## 4 Discussion
It is also irrelevant in the isotropic or semi-isotropic cases implemented in Ref. [18], since, in those cases, the transformation matrix was diagonal. Similarly to the isotropic version, it was possible to avoid the scaling of velocities resulting in a different definition of the internal pressure and a slightly simplified integrator. This possibility was tested here for the Lennard-Jones system and did not offer any specific advantage. It was, instead, expected to be less effective in more general settings, such as using constraints; thus, we did not test it further. An alternative option would be to use the molecular virial and scale only the molecular positions and, optionally, velocities. In this case, intramolecular distances and velocities would not be affected by the scaling procedure and one could, thus, use the formulation where velocities are not scaled also in the presence of intramolecular constraints. The choice of \(\tau_{P}\) should be determined with care. A too low of a value could result in systematic errors due to difficulties in the integration of the equation of motions. This type of error could be detected by comparing results for different values of \(\tau_{P}\) or, when using the time-reversible integrator, by monitoring the effective energy drift, which reports on the detailed balance violation. Although there is no unique prescription about which drift magnitude could be acceptable, one might, for instance, make sure that the drift is similar to the one obtained from a constant volume simulation of the same system. This result would suggest that the integration errors associated with the barostat are not exceeding those associated with the solution of the Hamilton equations of motion for the simulated particles. A too large value of \(\tau_{P}\), instead, would result in a slow volume relaxation. If an approximate estimate of the isothermal compressibility of the system \(\beta_{T}\) was allowed, it would be easy to choose a \(\tau_{P}\) small enough to allow fluctuations of the cell volume to be properly sampled on the desired time scale. An important advantage of the anisotropic SCR, when compared with standard barostats relying on second-order differential equations, is that the relaxation of the volume was more easily predictable and would not exhibit oscillations. This caused the introduced algorithm to be more robust in equilibration procedures. The relaxation of the individual components of the cell matrix seemed more difficult to predict. A possible extension would be to use a tensor compressibility so as to allow individual relaxation times to be controlled. The corresponding equations were developed in Ref. [25], but have not yet been tested. Additional material, including the implementations of the anisotropic SCR barostat in SimpleMD, GROMACS, and LAMMPS, and a Python notebook that can be used to reproduce all the figures of this article, can be found in the GitHub repository [[https://github.com/bussilab/crescale](https://github.com/bussilab/crescale)]([https://github.com/bussilab/crescale](https://github.com/bussilab/crescale)) (accessed on 5 December 2021) and in linked repositories. Conceptualization, G.B. ; methodology, V.D.T. and G.B. ; software, V.D.T., P.R. and G.B. ; writing, V.D.T., P.R., M.B. and G.B. ; supervision, P.R., M.B. and G.B. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Data Availability Statement: Supporting codes can be obtained at this GitHub repository [[https://github.com/bussilab/crescale](https://github.com/bussilab/crescale)]([https://github.com/bussilab/crescale](https://github.com/bussilab/crescale)) (accessed on 5 December 2021). Trajectories are available on Zenodo at [[https://doi.org/10.5281/zenodo.5753467](https://doi.org/10.5281/zenodo.5753467)]([https://doi.org/10.5281/zenodo.5753467](https://doi.org/10.5281/zenodo.5753467)) (accessed on 5 December 2021). P.R.