### Abstract

Inadequacy of perturbation treatment in chaotic dynamics is pointed out, especially for phase space distribution function. The coarse graining is introduced into phase space distribution function for describing macroscopic thermodynamic process as a necessary and inevitable procedure for the transition from microscopic to macroscopic levels. A concept of convergence in law is employed for coarse graining. Thus a new approach to the linear response theory is presented, which can remove the various difficulties in the conventional linear response theory. The derivation of the distribution function in the sense of convergence in law is left open, but it is expected that the principal results such as fluctuation-dissipation theorem, Kubo formula for kinetic coefficient remain valid, provided that an appropriate interpretation is applied. Furthermore the entropy is shown to increase and the susceptibility derived in this theory is adiabatic susceptibility expected as a thermodynamic process. The present formulation will provide an answer to the critical discussion by van Kampen.

Original language | English |
---|---|

Pages (from-to) | 3089-3105 |

Number of pages | 17 |

Journal | Journal of the Physical Society of Japan |

Volume | 58 |

Issue number | 9 |

Publication status | Published - 1989 Sep |

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### Keywords

- Chaotic dynamics
- Coarse graining
- Convergence in law
- Entropy
- Fluctuation-dissipation theorem
- Green-Kubo formula
- Liouville equation
- Susceptibilities

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Physical Society of Japan*,

*58*(9), 3089-3105.

**Linear response theory reformulated from the chaotic dynamics.** / Sait̂o, Nobuhiko; Matsunaga, Yasushi.

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 58, no. 9, pp. 3089-3105.

}

TY - JOUR

T1 - Linear response theory reformulated from the chaotic dynamics

AU - Sait̂o, Nobuhiko

AU - Matsunaga, Yasushi

PY - 1989/9

Y1 - 1989/9

N2 - Inadequacy of perturbation treatment in chaotic dynamics is pointed out, especially for phase space distribution function. The coarse graining is introduced into phase space distribution function for describing macroscopic thermodynamic process as a necessary and inevitable procedure for the transition from microscopic to macroscopic levels. A concept of convergence in law is employed for coarse graining. Thus a new approach to the linear response theory is presented, which can remove the various difficulties in the conventional linear response theory. The derivation of the distribution function in the sense of convergence in law is left open, but it is expected that the principal results such as fluctuation-dissipation theorem, Kubo formula for kinetic coefficient remain valid, provided that an appropriate interpretation is applied. Furthermore the entropy is shown to increase and the susceptibility derived in this theory is adiabatic susceptibility expected as a thermodynamic process. The present formulation will provide an answer to the critical discussion by van Kampen.

AB - Inadequacy of perturbation treatment in chaotic dynamics is pointed out, especially for phase space distribution function. The coarse graining is introduced into phase space distribution function for describing macroscopic thermodynamic process as a necessary and inevitable procedure for the transition from microscopic to macroscopic levels. A concept of convergence in law is employed for coarse graining. Thus a new approach to the linear response theory is presented, which can remove the various difficulties in the conventional linear response theory. The derivation of the distribution function in the sense of convergence in law is left open, but it is expected that the principal results such as fluctuation-dissipation theorem, Kubo formula for kinetic coefficient remain valid, provided that an appropriate interpretation is applied. Furthermore the entropy is shown to increase and the susceptibility derived in this theory is adiabatic susceptibility expected as a thermodynamic process. The present formulation will provide an answer to the critical discussion by van Kampen.

KW - Chaotic dynamics

KW - Coarse graining

KW - Convergence in law

KW - Entropy

KW - Fluctuation-dissipation theorem

KW - Green-Kubo formula

KW - Liouville equation

KW - Susceptibilities

UR - http://www.scopus.com/inward/record.url?scp=0012019307&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012019307&partnerID=8YFLogxK

M3 - Article

VL - 58

SP - 3089

EP - 3105

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 9

ER -