Emergence Of Order Parameters Research Articles

The reflection phenomenon and complexity engine as statistical physics tools for the advanced evolution phenomenon

We intend to uncover generative principles for complex, biological systems, looking the reflections as well as the analogs of decision making property in quantum physics: measurement, self-interaction of the electron, Berry phase and quantum anomalies. We assume that classical analogs of the mentioned phenomena could be related to the evolvability, growing of complexity and decision making in biological systems. The reflection is a map (coarse graining) from microscopic motions to a macroscopic scale that relates with a free-energy cost and is often accompanied by the emergence of order-parameters. In this context we identify the self-reflection phenomenon, which is exemplified by cognition, information transfer near the error threshold, and tightly related evolution-ecology phenomena. We propose that complex systems that have similar reflection structure are to be described by similar mathematical tools including stochastic (information) thermodynamics and the large deviation theory. We introduce the concept of complexity engine: the group of two (or more) autonomous features of complex systems that are in a partial conflict with each other. Analogues of this are wave-particle duality in quantum mechanics and data-program duality in digital life. We formulate a fundamental problem: does the three-dimensional space provide a complexity engine for the emergence of life?

Synchronization of coupled phase oscillators: Order parameter theory

Rhythmic behaviors, i.e. temporally periodic oscillations in a system, can be ubiquitously found in nature. Interactions among various rhythms can lead to self-organized behaviors and synchronizations. This mechanism is also responsible for many phenomena such as nonlinear waves, spatiotemporal patterns, and collective behaviors in populations emerging in complex systems. Mathematically different oscillations are described by limit-cycle oscillators (pacemakers) with different intrinsic frequencies, and the synchrony of these units can be described by the dynamics of coupled oscillators. Studies of microscopic dynamics reveal that the emergence of synchronization manifests itself as the dimension reduction of phase space, indicating that synchrony can be considered as no-equilibrium phase transition and can be described in terms of order parameters. The emergence of order parameters can be theoretically explored based on the synergetic theory, central manifold theorem and statistical physics. In this paper, we discuss the order-parameter theory of synchronization in terms of statistical physics and set up the dynamical equations of order parameters. We also apply this theory to studying the nonlinear dynamics and bifurcation of order parameters in several typical coupled oscillator systems.