A Framework for Non-Equilibrium Statistical Ensemble Theory

Since Gibbs synthesized a general equilibrium statistical ensemble theory, many theorists have attempted to generalized the Gibbsian theory to non-equilibrium phenomena domain, however the status of the theory of non-equilibrium phenomena can not be said as firm as well established as the Gibbsian ensemble theory. In this work, we present a framework for the non-equilibrium statistical ensemble formalism based on a subdynamic kinetic equation (SKE) rooted from the Brussels-Austin school and followed by some up-to-date works. The constructed key is to use a similarity transformation between Gibbsian ensembles formalism based on Liouville equation and the subdynamic ensemble formalism based on the SKE. Using this formalism, we study the spin-Boson system, as cases of weak coupling or strongly coupling, and obtain the reduced density operators for the Canonical ensembles easily.

Seasonal Prediction of June Rainfall over South China:Model Assessment and Statistical Downscaling

The performances of various dynamical models from the Asia-Pacific Economic Cooperation（APEC） Climate Center（APCC） multi-model ensemble（MME） in predicting station-scale rainfall in South China（SC） in June were evaluated.It was found that the MME mean of model hindcasts can skillfully predict the June rainfall anomaly averaged over the SC domain.This could be related to the MME＇s ability in capturing the observed linkages between SC rainfall and atmospheric large-scale circulation anomalies in the Indo-Pacific region.Further assessment of station-scale June rainfall prediction based on direct model output（DMO） over 97 stations in SC revealed that the MME mean outperforms each individual model.However,poor prediction abilities in some in-land and southeastern SC stations are apparent in the MME mean and in a number of models.In order to improve the performance at those stations with poor DMO prediction skill,a station-based statistical downscaling scheme was constructed and applied to the individual and MME mean hindcast runs.For several models,this scheme can outperform DMO at more than 30 stations,because it can tap into the abilities of the models in capturing the anomalous Indo-Paciric circulation to which SC rainfall is considerably sensitive.Therefore,enhanced rainfall prediction abilities in these models should make them more useful for disaster preparedness and mitigation purposes.

Ensemble prediction model of solar proton events associated with solar flares and coronal mass ejections

An ensemble prediction model of solar proton events （SPEs）, combining the information of solar flares and coronal mass ejections （CMEs）, is built. In this model, solar flares are parameterized by the peak flux, the duration and the longitude. In addition, CMEs are parameterized by the width, the speed and the measurement position angle. The importance of each parameter for the occurrence of SPEs is estimated by the information gain ratio. We find that the CME width and speed are more informative than the flare’s peak flux and duration. As the physical mechanism of SPEs is not very clear, a hidden naive Bayes approach, which is a probability-based calculation method from the field of machine learning, is used to build the prediction model from the observational data. As is known, SPEs originate from solar flares and/or shock waves associated with CMEs. Hence, we first build two base prediction models using the properties of solar flares and CMEs, respectively. Then the outputs of these models are combined to generate the ensemble prediction model of SPEs. The ensemble prediction model incorporating the complementary information of solar flares and CMEs achieves better performance than each base prediction model taken separately.

Eigen microstates and their evolutions in complex systems

Emergence refers to the existence or formation of collective behaviors in complex systems.Here,we develop a theoretical framework based on the eigen microstate theory to analyze the emerging phenomena and dynamic evolution of complex system.In this framework,the statistical ensemble composed of M microstates of a complex system with N agents is defined by the normalized N×M matrix A,whose columns represent microstates and order of row is consist with the time.The ensemble matrix A can be decomposed as■,where r=min(N,M),eigenvalueσIbehaves as the probability amplitude of the eigen microstate U_I so that■and U_I evolves following V_I.In a disorder complex system,there is no dominant eigenvalue and eigen microstate.When a probability amplitudeσIbecomes finite in the thermodynamic limit,there is a condensation of the eigen microstate UIin analogy to the Bose–Einstein condensation of Bose gases.This indicates the emergence of U_I and a phase transition in complex system.Our framework has been applied successfully to equilibrium threedimensional Ising model,climate system and stock markets.We anticipate that our eigen microstate method can be used to study non-equilibrium complex systems with unknown orderparameters,such as phase transitions of collective motion and tipping points in climate systems and ecosystems.