How thermostats change the thermodynamic, structural and dynamic properties of a Lennard-Jones liquid

Almost every molecular dynamics simulation is coupled to a thermostat, and every thermostat modifies the equations of motion whose solutions are then interpreted as the physics of the system. The algorithms are well established and their qualitative artefacts are well known, yet a quantitative comparison of the commonly used schemes under one protocol, with the statistical resolution needed to detect their effects, is rarely reported, presumably because such effects are small compared with the run-to-run scatter of a typical simulation. Such a comparison, however, is of practical importance, since it determines which observables a given thermostat can be trusted with. In this work, we compare six temperature-control schemes (windowed velocity rescaling, Berendsen, Nosé–Hoover chains, Langevin, the dissipative-particle-dynamics pair thermostat and canonical sampling through velocity rescaling) at up to four coupling strengths each against an energy-matched microcanonical reference, for the truncated-and-shifted Lennard-Jones liquid, with five independent realizations per case and with finite-size and timestep controls. We find that thermodynamic means and pair structure are the same for all schemes once the mean temperature is matched, whereas the fluctuations differ and the differences propagate into derived quantities such as the heat capacity. For transport, the decisive variable is whether the thermostat acts globally or locally, not how strongly it is coupled: the global schemes leave the self-diffusion coefficient and the viscosity equivalent to those of the microcanonical reference over the whole coupling range, whereas the local stochastic schemes damp diffusion once their friction approaches the intrinsic friction of the liquid. In particular, we show that the Langevin bias at five state points is reproduced to within 16%, with no fitted parameter, by a resistance-addition interpolation whose only input is the cage factor of overdamped Brownian dynamics, and that, once the periodic-box correction is carried over to the screened hydrodynamics of a Langevin liquid, the bath is predicted to remove in the thermodynamic limit a hydrodynamic contribution to diffusion that a finite box conceals. Our results also rationalize two implementation effects in LAMMPS, the kinetic-energy fluctuation deficit of strongly coupled Langevin dynamics and the failure of the stress-autocorrelation viscosity for a strongly coupled pair thermostat, which could otherwise be mistaken for physics. The comparison condenses into simple rules for the choice of a thermostat and its coupling time.