### Abstract

The standard theory of fluctuations in thermodynamic variables in various ensembles is generalized to nonthermodynamic variables: e.g., the mean-square fluctuations of the kinetic energy K in a classical microcanonical ensemble at fixed energy E is given, for large systems, by(δK)2K=T[1-32C), where T is the temperature (corresponding to the energy E) and C is the specific heat per particle (in units of Boltzmann's constant). The general results may be expressed in terms of the asymptotic behavior of the Ursell functions in various ensembles. Applications are made to molecular dynamic computations where time averages correspond (via ergodicity) to phase averages in an ensemble with fixed energy and momentum. The results are also useful for time-dependent correlations.

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

Pages (from-to) | 250-254 |

Number of pages | 5 |

Journal | Physical Review |

Volume | 153 |

Issue number | 1 |

DOIs | |

State | Published - 1967 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physical Review*,

*153*(1), 250-254. https://doi.org/10.1103/PhysRev.153.250

**Ensemble dependence of fluctuations with application to machine computations.** / Lebowitz, J. L.; Percus, Jerome; Verlet, L.

Research output: Contribution to journal › Article

*Physical Review*, vol. 153, no. 1, pp. 250-254. https://doi.org/10.1103/PhysRev.153.250

}

TY - JOUR

T1 - Ensemble dependence of fluctuations with application to machine computations

AU - Lebowitz, J. L.

AU - Percus, Jerome

AU - Verlet, L.

PY - 1967

Y1 - 1967

N2 - The standard theory of fluctuations in thermodynamic variables in various ensembles is generalized to nonthermodynamic variables: e.g., the mean-square fluctuations of the kinetic energy K in a classical microcanonical ensemble at fixed energy E is given, for large systems, by(δK)2K=T[1-32C), where T is the temperature (corresponding to the energy E) and C is the specific heat per particle (in units of Boltzmann's constant). The general results may be expressed in terms of the asymptotic behavior of the Ursell functions in various ensembles. Applications are made to molecular dynamic computations where time averages correspond (via ergodicity) to phase averages in an ensemble with fixed energy and momentum. The results are also useful for time-dependent correlations.

AB - The standard theory of fluctuations in thermodynamic variables in various ensembles is generalized to nonthermodynamic variables: e.g., the mean-square fluctuations of the kinetic energy K in a classical microcanonical ensemble at fixed energy E is given, for large systems, by(δK)2K=T[1-32C), where T is the temperature (corresponding to the energy E) and C is the specific heat per particle (in units of Boltzmann's constant). The general results may be expressed in terms of the asymptotic behavior of the Ursell functions in various ensembles. Applications are made to molecular dynamic computations where time averages correspond (via ergodicity) to phase averages in an ensemble with fixed energy and momentum. The results are also useful for time-dependent correlations.

UR - http://www.scopus.com/inward/record.url?scp=36049053866&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36049053866&partnerID=8YFLogxK

U2 - 10.1103/PhysRev.153.250

DO - 10.1103/PhysRev.153.250

M3 - Article

VL - 153

SP - 250

EP - 254

JO - Physical Review

JF - Physical Review

SN - 0031-899X

IS - 1

ER -