Flying ice cube

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The Flying ice cube [1] is an artificial situation encountered in molecular dynamics simulations whereby an incorrect equipartition of energy is brought about by thermostats that improperly implement some form of periodic velocity rescaling outside of the continuous equations of motion, such as the Berendsen thermostat. The artifact is due to these thermostats violating the balance condition that is a requirement of Monte Carlo simulations (molecular dynamics simulations with velocity rescaling thermostats can be thought of as Monte Carlo simulations with molecular dynamics moves and velocity rescaling moves).[2] The net result is that an instability forms where the kinetic energy may be drained from some degrees of freedom and be incorrectly fed into others. A manifestation of this would be the kinetic energy from the high frequency bond vibrations and angle bending in a system composed of, say, flexible water molecules ending up in the zero frequency mode of the kinetic energy of the system as a whole (i.e. centre of mass translation); the molecular motions would become frozen, resulting in a flying ice cube. Note that despite the name, this situation is not limited to simulations of water. This artifact is avoided by using a velocity rescaling thermostat that obeys the balance condition, such as the Bussi-Donadio-Parrinello thermostat.[2]