# fix grem command

## Syntax

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

-   ID, group-ID are documented in [fix](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

``` LAMMPS
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)](Kim2010),
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)](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](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](restart).

The [thermo_modify](thermo_modify) *press* option is supported by this
fix to add the rescaled kinetic pressure as part of [thermodynamic
output](thermo_style).

This fix computes a global scalar which can be accessed by various
[output commands](Howto_output). 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](Build_package) page
for more info.

## Related commands

[temper/grem](temper_grem), [fix nvt](fix_nh), [fix npt](fix_nh),
[thermo_modify](thermo_modify)

## Default

none

------------------------------------------------------------------------

::: {#Kim2010}
**(Kim)** Kim, Keyes, Straub, J Chem. Phys, 132, 224107 (2010).
:::

::: {#Malolepsza}
**(Malolepsza)** Malolepsza, Secor, Keyes, J Phys Chem B 119 (42),
13379-13384 (2015).
:::