Anomalous Effects of Velocity Rescaling Algorithms: The Flying Ice Cube Effect Revisited

The flying ice cube effect is a molecular
dynamics simulation artifact
in which the use of velocity rescaling thermostats sometimes causes
violation of the equipartition theorem, affecting both structural
and dynamic properties. The reason for this artifact and the conditions
under which it occurs have not been fully understood. Since the flying
ice cube effect was first demonstrated, a new velocity rescaling algorithm
(the CSVR thermostat) has been developed and become popular without
its effects on the equipartition theorem being truly known. Meanwhile,
the use of simple velocity rescaling and Berendsen (weak coupling)
thermostat algorithms has not abated but has actually continued to
grow. Here, we have calculated the partitioning of the kinetic energy
between translational, rotational, and vibrational modes in simulations
of diatomic molecules to explicitly determine whether the equipartition
theorem is violated under different thermostats and while rescaling
velocities to different kinetic energy distributions. We have found
that the underlying cause of the flying ice cube effect is a violation
of balance leading to systematic redistributions of kinetic energy
under simple velocity rescaling and the Berendsen thermostat. When
velocities are instead rescaled to the canonical ensemble’s
kinetic energy distribution, as is done with the CSVR thermostat,
the equipartition theorem is not violated, and we show that the CSVR
thermostat satisfies detailed balance. The critical necessity for
molecular dynamics practitioners to abandon the use of popular yet
incorrect velocity rescaling algorithms is underscored with an example
demonstrating that the main result of a highly cited study is entirely
due to artifacts resulting from the study’s use of the Berendsen
thermostat.

飞冰效应（flying ice cube effect）是一类分子动力学模拟假象：在模拟过程中使用速度缩放恒温器时，常会引发能量均分定理的违反，进而对体系的结构与动力学性质造成影响。目前学界尚未完全阐明该假象的成因与触发条件。自飞冰效应首次被证实以来，一种新型速度重整算法——CSVR恒温器（CSVR thermostat）——已得到广泛应用，但学界尚未明确其对能量均分定理的影响。与此同时，简单速度缩放与贝伦德森（Berendsen，弱耦合）恒温器算法的使用不仅未衰减，反而持续增长。本研究通过对双原子分子体系开展分子动力学模拟，计算了平动、转动与振动模式间的动能分配情况，以明确不同恒温器条件下、将速度重整至不同动能分布时，是否会违反能量均分定理。我们发现，飞冰效应的根本成因在于：简单速度缩放与贝伦德森恒温器会破坏体系的平衡条件，导致动能出现系统性重分布。而若如CSVR恒温器那般，将速度重整至正则系综的动能分布，则不会违反能量均分定理；同时我们证明了CSVR恒温器满足细致平衡条件。本研究通过一则示例强调，分子动力学研究者亟需摒弃这类流行却存在缺陷的速度缩放算法：某篇高引用研究的核心结论完全源于其使用贝伦德森恒温器所产生的模拟假象。