Issue |
Europhys. Lett.
Volume 72, Number 3, November 2005
|
|
---|---|---|
Page(s) | 355 - 361 | |
Section | General | |
DOI | https://doi.org/10.1209/epl/i2005-10248-2 | |
Published online | 30 September 2005 |
Linear instability and statistical laws of physics
1
Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria Via Valleggio 11, 22100 Como, Italy
2
CNR-INFM, Istituto Nazionale di Fisica Nucleare, Sezione di Milano - Milano, Italy
3
Department of Physics, National University of Singapore Singapore 117542, Republic of Singapore
4
Santa Fe Institute - 1399 Hyde Park Road, Santa Fe, NM 87501, USA
5
Centro Brasileiro de Pesquisas Físicas - Rua Xavier Sigaud 150 22290-180 Rio de Janeiro-RJ, Brazil
6
INFM-Dipartimento di Fisica, Università di Padova Via Marzolo 8, I-35131 Padova, Italy
7
Sezione INFN, Università di Padova - Via Marzolo 8, I-35131 Padova, Italy
Received:
29
July
2005
Accepted:
8
September
2005
We show that a meaningful statistical description is possible in
conservative and mixing systems with zero Lyapunov exponent in
which the dynamical instability is only linear in time. More
specifically, i) the sensitivity to initial
conditions is given by
with
; ii) the statistical entropy
in the infinitely fine graining limit (i.e.,
number of cells into which the
phase space has been partitioned
),
increases linearly with time only for
; iii) a
nontrivial, q-generalized, Pesin-like identity is
satisfied, namely the
. These facts
(which are in analogy to
the usual behaviour of strongly
chaotic systems with
), seem to open the door for a
statistical description of conservative many-body
nonlinear systems whose Lyapunov spectrum
vanishes.
PACS: 05.45.Ac – Low-dimensional chaos / 05.45.Mt – Quantum chaos; semiclassical methods / 03.67.Lx – Quantum computation
© EDP Sciences, 2005
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