<p>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.</p>
<p>The drift matrix should be given as an external file <em>Afile</em>,
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 <aclass="reference internal"href="#gle4md"><spanclass="std std-ref">(GLE4MD)</span></a>.</p>
<p>Equilibrium sampling a temperature T is obtained by specifiying the
target value as the <em>Tstart</em> and <em>Tstop</em> 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 <aclass="reference internal"href="#ceriotti2"><spanclass="std std-ref">(Ceriotti2)</span></a>. This is achieved specifying the
<em>noneq</em> keyword followed by the name of the file that contains the
static covariance matrix for the non-equilibrium dynamics.</p>
<p>Since integrating GLE dynamics can be costly when used together with
simple potentials, one can use the <em>every</em> 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.</p>
<p>The random number <em>seed</em> 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.</p>
<p>Note also that the Generalized Langevin Dynamics scheme that is
implemented by the <aclass="reference internal"href="fix_gld.html"><spanclass="doc">fix gld</span></a> 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 <aclass="reference internal"href="#"><spanclass="doc">fix gle</span></a>. While the GLE scheme is more
general, the form used by <aclass="reference internal"href="fix_gld.html"><spanclass="doc">fix gld</span></a> can be more directly
related to the representation of an implicit solvent environment.</p>
<p><strong>Restart, fix_modify, output, run start/stop, minimize info:</strong></p>
<p>The instantaneous values of the extended variables are written to
<aclass="reference internal"href="restart.html"><spanclass="doc">binary restart files</span></a>. 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 artefacts in the sampling.</p>
<p>This fix can ramp its target temperature over multiple runs, using the
<em>start</em> and <em>stop</em> keywords of the <aclass="reference internal"href="run.html"><spanclass="doc">run</span></a> command. See the
<aclass="reference internal"href="run.html"><spanclass="doc">run</span></a> command for details of how to do this.</p>
<p>The <aclass="reference internal"href="fix_modify.html"><spanclass="doc">fix_modify</span></a><em>energy</em> option is supported by this
fix to add the energy change induced by Langevin thermostatting to the
system’s potential energy as part of <aclass="reference internal"href="thermo_style.html"><spanclass="doc">thermodynamic output</span></a>.</p>
<p>This fix computes a global scalar which can be accessed by various
<aclass="reference internal"href="Section_howto.html#howto-15"><spanclass="std std-ref">output commands</span></a>. The scalar is the
cummulative energy change due to this fix. The scalar value
calculated by this fix is “extensive”.</p>
</div>
<divclass="section"id="restrictions">
<h2>Restrictions</h2>
<p>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.</p>
<p>In order to perform constant-pressure simulations please use
<aclass="reference internal"href="fix_press_berendsen.html"><spanclass="doc">fix press/berendsen</span></a>, rather than
<aclass="reference internal"href="fix_nh.html"><spanclass="doc">fix npt</span></a>, to avoid duplicate integration of the
equations of motion.</p>
<p>This fix is part of the USER-MISC package. It is only enabled if LAMMPS
was built with that package. See the <aclass="reference internal"href="Section_start.html#start-3"><spanclass="std std-ref">Making LAMMPS</span></a> section for more info.</p>
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