Nose-Hoover thermostat: Difference between revisions
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\mathcal{L} = \sum\limits_{i=1}^{N} \frac{m_{i}}{2} s^{2} \dot{\bold{r}}_{i}^{2} - U(\bold{r}) + \frac{Q}{2} \dot{s}^{2}-\frac{g}{\beta}\mathrm{ln}s. | \mathcal{L} = \sum\limits_{i=1}^{N} \frac{m_{i}}{2} s^{2} \dot{\bold{r}}_{i}^{2} - U(\bold{r}) + \frac{Q}{2} \dot{s}^{2}-\frac{g}{\beta}\mathrm{ln} s. | ||
</math> | </math> | ||
Revision as of 08:32, 31 May 2019
In the approach by Nosé and Hoover[1][2][3] an extra degree of freedom is introduced in the Hamiltonian. The heat bath is considered as an integral part of the system and has a fictious coordinate [math]\displaystyle{ s }[/math] which is introduced into the Lagrangian of the system. This Lagrangian for an [math]\displaystyle{ N }[/math] is written as
[math]\displaystyle{ \mathcal{L} = \sum\limits_{i=1}^{N} \frac{m_{i}}{2} s^{2} \dot{\bold{r}}_{i}^{2} - U(\bold{r}) + \frac{Q}{2} \dot{s}^{2}-\frac{g}{\beta}\mathrm{ln} s. }[/math]
References