## Thermostats and constant temperature MD Theoretically, from the establish algorithm, the constant energy is always a requirement for MD, so realizations other than [[Ensemble#Microcanonical ensemble|microcanonical ensemble]] is impossible (because we derived everything at constant $H$). But by using thermostats, people are able to handle constant $T$ case, i.e., canonical ensemble. But one should remember, that even for a system follows Maxwell-Boltzmann distribution, and $k_B T = m \langle v_\alpha ^2 \rangle$ There are fluctuation in temperature as $\frac{\sigma_{T_k}^2}{\langle T_k\rangle_{NVT}^2} = \frac{2}{3N}$ for large $N$ this gets smaller though, The variance is theoretical exists. >[!notice] >For $k_B T = m \langle v_\alpha ^2 \rangle$, $m$ is mass, and this equation only shows one dimensional result. > >And for the later equation, $\frac{\sigma_{T_k}^2}{\langle T_k\rangle_{NVT}^2} = \frac{2}{3N}$, left side is the relative variance of temperature, $\sigma_{T_k} =\langle T_k^2\rangle_{NVT}- \langle T_k\rangle_{NVT}^2$. So if we rescale the temperature by assigning different velocity, it would not properly characterize our system, because it does not correspond to any ensemble (with no temperature fluctuation at all!) ^edca50 >[!info] >Read the following two chapters for more information! >[[Velocity rescaling]] >[[Thermostats by stochastic collision]] > >For implementation in CP2K, check https://manual.cp2k.org/trunk/CP2K_INPUT/MOTION/MD/THERMOSTAT.html