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61.
Pierre Gaspard 《Journal of statistical physics》2004,117(3-4):599-615
A concept of time-reversed entropy per unit time is introduced in analogy with the entropy per unit time by Shannon, Kolmogorov, and Sinai. This time-reversed entropy per unit time characterizes the dynamical randomness of a stochastic process backward in time, while the standard entropy per unit time characterizes the dynamical randomness forward in time. The difference between the time-reversed and standard entropies per unit time is shown to give the entropy production of Markovian processes in nonequilibrium steady states. 相似文献
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Let X1, X2, …, Xn be random vectors that take values in a compact set in Rd, d ≥ 1. Let Y1, Y2, …, Yn be random variables (“the responses”) which conditionally on X1 = x1, …, Xn = xn are independent with densities f(y | xi, θ(xi)), i = 1, …, n. Assuming that θ lives in a sup-norm compact space Θq,d of real valued functions, an optimal L1-consistent estimator
of θ is constructed via empirical measures. The rate of convergence of the estimator to the true parameter θ depends on Kolmogorov's entropy of Θq,d. 相似文献
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66.
We examine asymptotically periodic density evolution in one-dimensional maps perturbed by noise, associating the macroscopic state of these dynamical systems with a phase space density. For asymptotically periodic systems density evolution becomes periodic in time, as do some macroscopic properties calculated from them. The general formalism of asymptotic periodicity is examined and used to calculate time correlations along trajectories of these maps as well as their limiting conditional entropy. The time correlation is shown to naturally decouple into periodic and stochastic components. Finally, asymptotic periodicity is studied in a noise-perturbed piecewise linear map, focusing on how the variation of noise amplitude can cause a transition from asymptotic periodicity to asymptotic stability in the density evolution of this system. 相似文献
67.
Polycrystalline perovskite La0.67Ca0.33MnO3 was synthesized by a sol–gel method. Its adiabatic temperature change ΔTad induced by a magnetic field change was measured directly. At 268 K, near its Curie temperature TC, ΔTad of La0.67Ca0.33MnO3 induced by a magnetic field change of 2.02 T reaches 2.4 K. The latent heat Q and magnetic entropy change −ΔSM induced by a magnetic field change were calculated from the temperature dependence of ΔTad and zero-field heat capacity Cp. The maximum values of Q and −ΔSM in La0.67Ca0.33MnO3 induced by a magnetic field change of 2.02 T are 1.85 J g−1 and 6.9 J kg−1 K−1, respectively. The former is larger than the phase transition latent heat of heating or cooling, which is about 1.70 J g−1. 相似文献
68.
We define a classical probability analogue of Voiculescu's free entropy dimension that we shall call the classical probability entropy dimension of a probability measure on Rn. We show that the classical probability entropy dimension of a measure is related with diverse other notions of dimension. First, it can be viewed as a kind of fractal dimension. Second, if one extends Bochner's inequalities to a measure by requiring that microstates around this measure asymptotically satisfy the classical Bochner's inequalities, then we show that the classical probability entropy dimension controls the rate of increase of optimal constants in Bochner's inequality for a measure regularized by convolution with the Gaussian law as the regularization is removed. We introduce a free analogue of the Bochner inequality and study the related free entropy dimension quantity. We show that it is greater or equal to the non-microstates free entropy dimension. 相似文献
69.
Model or variable selection is usually achieved through ranking models according to the increasing order of preference. One of methods is applying Kullback–Leibler distance or relative entropy as a selection criterion. Yet that will raise two questions, why use this criterion and are there any other criteria. Besides, conventional approaches require a reference prior, which is usually difficult to get. Following the logic of inductive inference proposed by Caticha [Relative entropy and inductive inference, in: G. Erickson, Y. Zhai (Eds.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, AIP Conference Proceedings, vol. 707, 2004 (available from arXiv.org/abs/physics/0311093)], we show relative entropy to be a unique criterion, which requires no prior information and can be applied to different fields. We examine this criterion by considering a physical problem, simple fluids, and results are promising. 相似文献
70.
在相对论σ-ω-ρ模型的平均场近似下, 研究了质子中子星物质在均熵状态下的组成、温度和物态方程. 如给定每一个重子的熵, 一些热力学量的值将随重子密度的增加而增加, 当考虑超子时, 这些值会减小. 给定重子密度, 中子在S=2时的组分比S=1时的小, 而质子、电子、μ子在S=2时的组分比S=1时的大, 特别是在低密度区域. S是每个重子的熵. 保持重子密度不变, 在低密度区域, 超子在S=2时的组分比S=1时的大, 在高密度区域则相反. 同样, 在同一重子密度处, S=2时的温度、能量密度及压强分别比S=1时的大. 另外, 有限熵对粒子组分和温度的影响比对质子中子星物质的物态方程的影响大. 还研究了反粒子的贡献, 他们确实很小. 相似文献