Master Equation and Fokker-Planck Equation: Comparison of Entropy and of Rate Constants

Letters in Mathematical Physics

Volumn 40, Issue 2, 1977, Pages 101-115

  Gaveau, Bernard ^a   Moreau, Michel ^a   Toth, Janos ^b  

^a SORBONNE UNIVERSITÉ   (France)

^b SZENT ISTVÁN UNIVERSITY   (Hungary)

Author keywords

Entropy; Fokker Planck equation; Master equation; Rate constants

Indexed keywords

EID: 0004483570     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1007362811930     Document Type: Review

References (16)

1. Van Kampen, N. G.: Stochastic Processes in Physics, Nicolis, G. and Prigogine, I.: Self-organization in Non-equilibrium Systems, Wiley, New York, 1977.
2. Van Kampen, N. G.: Stochastic Processes in Physics, Nicolis, G. and Prigogine, I.: Self-organization in Non-equilibrium Systems, Wiley, New York, 1977.
3. Moreau, M.: Note on the entropy production in a discrete Markov system, J. Math. Phys. 19 (1978), 2494-2498; Lett. Math. Phys. 1 (1975), 7.
4. Moreau, M.: Note on the entropy production in a discrete Markov system, J. Math. Phys. 19 (1978), 2494-2498; Lett. Math. Phys. 1 (1975), 7.
5. Gaveau, B. and Schulman, L.S.: Master equation based formulations of nonequilibrium statistical mechanics, to appear in J. Math. Phys (1996).
6. Gardiner, H.: Handbook of Stochastic Methods, Springer-Verlag, Berlin, 1983.
7. Kubo, R., Matsuo, K. and Kitahara, K.: J. Stat. Phys. 9 (1973), 51; Kubo, R., Toda, M. and Hashitsume, N.: Nonequilibrium statistical mechanics, in Statistical Physics II, Springer-Verlag, New York, 1986; Lemarchand, H.: Asymptotic solutions of the master equation near a nonequilibrium transition: the stationary solution, Physica 101 (1980), 518-534.
8. Kubo, R., Matsuo, K. and Kitahara, K.: J. Stat. Phys. 9 (1973), 51; Kubo, R., Toda, M. and Hashitsume, N.: Nonequilibrium statistical mechanics, in Statistical Physics II, Springer-Verlag, New York, 1986; Lemarchand, H.: Asymptotic solutions of the master equation near a nonequilibrium transition: the stationary solution, Physica 101 (1980), 518-534.
9. Kubo, R., Matsuo, K. and Kitahara, K.: J. Stat. Phys. 9 (1973), 51; Kubo, R., Toda, M. and Hashitsume, N.: Nonequilibrium statistical mechanics, in Statistical Physics II, Springer-Verlag, New York, 1986; Lemarchand, H.: Asymptotic solutions of the master equation near a nonequilibrium transition: the stationary solution, Physica 101 (1980), 518-534.
10. Gaveau, B., Moreau, M. and Toth, J.: Decay of the metastable state: different predictions between discrete and continuous models, Lett. Math. Phys. 37 (1996), 285-292.
11. Ventsel, A. and Freidlin, M.: On small random perturbation of dynamical systems, Russian Math. Surveys 25 (1970), 1-55.
12. Ludwig, D.: Persistence of dynamical systems under random perturbation, SIAM Rev. 17 (1975), 605-640.
13. Gaveau, B. and Schulman, L.: Finite-size scaling for mean field percolation, J. Stat. Phys. 70 (1993), 613-634.
14. Vlad, M. and Ross, J.: Fluctuation-dissipation relations for chemical systems far from equilibrium, J. Chem. Phys 100 (1994), 7268-7278; Vlad, M. and Ross, J.: Random paths and fluctuation-dissipation dynamics for one variable chemical systems far from equilibrium, J. Chem. Phys. 100 (1994), 7279-7294.
15. Vlad, M. and Ross, J.: Fluctuation-dissipation relations for chemical systems far from equilibrium, J. Chem. Phys 100 (1994), 7268-7278; Vlad, M. and Ross, J.: Random paths and fluctuation-dissipation dynamics for one variable chemical systems far from equilibrium, J. Chem. Phys. 100 (1994), 7279-7294.
16. Toth, J. and Török, T. L.: Stationary distributions in stochastic kinetics, Adv. Physiol. Sci. 34 (1980), 103-111.