Added basic documentation for grem fix

\documentclass[12pt]{article}

\begin{document}

$$

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

$$

\end{document}

 No newline at end of file

"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c

:link(lws,http://lammps.sandia.gov)

:link(ld,Manual.html)

:link(lc,Section_commands.html#comm)

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fix grem command :h3

[Syntax:]

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

ID, group-ID are documented in "fix"_fix.html 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 thermostat 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 generlized replica 

exchange method (gREM) originally developed by "(Kim)"_#Kim,

which uses non-Boltzmann ensembles to sample over first

order phase transitions.

The is done by defining replicas with an effective temperature

:c,image(Eqs/fix_grem.jpg)

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 simliar 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)"_#Malolepsza.

This fix requires a thermostat, with ID passed to fix_grem

by {thermostat-ID}. Two distinct temperatures exist in this

generlized 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, different replicas only differ by {lambda}

for simplicity, but this is not necessary. Multi-replica 

runs need to be run outside of LAMMPS. An example of this 

can be found in examples/USER/misc/grem .

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 optimze 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} distribtuion identifies

regions where small changes in enthalpy lead to large temperature

changes. Replicas are easily added where needed. 

:line

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

No information about this fix is written to "binary restart

files"_restart.html.

The "thermo_modify"_thermo_modify.html {press} option is supported

by this fix to add the rescaled kinetic pressure as part of 

"thermodynamic output"_thermo_style.html.

[Restrictions:]

This fix is part of the USER-MISC package. It is only enabled if 

LAMMPS was built with that package. See the "Making 

LAMMPS"_Section_start.html#start_3 section for more info.

[Related commands:]

"fix_nh"_fix_nh.html

"thermo_modify"_thermo_modify.html

[Default:] none

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:link(Kim)

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

:link(Malolepsza)

[(Brooks)] Malolepsza, Secor, Keyes, J. Phys. Chem. B. 119 (42), 

13379-13384 (2015).