Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen, 361005, China.
Collaborative Innovation Center of Chemistry for Energy Materials, Xiamen University, Xiamen, 361005, China.
Sci Rep. 2017 Jun 14;7(1):3460. doi: 10.1038/s41598-017-03694-w.
A logarithmic oscillator has been proposed to serve as a thermostat recently since it has a peculiar property of infinite heat capacity according to the virial theorem. In order to examine its feasibility in numerical simulations, a modified logarithmic potential has been applied in previous studies to eliminate the singularity at the origin. The role played by the modification has been elucidated in the present study. We argue that the virial theorem is practically violated in finite-time simulations of the modified log-oscillator illustrated by a linear dependence of kinetic temperature on energy. Furthermore, as far as a thermalized log-oscillator is concerned, our calculation based on the canonical ensemble average shows that the generalized equipartition theorem is broken if the temperature is higher than a critical temperature. Finally, we show that log-oscillators fail to serve as thermostats for their incapability of maintaining a nonequilibrium steady state even though their energy is appropriately assigned.
最近，有人提出对数振荡器可以作为恒温器，因为根据维里定理，它具有无限热容的奇特性质。为了在数值模拟中检验其可行性，先前的研究中应用了修正对数势来消除原点处的奇点。本研究阐明了这种修正的作用。我们认为，修正后的对数振荡器在有限时间模拟中实际上违反了维里定理，表现为动能温度与能量呈线性关系。此外，就热化的对数振荡器而言，如果温度高于临界温度，我们基于正则系综平均值的计算表明广义能量均分定理被打破。最后，我们表明，对数振荡器无法维持非平衡稳态，因此不能用作恒温器，即使它们的能量得到了适当的分配。
