We demonstrate that the susceptible-infected-susceptible (SIS) model on complex networks can have an inactive Griffiths phase characterized by a slow relaxation dynamics. It contrasts with the mean-field theoretical prediction that the SIS model on complex networks is active at any nonzero infection rate. The dynamic fluctuation of infected nodes, ignored in the mean field approach, is responsible for the inactive phase. It is proposed that the question whether the epidemic threshold of the SIS model on complex networks is zero or not can be resolved by the percolation threshold in a model where nodes are occupied in degree-descending order. Our arguments are supported by the numerical studies on scale-free network models.

We study the entropy production in a macroscopic nonequilibrium system that undergoes an order-disorder phase transition. Entropy production is a characteristic feature of nonequilibrium dynamics with broken detailed balance. It is found that the entropy production rate per particle vanishes in the disordered phase and becomes positive in the ordered phase following critical scaling laws. We derive the scaling relations for associated critical exponents. Our study reveals that a nonequilibrium ordered state is sustained at the expense of macroscopic time-reversal symmetry breaking with an extensive entropy production while a disordered state costs only a subextensive entropy production.PACS numbers: 05.70.Fh, 05.70.Ln, 64.60.Cn Detailed balance is the hallmark of the thermal equilibrium state. A system is said to obey detailed balance if the probability current along any microscopic trajectory in the phase space is balanced by that along the timereversed one [1]. Consequently, time-reversal symmetry is preserved in thermal equilibrium.Thermodynamics of nonequilibrium systems, where detailed balance and time-reversal symmetry are broken with a positive entropy production, has been attracting a lot of interests [2][3][4][5][6][7][8]. Recent studies have been focused on microscopic systems with a few degrees of freedom where the effect of thermal fluctuations are strong. Under the framework of stochastic thermodynamics, various fluctuation theorems are discovered, which provide useful insights on the nature of nonequilibrium fluctuations. Theoretical works foster experimental studies of microscopic systems such as molecular motors, nano heat engines, biomolecules, and so on [9][10][11][12][13][14].Macroscopic systems pose an intriguing question on the level of irreversibility. Consider a many-particle system displaying an order-disorder phase transition whose microscopic dynamics does not obey detailed balance. Does the broken detailed balance result in time-reversal symmetry breaking at the macroscopic level? On the one hand, one may expect that entropy productions of each particle add up to a macroscopic amount irrespective of a macroscopic state. On the other hand, if the system is in a disordered phase so that all configurations are almost equally likely, then irreversibility may not show up on a macroscopic level producing only a subextensive amount of entropy. A system in an ordered state has a lower entropy than in a disordered state. Then, which phase produces more total entropy including the system entropy and the environmental entropy? These questions lead us to the study of the entropy production in a model system undergoing nonequilibrium phase transition.In this paper, we investigate the emergence of macroscopic irreversibility out of microscopic dynamics with broken detailed balance. We find that the total entropy production changes its character from being subextensive to being extensive as the system undergoes an orderdisorder phase transition. The entropy production rate per particle exhibits c...

In geoscientific studies, conventional bilinear interpolation has been widely used for remapping between logically rectangular grids on the surface of a sphere. Recently, various spherical grid systems including geodesic grids have been suggested to tackle the singularity problem caused by the traditional latitude–longitude grid. We suggest an alternative to pre-existing bilinear interpolation methods for remapping between any spherical grids, even for randomly distributed points on a sphere. This method supports any geometrical configuration of four source points neighboring a target point for interpolation, and provides remapping accuracy equivalent to the conventional bilinear method. In addition, for efficient search of neighboring source points, we use the linked-cell mapping method with a cubed-sphere as a reference frame. As a result, the computational cost is proportional to NlogN instead of N 2 (N being the number of grid points), even for the remapping of randomly distributed points on a sphere.

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We investigate the critical phenomena of the degree-ordered percolation (DOP) model on the hierarchical (u, v) flower network. Using the renormalization-group like procedure, we derive the recursion relations for the percolating probability and the percolation order parameter, from which the percolation threshold and the critical exponents are obtained. When u = 1, the DOP critical behavior turns out to be identical to that of the bond percolation with a shifted nonzero percolation threshold. When u = 1, the DOP and the bond percolation have the same vanishing percolation threshold but the critical behaviors are different. Implication to an epidemic spreading phenomenon is discussed.