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# 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

$T_{eff} = \lambda + \eta (H - H_0)$

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. $$H_0$$ 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 ideology 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 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/PACKAGES/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¶

No information about this fix is written to binary restart files.

The thermo_modify press option is supported by this fix to add the rescaled kinetic pressure as part of thermodynamic output.

This fix computes a global scalar which can be accessed by various output commands. The scalar is the effective temperature $$T_{eff}$$. The scalar value calculated by this fix is “intensive”.

## Restrictions¶

This fix is part of the REPLICA package. It is only enabled if LAMMPS was built with that package. See the Build package page for more info.

## Default¶

none

(Kim) Kim, Keyes, Straub, J Chem. Phys, 132, 224107 (2010).

(Malolepsza) Malolepsza, Secor, Keyes, J Phys Chem B 119 (42), 13379-13384 (2015).