## Abstract

Two methods for computing the entropy of hard-sphere systems using a spherical tether model are explored which allow the efficient use of event-driven molecular-dynamics simulations. An intuitive derivation is given that relates the

rate of particle collisions, either between two particles or between a particle and its respective tether, to an associated hypersurface area which bounds the system’s accessible configurational phase-space. Integrating the particle-particle collision rates with respect to sphere diameter (or, equivalently, density) or the particle-tether collision rates with respect to tether length then directly determines the volume of accessible phase space and, therefore, the system entropy. The approach is general and can be used for any system composed of particles interacting with discrete potentials in fluid, solid, or glassy states. The entropies calculated for the liquid and crystalline hard-sphere states using these methods are found to agree closely with the current best estimates in the literature, demonstrating the accuracy of the approach

rate of particle collisions, either between two particles or between a particle and its respective tether, to an associated hypersurface area which bounds the system’s accessible configurational phase-space. Integrating the particle-particle collision rates with respect to sphere diameter (or, equivalently, density) or the particle-tether collision rates with respect to tether length then directly determines the volume of accessible phase space and, therefore, the system entropy. The approach is general and can be used for any system composed of particles interacting with discrete potentials in fluid, solid, or glassy states. The entropies calculated for the liquid and crystalline hard-sphere states using these methods are found to agree closely with the current best estimates in the literature, demonstrating the accuracy of the approach

Original language | English |
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Article number | 064504 |

Number of pages | 11 |

Journal | The Journal of Chemical Physics |

Volume | 155 |

Issue number | 6 |

Early online date | 11 Aug 2021 |

DOIs | |

Publication status | Published - 14 Aug 2021 |

### Bibliographical note

Open Access via the AIP AgreementACKNOWLEDGEMENTS

The authors acknowledge the support of the Maxwell computing service at the University of Aberdeen, and the Aberdeen-Curtin Alliance26 between the University of Aberdeen (Scotland, U.K.) and Curtin University (Perth, Australia) which funded the Ph.D. of C.M.