## Abstract

We consider a classical system, in a ν-dimensional cube Ω, with pair potential of the form q(r) + γ^{v}φ(γr). Dividing Ω into a network of cells ω_{1}, ω_{2},..., we regard the system as in a metastable state if the mean density of particles in each cell lies in a suitable neighborhood of the overall mean density ρ, with ρ and the temperature satisfying {Mathematical expression} and {Mathematical expression} where f(ρ, 0+) is the Helmholz free energy density (HFED) in the limit γ→ 0; α = ∫ φ(r)d^{v}r and f_{0}(ρ) is the HFED for the case φ = 0. It is shown rigorously that, for periodic boundary conditions, the conditional probability for a system in the grand canonical ensemble to violate the constraints at time t > 0, given that it satisfied them at time 0, is at most λt, where λ is a quantity going to 0 in the limit {Mathematical expression} Here, r_{0} is a length characterizing the potential q, and x ≫ y means x/y → +∞. For rigid walls, the same result is proved under somewhat more restrictive conditions. It is argued that a system started in the metastable state will behave (over times ≪λ^{-1}) like a uniform thermodynamic phase with HFED f_{0}(ρ) + 1/2αρ^{2}, but that having once left this metastable state, the system is unlikely to return.

Original language | English (US) |
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Pages (from-to) | 211-236 |

Number of pages | 26 |

Journal | Journal of Statistical Physics |

Volume | 3 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1971 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

## Keywords

- Fluids
- constraints
- metastability
- phase coexistence
- statistical mechanics