Model simplification and loss of irreversibility.
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 nonadiabatic 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.
Beijing Computational Science Research Center, Beijing 100094, People's Republic of China and Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, Texas 75080, USA.
Chen
C
Jia