### Abstract

A statistical theory of an excitable membrane is proposed under the assumptions that the membrane is composed of an ensemble of a number of active patches, and that the flip-flop transition of an active patch is governed by the dissipative interaction caused by an electric eddy current. By the method of expanding the master equation in the system size together with the Gaussian approximation, the time course of an excitation and the steady N-shaped relation between current and voltage are derived from the ensemble theory of open systems. The fluctuation of electric current under a fixed voltage becomes anomalously large in the marginal state at the threshold potential. The fluctuation associated with an action potential increases sharply at the jump-up transition, but it is not so large at the flip-back catastrophe. The fluctuation-dissipation relation at the steady state of the membrane system is discussed on the basis of a variational principle.

Original language | English |
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Pages (from-to) | 129-139 |

Number of pages | 11 |

Journal | Journal of Statistical Physics |

Volume | 15 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1976 Aug |

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### Keywords

- action potential
- ensemble theory
- Excitable membrane
- fluctuation-dissipation relation
- N-shaped I-V relation
- Onsager principle
- open system
- system-size expansion

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*,

*15*(2), 129-139. https://doi.org/10.1007/BF01012032

**A statistical theory of excitable membranes. Nonlinear force-flux relation and fluctuation.** / Aizawa, Yoji; Kobatake, Yonosuke.

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, vol. 15, no. 2, pp. 129-139. https://doi.org/10.1007/BF01012032

}

TY - JOUR

T1 - A statistical theory of excitable membranes. Nonlinear force-flux relation and fluctuation

AU - Aizawa, Yoji

AU - Kobatake, Yonosuke

PY - 1976/8

Y1 - 1976/8

N2 - A statistical theory of an excitable membrane is proposed under the assumptions that the membrane is composed of an ensemble of a number of active patches, and that the flip-flop transition of an active patch is governed by the dissipative interaction caused by an electric eddy current. By the method of expanding the master equation in the system size together with the Gaussian approximation, the time course of an excitation and the steady N-shaped relation between current and voltage are derived from the ensemble theory of open systems. The fluctuation of electric current under a fixed voltage becomes anomalously large in the marginal state at the threshold potential. The fluctuation associated with an action potential increases sharply at the jump-up transition, but it is not so large at the flip-back catastrophe. The fluctuation-dissipation relation at the steady state of the membrane system is discussed on the basis of a variational principle.

AB - A statistical theory of an excitable membrane is proposed under the assumptions that the membrane is composed of an ensemble of a number of active patches, and that the flip-flop transition of an active patch is governed by the dissipative interaction caused by an electric eddy current. By the method of expanding the master equation in the system size together with the Gaussian approximation, the time course of an excitation and the steady N-shaped relation between current and voltage are derived from the ensemble theory of open systems. The fluctuation of electric current under a fixed voltage becomes anomalously large in the marginal state at the threshold potential. The fluctuation associated with an action potential increases sharply at the jump-up transition, but it is not so large at the flip-back catastrophe. The fluctuation-dissipation relation at the steady state of the membrane system is discussed on the basis of a variational principle.

KW - action potential

KW - ensemble theory

KW - Excitable membrane

KW - fluctuation-dissipation relation

KW - N-shaped I-V relation

KW - Onsager principle

KW - open system

KW - system-size expansion

UR - http://www.scopus.com/inward/record.url?scp=34250382590&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250382590&partnerID=8YFLogxK

U2 - 10.1007/BF01012032

DO - 10.1007/BF01012032

M3 - Article

AN - SCOPUS:34250382590

VL - 15

SP - 129

EP - 139

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 2

ER -