THERMODYNAMIC CONSTRAINTS

In theoretical developments, thermodynamic constraints are introduced by putting the system of interest in contact with some other virtually infinite system, the `reservoir', with a coupling vanishingly small in the thermodynamic limit. Neither ofthese `infinite' conditions can be reproduced in molecular dynamics simulations where the time evolution of an isolated system with a finite number of degrees of freedom is numerically integrated, producing trajectories representative of the microcanonical ensemble. Several ways have been proposed to overcome this limitation. Here the case of MD simulations at constant temperature and/or pressure will be treated within the extended system framework introduced by Andersen in his1980 seminal paper, and later generalised mainly by Nos\'e.The $N$-particle physical system of interest is put in contact with externalreservoirs, which are, in contrast to theoretical infinite ones, represented just bya few degrees of freedom. The equations of motion for the extended system are chosenin such a way that the dynamical trajectory in the phase space of the system ofinterest is representative of the desired ensemble. Moreover the coupling isnon-linear yielding good ergodic properties and can be chosen to be weak enough to leavethe dynamical properties of the system of interest unaltered.