2010/06/30 by Alexander N. Gorban, A. N. Gorban · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · Psychology · #Advanced Thermodynamics and Statistical Mechanics #Applied mathematics #Classical mechanics #Ergodicity #Gene Regulatory Network Analysis #Kinetic energy #Kinetic scheme #Kinetics #Markov chain #Master equation #Mathematical analysis #Mathematics #Mental Health Research Topics #Perturbation (astronomy) #Physics #Quantum mechanics #Relaxation (psychology) #Statistical physics #Statistics #Thermodynamics #Uniqueness #physics.comp-ph
paper · pdf · doi:10.1016/j.physa.2010.11.030
published in Physica A Statistical Mechanics and its Applications 390(6), 1009-1025 (Elsevier BV) · The final journal version
openalex publication_date 2010/12/08 · arxiv created 2011/02/01 · arxiv updated 2011/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the Master equation with time--dependent coefficients, a linear kinetic equation for the Markov chains or for the monomolecular chemical kinetics. For the solution of this equation a path summation formula is proved. This formula represents the solution as a sum of solutions for simple kinetic schemes (kinetic paths), which are available in explicit analytical form. The relaxation rate is studied and a family of estimates for the relaxation time and the ergodicity coefficient is developed. To calculate the estimates we introduce the multi--sheeted extensions of the initial kinetics. This approach allows us to exploit the internal ("micro")structure of the extended kinetics without perturbation of the base kinetics.