Quasi-stationary time asymmetry on topologically irreversible Markov chains

Area of Science:

• Statistical Mechanics
• Information Theory
• Computational Biology

Background:

• Many natural processes are time-irreversible due to structural constraints.
• Traditional measures of irreversibility, like entropy production rate, are undefined for these systems.
• Topologically irreversible Markov chains present a specific challenge for quantifying time asymmetry.

Purpose of the Study:

• To develop a novel method for assessing time asymmetry in intrinsically time-irreversible systems.
• To introduce a new metric, the quasi-stationary irreversibility index, as an analog to entropy production rate.
• To demonstrate the applicability of this method to both theoretical models and biological data.

Main Methods:

• Focusing on topologically irreversible Markov chains.
• Constructing a conditioned Markov chain on the 'reversible interior' of trajectories.
• Defining the quasi-stationary irreversibility index using Kullback-Leibler divergence between forward and reversed path distributions.

Main Results:

• The proposed method provides a well-defined measure of irreversibility for systems where entropy production is undefined.
• Analytical calculations for a simple Markov chain model validate the approach.
• The method is successfully applied to mitochondrial DNA sequences from Hominidae species.

Conclusions:

• The quasi-stationary irreversibility index offers a robust measure of time asymmetry in intrinsically irreversible systems.
• This approach extends the quantification of irreversibility to a broader class of dynamic processes.
• The study highlights the utility of this method in analyzing complex biological systems.