Model simplification and loss of irreversibility

TL;DR

This paper explores how simplifying continuous-time Markov chain models affects their thermodynamic irreversibility, showing that simplification reduces entropy production but preserves most dynamic information.

Contribution

It establishes a general relationship between model simplification and irreversibility, revealing the thermodynamic trade-offs involved in reducing Markov chain complexity.

Findings

Simplification decreases entropy production rate.

Both state removal and aggregation reduce the adiabatic entropy component.

Non-adiabatic entropy remains unchanged after simplification.

Abstract

In this paper, we reveal a general relationship between model simplification and irreversibility based on the model of continuous-time Markov chains with time-scale separation. According to the topological structure of the fast process, we divide the states of the chain into the transient states and the recurrent states. We show that a two-time-scale chain can be simplified to a reduced chain in two different ways: removal of the transient states and aggregation of the recurrent states. Both the two operations will lead to a decrease in the entropy production rate and its adiabatic part and will keep its non-adiabatic part the same. This suggests that although model simplification can retain almost all the dynamic information of the chain, it will lose some thermodynamic information as a trade-off.