The Berendsen thermostat is an algorithm to re-scale the velocities of particles in molecular dynamics

Molecular dynamics

Molecular dynamics is a computer simulation of physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms...

 simulations to control the simulation temperature.

Basic Description

In this scheme, the system is weakly coupled to a heat bath with some temperature. The thermostat

Thermostat

A thermostat is the component of a control system which regulates the temperature of a system so that the system's temperature is maintained near a desired setpoint temperature. The thermostat does this by switching heating or cooling devices on or off, or regulating the flow of a heat transfer...

 suppresses fluctuations of the kinetic energy

Kinetic energy

The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

 of the system and therefore cannot produce trajectories consistent with the canonical ensemble

Canonical ensemble

The canonical ensemble in statistical mechanics is a statistical ensemble representing a probability distribution of microscopic states of the system...

. The temperature of the system is corrected such that the deviation exponentially decays with some time constant .


Though the thermostat does not generate a correct canonical ensemble

Canonical ensemble

The canonical ensemble in statistical mechanics is a statistical ensemble representing a probability distribution of microscopic states of the system...

 (especially for small systems), for large systems on the order of hundreds or thousands of atoms/molecules, the approximation yields roughly correct results for most calculated properties. The scheme is widely used due to the efficiency with which it relaxes a system to some target (bath) temperature. In many instances, systems are initially equilibrated using the Berendsen scheme, while properties are calculated using the widely known Nosé-Hoover thermostat

Nosé-Hoover thermostat

The Nosé–Hoover thermostat is a deterministic method used in molecular dynamics to keep the temperature around an average. It was originally introduced by Nosé and developed further by Hoover...

, which correctly generates trajectories consistent with a canonical ensemble.