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Space–time intrinsic randomness of dynamical systems and statistical mechanics
Author(s) -
Courbage M.,
Kamiński B.
Publication year - 2004
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.10838
Subject(s) - randomness , phase space , statistical physics , lorentz transformation , ideal (ethics) , statistical mechanics , space (punctuation) , physics , dynamical systems theory , ideal gas , property (philosophy) , thermodynamic limit , classical mechanics , mathematics , quantum mechanics , computer science , philosophy , statistics , epistemology , operating system
The concept of intrinsically random systems is introduced to modelize a class of dynamical systems that can be transformed exactly, through positivity preserving invertible transformations or projections, into strongly irreversible Markov processes. The property holds for all K‐dynamical evolutions. Systems of infinite noninteracting particles, such as Ideal gas and Lorentz gas, are described by Poisson distributions over one‐particle phase space. As dynamical systems, they have strong mixing properties: they are K‐systems. Therefore, the intrinsic randomness property seems not to discriminate between Lorentz gas and Ideal gas. We show that a discrimination between them requires the consideration, in the thermodynamic limit, of multidimensional space–time group. The concept of intrinsic randomness is extended to such Z d ‐ actions and K‐property of the action is proved to be a necessary and sufficient condition of space–time intrinsic randomness. This leads to a discrimination between the Lorentz gas, which is space–time intrinsically random, and the Ideal gas, which is not. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004