.. index:: fix gle

fix gle command
===============

Syntax
""""""

.. code-block:: LAMMPS

   fix ID id-group gle Ns Tstart Tstop seed Amatrix [noneq Cmatrix] [every stride]

* ID, group-ID are documented in :doc:`fix <fix>` command
* gle = style name of this fix command
* Ns = number of additional fictitious momenta
* Tstart, Tstop = temperature ramp during the run
* Amatrix = file to read the drift matrix A from
* seed = random number seed to use for generating noise (positive integer)
* zero or more keyword/value pairs may be appended

  .. parsed-literal::

       keyword = *noneq* or *every*
         *noneq* Cmatrix  = file to read the non-equilibrium covariance matrix from
         *every* stride   = apply the GLE once every time steps. Reduces the accuracy
             of the integration of the GLE, but has \*no effect\* on the accuracy of equilibrium
             sampling. It might change sampling properties when used together with *noneq*\ .

Examples
""""""""

.. code-block:: LAMMPS

   fix 3 boundary gle 6 300 300 31415 smart.A
   fix 1 all gle 6 300 300 31415 qt-300k.A noneq qt-300k.C

Description
"""""""""""

Apply a Generalized Langevin Equation (GLE) thermostat as described
in :ref:`(Ceriotti) <Ceriotti>`. The formalism allows one to obtain a number
of different effects ranging from efficient sampling of all
vibrational modes in the system to inexpensive (approximate)
modelling of nuclear quantum effects. Contrary to
:doc:`fix langevin <fix_langevin>`, this fix performs both
thermostatting and evolution of the Hamiltonian equations of motion, so it
should not be used together with :doc:`fix nve <fix_nve>` -- at least not
on the same atom groups.

Each degree of freedom in the thermostatted group is supplemented
with Ns additional degrees of freedom s, and the equations of motion
become

.. parsed-literal::

   dq/dt=p/m
   d(p,s)/dt=(F,0) - A(p,s) + B dW/dt

where F is the physical force, A is the drift matrix (that generalizes
the friction in Langevin dynamics), B is the diffusion term and dW/dt
un-correlated Gaussian random forces. The A matrix couples the physical
(q,p) dynamics with that of the additional degrees of freedom,
and makes it possible to obtain effectively a history-dependent
noise and friction kernel.

The drift matrix should be given as an external file *Afile*,
as a (Ns+1 x Ns+1) matrix in inverse time units. Matrices that are
optimal for a given application and the system of choice can be
obtained from :ref:`(GLE4MD) <GLE4MD>`.

Equilibrium sampling a temperature T is obtained by specifying the
target value as the *Tstart* and *Tstop* arguments, so that the diffusion
matrix that gives canonical sampling for a given A is computed automatically.
However, the GLE framework also allow for non-equilibrium sampling, that
can be used for instance to model inexpensively zero-point energy
effects :ref:`(Ceriotti2) <Ceriotti2>`. This is achieved specifying the *noneq*
keyword followed by the name of the file that contains the static covariance
matrix for the non-equilibrium dynamics.  Please note, that the covariance
matrix is expected to be given in **temperature units**\ .

Since integrating GLE dynamics can be costly when used together with
simple potentials, one can use the *every* optional keyword to
apply the Langevin terms only once every several MD steps, in a
multiple time-step fashion. This should be used with care when doing
non-equilibrium sampling, but should have no effect on equilibrium
averages when using canonical sampling.

The random number *seed* must be a positive integer.  A Marsaglia random
number generator is used.  Each processor uses the input seed to
generate its own unique seed and its own stream of random numbers.
Thus the dynamics of the system will not be identical on two runs on
different numbers of processors.

Note also that the Generalized Langevin Dynamics scheme that is
implemented by the :doc:`fix gld <fix_gld>` scheme is closely related
to the present one. In fact, it should be always possible to cast the
Prony series form of the memory kernel used by GLD into an appropriate
input matrix for :doc:`fix gle <fix_gle>`. While the GLE scheme is more
general, the form used by :doc:`fix gld <fix_gld>` can be more directly
related to the representation of an implicit solvent environment.

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

The instantaneous values of the extended variables are written to
:doc:`binary restart files <restart>`.  Because the state of the
random number generator is not saved in restart files, this means you
cannot do "exact" restarts with this fix, where the simulation
continues on the same as if no restart had taken place. However, in a
statistical sense, a restarted simulation should produce the same
behavior.  Note however that you should use a different seed each time
you restart, otherwise the same sequence of random numbers will be
used each time, which might lead to stochastic synchronization and
subtle artifacts in the sampling.

The cumulative energy change in the system imposed by this fix is
included in the :doc:`thermodynamic output <thermo_style>` keywords
*ecouple* and *econserve*.  See the :doc:`thermo_style <thermo_style>`
doc page for details.

This fix computes a global scalar which can be accessed by various
:doc:`output commands <Howto_output>`.  The scalar is the same
cumulative energy change due to this fix described in the previous
paragraph.  The scalar value calculated by this fix is "extensive".

This fix can ramp its target temperature over multiple runs, using the
*start* and *stop* keywords of the :doc:`run <run>` command.  See the
:doc:`run <run>` command for details of how to do this.

This fix is not invoked during :doc:`energy minimization <minimize>`.

Restrictions
""""""""""""

The GLE thermostat in its current implementation should not be used
with rigid bodies, SHAKE or RATTLE. It is expected that all the
thermostatted degrees of freedom are fully flexible, and the sampled
ensemble will not be correct otherwise.

In order to perform constant-pressure simulations please use
:doc:`fix press/berendsen <fix_press_berendsen>`, rather than
:doc:`fix npt <fix_nh>`, to avoid duplicate integration of the
equations of motion.

This fix is part of the EXTRA-FIX package.  It is only enabled if
LAMMPS was built with that package.  See the :doc:`Build package <Build_package>` page for more info.

Related commands
""""""""""""""""

:doc:`fix nvt <fix_nh>`, :doc:`fix temp/rescale <fix_temp_rescale>`, :doc:`fix viscous <fix_viscous>`, :doc:`fix nvt <fix_nh>`, :doc:`pair_style dpd/tstat <pair_dpd>`, :doc:`fix gld <fix_gld>`

----------

.. _Ceriotti:

**(Ceriotti)** Ceriotti, Bussi and Parrinello, J Chem Theory Comput 6,
1170-80 (2010)

.. _GLE4MD:

**(GLE4MD)** `https://gle4md.org/ <https://gle4md.org/>`_

.. _Ceriotti2:

**(Ceriotti2)** Ceriotti, Bussi and Parrinello, Phys Rev Lett 103,
030603 (2009)
