title: Phase transitions and entropies for synchronizing oscillators.
abstract: We study a generic model of coupled oscillators. In the model there is competition between phase synchronization and diffusive effects. For a model with a finite number of states we derive how a phase transition occurs when the coupling parameter is varied. The phase transition is characterized by a symmetry breaking and a discontinuity in the first derivative of the order parameter. We quantitatively account for how the synchronized pulse is a low-entropy structure that facilitates the production of more entropy by the system as a whole. For a model with many states we apply a continuum approximation and derive a potential Burgers' equation for a propagating pulse. No phase transition occurs in that case. However, positive entropy production by diffusive effects still exceeds negative entropy production by the shock formation.
authors: M. Smoluchowski Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland.|Department of Physics, East Carolina University, Greenville, North Carolina 27858, USA.
authors: Martin
authors: M
authors: Bier
authors: M. Smoluchowski Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland.|Unit of Pharmacoepidemiology and Pharmacoeconomics, Faculty of Pharmacy, Jagiellonian University Medical College, ul. Medyczna 9, 30-688 Kraków, Poland.
authors: Bartosz
authors: B
authors: Lisowski
authors: M. Smoluchowski Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland.|Mark Kac Center for Complex Systems Research and Malopolska Center of Biotechnology, Jagiellonian University, Gronostajowa 7A, 30-387 Kraków, Poland.
authors: Ewa
authors: E
authors: Gudowska-Nowak
mesh_terms: D004058:Diffusion; D019277:Entropy; D008962:Models, Theoretical; D044367:Phase Transition