Conflict between fastest relaxation of a Markov process and detailed balance condition

Kazutaka Takahashi, Masayuki Ohzeki

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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.

Original languageEnglish
Article number012129
JournalPhysical Review E
Issue number1
Publication statusPublished - 2016 Jan 19
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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