NVT ensemble

Summary

The NVT ensemble (canonical ensemble) retains number of atoms, volume, and temperature in a molecular dynamics simulation. It simulates at an external temperature bath at a target temperature. Spontaneous changes in NVT simulations cannot lead to increases in Helmholtz free energy (1).

Details

(2) note that it is common to first equilibrate temperature in an NVT ensemble before applying the barostat:

“…it is often more robust to first equilibrate the temperature of a system before applying a barostat to control the temperature. The simultaneous combination of velocity generation and coordinate scaling under the influence of the barostat can introduce instabilities in a system that may be far from equilibrium.”

Langevin dynamics is an example of an NVT ensemble (3):

$$d\mathbf{x}=M^{-1}\mathbf{p}dt\text{\hspace{1em}(1)}$$ $$d\mathbf{p}=\left(-{\nabla }_{\mathbf{x}}U(\mathbf{x})-\gamma \mathbf{p}\right)dt+\sqrt{\frac{2\gamma M}{\beta }}d{\mathbf{W}}_t\text{\hspace{1em}(2)}$$

This reduces to Hamiltonian dynamics (NVE ensemble) when $\gamma =0$.

See Mathematical terms in MD for notation.

1.

Understanding Molecular Simulation. 2002; Available from: https://doi.org/10.1016/b978-0-12-267351-1.x5000-7

2.

Lemkul JA. From Proteins to Perturbed Hamiltonians: A Suite of Tutorials for the GROMACS-2018 Molecular Simulation Package [Article v1.0]. Living Journal of Computational Molecular Science. 2018;1(1):5068. Available from: https://doi.org/10.33011/livecoms.1.1.5068

3.

Hénin J, Lelièvre T, Shirts MR, Valsson O, Delemotte L. Enhanced Sampling Methods for Molecular Dynamics Simulations [Article v1.0]. Living Journal of Computational Molecular Science. 2022;4(1):1583. Available from: https://doi.org/10.33011/livecoms.4.1.1583