%0 Book Section %1 statphys23_0629 %A Ichiki, A. %A Shiino, M. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K coupled field mean network neural nonequilibrium oscillators phase statphys23 stochastic system topic-11 transition %T Mean Field Theory for Stochastic Dynamical Systems %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=629 %X We investigate the statistical properties of stochastic systems in which the mean field approximation becomes exact at thermodynamic limit. Especially, we focus on the systems of coupled elements with temporally fluctuating coupling strength. Such systems, in general, has no energy function and thus defy the use of standard statistical techniques such as Boltzmann-Gibbs statistics.However the statistical properties in some classes of such systems can be investigated exactly analytically since the mean field approach becomes exact in such systems. We present two types of such examples: (i) coupled oscillator system with fluctuating coupling strength, (ii) associative memory neural network model with temporally fluctuating coupling strength. The first example are found to show the chaos-nonchaos nonequilibrium phase transition. This fact gives us a dynamical aspect of mean field theory for the system with fluctuating couplings. The second example are found to be analyzed by standard statistical methods, e. g., replica method or cavity method to investigate the equilibrium properties of the system. However the effect of the fluctuating couplings modifies the temperature of the system. This results are confirmed by the self-averaging property at thermodynamic limit. This fact gives us a static aspect of mean field theory for the system with fluctuating couplings.

@incollection{statphys23_0629, abstract = {We investigate the statistical properties of stochastic systems in which the mean field approximation becomes exact at thermodynamic limit. Especially, we focus on the systems of coupled elements with temporally fluctuating coupling strength. Such systems, in general, has no energy function and thus defy the use of standard statistical techniques such as Boltzmann-Gibbs statistics.However the statistical properties in some classes of such systems can be investigated exactly analytically since the mean field approach becomes exact in such systems. We present two types of such examples: (i) coupled oscillator system with fluctuating coupling strength, (ii) associative memory neural network model with temporally fluctuating coupling strength. The first example are found to show the chaos-nonchaos nonequilibrium phase transition. This fact gives us a dynamical aspect of mean field theory for the system with fluctuating couplings. The second example are found to be analyzed by standard statistical methods, e. g., replica method or cavity method to investigate the equilibrium properties of the system. However the effect of the fluctuating couplings modifies the temperature of the system. This results are confirmed by the self-averaging property at thermodynamic limit. This fact gives us a static aspect of mean field theory for the system with fluctuating couplings.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Ichiki, A. and Shiino, M.}, biburl = {https://www.bibsonomy.org/bibtex/2a74a4fa20f0e910cee20447707f9032b/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {0f8f20aa08ccc4bdf0824acc0448703c}, intrahash = {a74a4fa20f0e910cee20447707f9032b}, keywords = {coupled field mean network neural nonequilibrium oscillators phase statphys23 stochastic system topic-11 transition}, month = {9-13 July}, timestamp = {2007-06-20T10:16:25.000+0200}, title = {Mean Field Theory for Stochastic Dynamical Systems}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=629}, year = 2007 }