### Abstract

Equivalence (allowing for convex combinations) of microcanonical, canonical and grandcanonical ensembles for states of classical systems is established under very mild assumptions on the limiting state. We introduce the notion of conditional equilibrium (C.E.), a property of states of infinite systems which characterizes convex combinations of limits of microcanonical ensembles. It is shown that C.E. states are, under quite general conditions, mixtures of Gibbs states.

Original language | English (US) |
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Pages (from-to) | 279-302 |

Number of pages | 24 |

Journal | Communications In Mathematical Physics |

Volume | 62 |

Issue number | 3 |

DOIs | |

State | Published - Oct 1 1978 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Aizenman, M., Goldstein, S., & Lebowitz, J. L. (1978). Conditional equilibrium and the equivalence of microcanonical and grandcanonical ensembles in the thermodynamic limit.

*Communications In Mathematical Physics*,*62*(3), 279-302. https://doi.org/10.1007/BF01202528