Prog. Theor. Phys. Vol. 103 No. 1 (2000) pp. 1-52
Thermodynamic Irreversibility from High-Dimensional Hamiltonian Chaos
Department of Pure and Applied Sciences, University of Tokyo
Tokyo 153-8901, Japan
(Received November 9, 1999)
This paper discusses the thermodynamic irreversibility realized
in high-dimensional Hamiltonian systems with a time-dependent
A new quantity, the irreversible information loss, is defined from
the Lyapunov analysis so as to characterize the thermodynamic
irreversibility. It is proved that this new quantity satisfies an
inequality associated with the second law of thermodynamics.
Based on the assumption that these systems possess the mixing property
and certain large deviation properties in the thermodynamic limit,
it is argued reasonably that the most probable value of the irreversible
information loss is equal to the change of the Boltzmann entropy
in statistical mechanics, and that it is always a non-negative value.
The consistency of our argument is confirmed by numerical experiments
with the aid of the definition of a quantity we refer to as the
excess information loss.
DOI : 10.1143/PTP.103.1
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