Dynamical Decomposition of Markov Processes without Detailed Balance
AO Ping1,3**, CHEN Tian-Qi2, SHI Jiang-Hong2
1Key Laboratory of Systems Biomedicine of Ministry of Education, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai 200240 2Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240 3Department of Physics, Shanghai Jiao Tong University, Shanghai 200240
Abstract：We introduce a dynamical decomposition view in dealing with Markov processes without detailed balance. This work generalizes a previous decomposition framework on continuous-state Markov processes and explicitly gives its correspondence in discrete-state case. We investigate the dynamical roles of decomposed parts by studying the evolution of relative-entropy-like functions. We find a special definition of relative entropy to unify the dynamical roles played by the detailed balance part and the breaking detailed balance part. The evolution of the relative entropy naturally bounds the convergence of the process.
2013, Vol. 30 
