Abstract
Finite segments of infinite chains of classical coupled harmonic oscillators are treated as models of thermodynamic systems in contact with a heat bath, i.e., canonical ensembles. The Liouville function ρ for the infinite chain is reduced by integrating over the "outside" variables to a function ρN of the variables of the N-particle segment that is the thermodynamic system. The reduced Liouville function ρN which is calculated from the dynamics of the infinite chain and the statistical knowledge of the coordinates and momenta at t = 0, is a time-dependent probability density in the 2N-dimensional phase space of the system. A Gibbs entropy defined in terms of ρN measures the evolution of knowledge of the system (more accurately, the growth of missing pertinent information) in the sense of information theory. As |t
| Original language | English (US) |
|---|---|
| Pages (from-to) | 393-414 |
| Number of pages | 22 |
| Journal | Journal of Statistical Physics |
| Volume | 1 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 1 1969 |
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Keywords
- approach to equilibrium
- coupled harmonic oscillators
- entropy
- information theory
- Liouville function
- nonequilibrium statistical mechanics
ASJC Scopus subject areas
- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
Cite this
Entropy, information theory, and the approach to equilibrium of coupled harmonic oscillator systems. / Huerta, Manuel A.; Robertson, Harry S.
In: Journal of Statistical Physics, Vol. 1, No. 3, 01.09.1969, p. 393-414.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Entropy, information theory, and the approach to equilibrium of coupled harmonic oscillator systems
AU - Huerta, Manuel A.
AU - Robertson, Harry S.
PY - 1969/9/1
Y1 - 1969/9/1
N2 - Finite segments of infinite chains of classical coupled harmonic oscillators are treated as models of thermodynamic systems in contact with a heat bath, i.e., canonical ensembles. The Liouville function ρ for the infinite chain is reduced by integrating over the "outside" variables to a function ρN of the variables of the N-particle segment that is the thermodynamic system. The reduced Liouville function ρN which is calculated from the dynamics of the infinite chain and the statistical knowledge of the coordinates and momenta at t = 0, is a time-dependent probability density in the 2N-dimensional phase space of the system. A Gibbs entropy defined in terms of ρN measures the evolution of knowledge of the system (more accurately, the growth of missing pertinent information) in the sense of information theory. As |t
AB - Finite segments of infinite chains of classical coupled harmonic oscillators are treated as models of thermodynamic systems in contact with a heat bath, i.e., canonical ensembles. The Liouville function ρ for the infinite chain is reduced by integrating over the "outside" variables to a function ρN of the variables of the N-particle segment that is the thermodynamic system. The reduced Liouville function ρN which is calculated from the dynamics of the infinite chain and the statistical knowledge of the coordinates and momenta at t = 0, is a time-dependent probability density in the 2N-dimensional phase space of the system. A Gibbs entropy defined in terms of ρN measures the evolution of knowledge of the system (more accurately, the growth of missing pertinent information) in the sense of information theory. As |t
KW - approach to equilibrium
KW - coupled harmonic oscillators
KW - entropy
KW - information theory
KW - Liouville function
KW - nonequilibrium statistical mechanics
UR - http://www.scopus.com/inward/record.url?scp=0011519626&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0011519626&partnerID=8YFLogxK
U2 - 10.1007/BF01106579
DO - 10.1007/BF01106579
M3 - Article
AN - SCOPUS:0011519626
VL - 1
SP - 393
EP - 414
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
SN - 0022-4715
IS - 3
ER -