Computing the minimal rebinding effect for non-reversible processes

TL;DR

This paper investigates the rebinding effect in Markov processes, proposing a method to compute its minimal bound through optimization, applicable to both reversible and non-reversible systems.

Contribution

It introduces a generalized approach using membership functions to quantify and optimize the minimal rebinding effect in projected Markov processes.

Findings

Derived a minimal rebinding effect bound for non-reversible processes

Developed an optimization framework for the rebinding effect

Applicable to systems with overlapping macro states

Abstract

The aim of this paper is to investigate the rebinding effect, a phenomenon describing a "short-time memory" which can occur when projecting a Markov process onto a smaller state space. For guaranteeing a correct mapping by the Markov State Model, we assume a fuzzy clustering in terms of membership functions, assigning degrees of membership to each state. The macro states are represented by the membership functions and may be overlapping. The magnitude of this overlap is a measure for the strength of the rebinding effect, caused by the projection and stabilizing the system. A minimal bound for the rebinding effect included in a given system is computed as the solution of an optimization problem. Based on membership functions chosen as a linear combination of Schur vectors, this generalized approach includes reversible as well as non-reversible processes.