  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.
