the E-H distribution at each temperature. [1] We further demonstrate a transition matrix procedure that instead ensures uniform sampling in physical entropy.