### Abstract

The claim that nonlinear instabilities leading to "dissipative structures" far from thermodynamic equilibrium are analogous to equilibrium phase transitions is investigated. As a representative model, the spin wave instability occurring in a driven ferromagnetic sample is studied in arbitrary dimension. Broken symmetry of the type occurring in equilibrium phase transitions is not found in any dimension, nor does there appear to be an upper critical dimension beyond which mean field theory is correct. The Bénard instability and "Brusselator," which are known to disobey mean field theory in three dimensions, are also studied in higher dimensions; it is found here that although broken symmetry may occur in higher dimensions, again no upper critical dimension exists. Finally, we speculate under what conditions a "dissipative structure" may exhibit true broken symmetry, and a consequent generalized rigidity, in three dimensions.

Original language | English (US) |
---|---|

Pages (from-to) | 2869-2874 |

Number of pages | 6 |

Journal | The Journal of chemical physics |

Volume | 72 |

Issue number | 4 |

State | Published - 1980 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of chemical physics*,

*72*(4), 2869-2874.

**Dissipative structures, broken symmetry, and the theory of equilibrium phase transitions.** / Stein, D. L.

Research output: Contribution to journal › Article

*The Journal of chemical physics*, vol. 72, no. 4, pp. 2869-2874.

}

TY - JOUR

T1 - Dissipative structures, broken symmetry, and the theory of equilibrium phase transitions

AU - Stein, D. L.

PY - 1980

Y1 - 1980

N2 - The claim that nonlinear instabilities leading to "dissipative structures" far from thermodynamic equilibrium are analogous to equilibrium phase transitions is investigated. As a representative model, the spin wave instability occurring in a driven ferromagnetic sample is studied in arbitrary dimension. Broken symmetry of the type occurring in equilibrium phase transitions is not found in any dimension, nor does there appear to be an upper critical dimension beyond which mean field theory is correct. The Bénard instability and "Brusselator," which are known to disobey mean field theory in three dimensions, are also studied in higher dimensions; it is found here that although broken symmetry may occur in higher dimensions, again no upper critical dimension exists. Finally, we speculate under what conditions a "dissipative structure" may exhibit true broken symmetry, and a consequent generalized rigidity, in three dimensions.

AB - The claim that nonlinear instabilities leading to "dissipative structures" far from thermodynamic equilibrium are analogous to equilibrium phase transitions is investigated. As a representative model, the spin wave instability occurring in a driven ferromagnetic sample is studied in arbitrary dimension. Broken symmetry of the type occurring in equilibrium phase transitions is not found in any dimension, nor does there appear to be an upper critical dimension beyond which mean field theory is correct. The Bénard instability and "Brusselator," which are known to disobey mean field theory in three dimensions, are also studied in higher dimensions; it is found here that although broken symmetry may occur in higher dimensions, again no upper critical dimension exists. Finally, we speculate under what conditions a "dissipative structure" may exhibit true broken symmetry, and a consequent generalized rigidity, in three dimensions.

UR - http://www.scopus.com/inward/record.url?scp=36749110798&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36749110798&partnerID=8YFLogxK

M3 - Article

VL - 72

SP - 2869

EP - 2874

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 4

ER -