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经典理想气体模型的信息几何结构及不稳定性

DOI: 10.15918/j.tbit1001-0645.2015.04.019

Keywords: 经典理想气体 几何结构 不稳定性

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Abstract:

从信息几何的角度研究了经典理想气体模型.探讨了经典理想气体模型的α-几何结构.借助于几何结构,通过测地弧长、体积元以及Jacobi向量场分析了模型的不稳定性.并且给出了模型的Lyapunov指数

References

[1]  Amari S. Differential geometrical methods in statistics[M]. [S.l.]: Springer Lecture Notes in Statistics, 1985.
[2]  Amari S, Nagaoka H. Methods of information geometry[M]. Oxford: Oxford University Press, 2000.
[3]  Takafumi K. Pool-based active learning with optimal sampling distribution and its information geometrical interpretation[J]. Neurocomputing, 2007, 71: 353-362.
[4]  Amari S. The EM algorithm and information geometry in neural network learning [J]. Neural Computation, 1995,7:13-18.
[5]  Peng L, Sun H, Sun D, et al. The geometric structures and instability of entropic dynamical models[J]. Advances in Mathematics, 2011,227:459-471.
[6]  Cao L, Sun H, Zhang Z. The geometric description of the fibre bundle surface for the Birkhoff system[J]. Chinese Physics Letters, 2009,26:1-2.
[7]  Zhang Z, Sun H ,Zhong F. Natural gradient-projection algorithm for distribution control[J]. Optimal Control Application and Methods, 2009,30:495-504.
[8]  Cengel Y, Boles M. Thermodynamics: an engineering approach[M]. 4th ed. [S.l.]: McGraw-Hill Science, 2001.
[9]  Do Carmo M. Riemannian geometry[M]. Boston: Birkhuser, 1992.
[10]  Casetti L, Pettini M, Cohen E. Geometric approach to Hamiltonian dynamics and statistical mechanics[J]. Physics Reports A, 2000,337:237-341.
[11]  Casetti L, Clementi C, Pettini M. Riemannian theory of Hamiltonian chaos and Lyapunov exponents[J]. Physical Review E, 1996,54:5969-5984.
[12]  Brody D,Rivier N. Geometrical aspects of statistical mechanics[J]. Physical Review E, 1995,51:1006-1011.

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