We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the shared information between the two subsystems. If the correlation length is finite, the estimators stay finite for large system sizes. If the correlation length diverges, so do the estimators. The definition of the estimators is inspired by information theory. We look at several models and compare the behavior of the estimators in the finite-size scaling limit. Analytical and numerical methods as well as Monte Carlo simulations are used. We show how the finite-size scaling functions change for various phase transitions, including the case where one has conformal invariance.
Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states
Quasi-stationary criticality of the Order-Parameter of the d=3 Random-Field Ising Antiferromagnet Fe(0.85)Zn(0.15)F2: A Synchrotron X-ray Scattering Study
Nonlinear Stochastic Dynamics of Complex Systems, II: Potential of Entropic Force in Markov Systems with Nonequilibrium Steady State, Generalized Gibbs Function and Criticality
Zero-temperature criticality in a simple glass model
我们介绍强相互作用陷阱模型，一个版本的布绍的陷阱模型的玻璃[布绍J-P 1992 { \em J. Phys. I France { \bf 2}} 1705]。在有限的温度下，该模型表现出玻璃态松弛在中间的时间范围内，但在有限的时间达到稳定状态。在零温度的限制下，并且利用适当的重整时间尺度，模型映射到在自组织临界性的背景下广泛研究的Bak-Sneppen模型[Bak P和Sneppen K 1993 { \em Phys. Rev. Lett. { \bf 71}} 4083]。因此，零温度是所有维度的临界点。这些主张支持的平均场分析的固定的解决方案和数值模拟的有限维晶格模型。
