title: Conflict between fastest relaxation of a Markov process and detailed balance condition.
abstract: We consider the optimization of Markovian dynamics to pursue the fastest convergence to the stationary state. The brachistochrone method is applied to the continuous-time master equation for finite-size systems. The principle of least action leads to a brachistochrone equation for the transition-rate matrix. Three-state systems are explicitly analyzed, and we find that the solution violates the detailed balance condition. The properties of the solution are studied in detail to observe the optimality of the solution. We also discuss the counterdiabatic driving for the Markovian dynamics. The transition-rate matrix is then divided into two parts, and the state is given by an eigenstate of the first part. The second part violates the detailed balance condition and plays the role of a counterdiabatic term.
authors: Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan.
authors: Kazutaka
authors: K
authors: Takahashi
authors: Department of Systems Science, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.
authors: Masayuki
authors: M
authors: Ohzeki