Thermodynamic Constraints

Abstract

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 of these ‘ 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 his 1980 seminal paper, and later generalised mainly by Nosé. The N-particle physical system of interest is put in contact with external reservoirs, which are, in contrast to theoretical infinite ones, represented just by a few degrees of freedom. The equations of motion for the extended system are chosen in such a way that the dynamical trajectory in the phase space of the system of interest is representative of the desired ensemble. Moreover the coupling is non-linear yielding good ergodic properties and can be chosen to be weak enough to leave the dynamical properties of the system of interest unaltered.