fix grem command

Syntax

fix ID group-ID grem lambda eta H0 thermostat-ID

• ID, group-ID are documented in fix command
• grem = style name of this fix command
• lambda = intercept parameter of linear effective temperature function
• eta = slope parameter of linear effective temperature function
• H0 = shift parameter of linear effective temperature function
• thermostat-ID = ID of Nose-Hoover thermostat or barostat used in simulation

Examples

fix             fxgREM all grem 400 -0.01 -30000 fxnpt
thermo_modify   press fxgREM_press

fix             fxgREM all grem 502 -0.15 -80000 fxnvt


Description

This fix implements the molecular dynamics version of the generalized replica exchange method (gREM) originally developed by (Kim), which uses non-Boltzmann ensembles to sample over first order phase transitions. The is done by defining replicas with an enthalpy dependent effective temperature

with eta negative and steep enough to only intersect the characteristic microcanonical temperature (Ts) of the system once, ensuring a unimodal enthalpy distribution in that replica. Lambda is the intercept and effects the generalized ensemble similar to how temperature effects a Boltzmann ensemble. H0 is a reference enthalpy, and is typically set as the lowest desired sampled enthalpy. Further explanation can be found in our recent papers (Malolepsza).

This fix requires a Nose-Hoover thermostat fix reference passed to the grem as thermostat-ID. Two distinct temperatures exist in this generalized ensemble, the effective temperature defined above, and a kinetic temperature that controls the velocity distribution of particles as usual. Either constant volume or constant pressure algorithms can be used.

The fix enforces a generalized ensemble in a single replica only. Typically, this ideaology is combined with replica exchange with replicas differing by lambda only for simplicity, but this is not required. A multi-replica simulation can be run within the LAMMPS environment using the temper/grem command. This utilizes LAMMPS partition mode and requires the number of available processors be on the order of the number of desired replicas. A 100-replica simulation would require at least 100 processors (1 per world at minimum). If a many replicas are needed on a small number of processors, multi-replica runs can be run outside of LAMMPS. An example of this can be found in examples/USER/misc/grem and has no limit on the number of replicas per processor. However, this is very inefficient and error prone and should be avoided if possible.

In general, defining the generalized ensembles is unique for every system. When starting a many-replica simulation without any knowledge of the underlying microcanonical temperature, there are several tricks we have utilized to optimize the process. Choosing a less-steep eta yields broader distributions, requiring fewer replicas to map the microcanonical temperature. While this likely struggles from the same sampling problems gREM was built to avoid, it provides quick insight to Ts. Initially using an evenly-spaced lambda distribution identifies regions where small changes in enthalpy lead to large temperature changes. Replicas are easily added where needed.

Restart, fix_modify, output, run start/stop, minimize info: