.. index:: fix nvt/sllod
.. index:: fix nvt/sllod/intel
.. index:: fix nvt/sllod/omp
.. index:: fix nvt/sllod/kk

fix nvt/sllod command
=====================

Accelerator Variants: *nvt/sllod/intel*, *nvt/sllod/omp*, *nvt/sllod/kk*

Syntax
""""""

.. code-block:: LAMMPS

   fix ID group-ID nvt/sllod keyword value ...

* ID, group-ID are documented in :doc:`fix <fix>` command
* nvt/sllod = style name of this fix command
* zero or more keyword/value pairs may be appended

  .. parsed-literal::

    keyword = *psllod* or *peculiar* or *kick* or *integrator*
      *psllod* value = *no* or *yes* = use SLLOD or p-SLLOD variant, respectively
      *peculiar* value = *no* or *yes* = store velocity in the lab frame or peculiar frame, respectively
      *kick* value = *no* or *yes* = whether to superimpose streaming velocity
      *integrator* value = *reversible* or *legacy*
        reversible = use reversible integration scheme
        legacy = use old integration scheme (see below for details)


* additional thermostat related keyword/value pairs from the :doc:`fix nvt <fix_nh>`
  command can be appended

Examples
""""""""

.. code-block:: LAMMPS

   fix 1 all nvt/sllod temp 300.0 300.0 100.0
   fix 1 all nvt/sllod temp 300.0 300.0 100.0 drag 0.2

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

Perform constant NVT integration to update positions and velocities
each timestep for atoms in the group using a Nose/Hoover temperature
thermostat.  V is volume; T is temperature.  This creates a system
trajectory consistent with the canonical ensemble.

This thermostat is used for a simulation box that is changing size
and/or shape, for example in a non-equilibrium MD (NEMD) simulation.
The size/shape change is induced by use of the :doc:`fix deform
<fix_deform>` command, so each point in the simulation box can be
thought of as having a "streaming" velocity.  This position-dependent
streaming velocity is subtracted from each atom's actual velocity to
yield a thermal velocity which is used for temperature computation and
thermostatting.  For example, if the box is being sheared in x,
relative to y, then points at the bottom of the box (low y) have a
small x velocity, while points at the top of the box (hi y) have a
large x velocity.  These velocities do not contribute to the thermal
"temperature" of the atom.

.. note::

   :doc:`Fix deform <fix_deform>` has an option for remapping either
   atom coordinates or velocities to the changing simulation box.  To use
   fix nvt/sllod, fix deform should NOT remap atom positions, because fix
   nvt/sllod adjusts the atom positions and velocities to create a
   velocity profile that matches the changing box size/shape.  For *peculiar*
   = *no*, fix deform SHOULD remap atom velocities when atoms cross periodic
   boundaries since that is consistent with maintaining the velocity profile
   created by fix nvt/sllod.  For *peculiar* = *yes*, fix deform SHOULD NOT
   remap velocities.  LAMMPS will give an error if this setting is not
   consistent.

The SLLOD equations of motion, originally proposed by Hoover and Ladd
(see :ref:`(Evans and Morriss) <Evans3>`), were proven to be equivalent
to Newton's equations of motion for shear flow by :ref:`(Evans and
Morriss) <Evans3>`. They were later shown to generate the desired
velocity gradient and the correct production of work by stresses for all
forms of homogeneous flow by :ref:`(Daivis and Todd) <Daivis>`.

.. versionchanged:: 8Feb2023

For the default (*psllod* = *no*), the LAMMPS implementation adheres to
the standard SLLOD equations of motion, as defined by :ref:`(Evans and
Morriss) <Evans3>`.  The option *psllod* = *yes* invokes the slightly
different SLLOD variant first introduced by :ref:`(Tuckerman et al.)
<Tuckerman>` as g-SLLOD and later by :ref:`(Edwards) <Edwards>` as
p-SLLOD.  In all cases, the equations of motion are coupled to a
Nose/Hoover chain thermostat in a velocity Verlet formulation, closely
following the implementation used for the :doc:`fix nvt <fix_nh>`
command.

.. note::

   A recent (2017) book by :ref:`(Todd and Daivis) <Todd-sllod>`
   discusses use of the SLLOD method and non-equilibrium MD (NEMD)
   thermostatting generally, for both simple and complex fluids,
   e.g. molecular systems.  The latter can be tricky to do correctly.

.. versionchanged:: 11Feb2026

With *integrator* = *reversible* (the default), the numerical integration
scheme closely follows the one described by :ref:`(Sanderson and Searles) <Sanderson>`,
and has been validated to produce work equal to the expected analytical
value and thereby preserve a conserved quantity. With *integrator* = *legacy*
(the behavior of previous LAMMPS versions), this quantity is not precisely
conserved, and stresses may be slightly too high under high flow rates.

For SLLOD simulations with a constant flow tensor, e.g. for calculating viscosity,
:doc:`fix deform <fix_deform>` should be used with the *trate* style for x/y/z
deformation and either the *erate* or *erate/rescale* style for xy/xz/yz.
For mixed flows, *erate/rescale* is required to maintain a constant flow tensor,
and LAMMPS will issue a warning in such cases. These warnings can be safely
ignored if using fix nvt/sllod only to adjust the system size before an
equilibration step.

The *peculiar* flag specifies whether velocity should be stored
in the peculiar frame of reference (i.e. relative to the flow),
or in the laboratory frame.
With *peculiar* = *no* (the default), velocity is stored in the
lab-frame, and will include the streaming component due to
the flow.  This is needed for calculating properties like angular
velocity, but makes the SLLOD equations of motion more difficult
to integrate and can be less performant.  With *peculiar* = *yes*,
the streaming component is NOT stored, so the velocities reported
by LAMMPS are the ones relative to the streaming velocity.  If
lab-frame velocities are not required, storing velocity in the
peculiar frame should generally give the same results with
better performance.

A key aspect of the SLLOD algorithm is that when the flow is
"turned on", particles receive an initial "kick" to their momentum
as viewed from the lab-frame, equivalent to superimposing the
streaming velocity.  This reduces the time required to reach a
steady state, and is required to preserve connections with response
theory.  This "kick" can be applied manually using the :doc:`velocity <velocity>`
command, but care must be taken to ensure velocities are compatible with
the box deformation, which requires treating the effective origin
for elongational flows as the center of the box (ignoring tilt factors),
while using the lower box corner as the origin for shear flows.
Instead, to apply the kick automatically when :doc:`run <run>` or
another similar command is next called, set *kick* = *yes* (the default
when *peculiar* = *no*).  The kick will only be applied ONCE.  If
another kick is required (e.g. if changing parameters of
:doc:`fix deform <fix_deform>`), it can be queued up by using the
:doc:`fix_modify <fix_modify>` command. Note, the kick will be
applied even when using :code:`run 0`, which can be useful to
first remove the current streaming velocity and then apply a
new one. For example:

.. code-block:: LAMMPS

   fix 1 all deform 0 xy erate 0.5 remap v
   fix 2 all nvt/sllod temp 1 1 0.1 peculiar no kick yes
   run 100    # Streaming velocity superimposed here
   # Remove current streaming velocity
   unfix 1
   fix 1 all deform 0 xy erate -0.5 remap v
   fix_modify 2 kick yes
   run 0
   # Continue with new streaming velocity
   unfix 1
   fix 1 all deform 0 xy erate 1.0 remap v
   fix_modify 2 kick yes
   run 100

If velocity is stored in the peculiar frame (*peculiar* = *yes*),
then the *kick* flag is ignored and the same behavior as above
can be achieved with

.. code-block:: LAMMPS

   fix 1 all deform 0 xy erate 0.5 remap v
   fix 2 all nvt/sllod temp 1 1 0.1 peculiar yes
   run 100
   # Switch to new deformation rate
   unfix 1
   fix 1 all deform 0 xy erate 1.0 remap v
   run 100

.. note::

   Some :doc:`fix deform <fix_deform>` styles like *final*, *scale*,
   *vel* and *delta* set the deformation rate to zero when "run 0" is
   called, in which case no kick will be applied for those components
   of the flow. If a kick is desired in such cases, it is recommended
   to initialize fix nvt/sllod with "kick no", and then set "kick yes"
   using :doc:`fix_modify <fix_modify>` immediately before the next
   :doc:`run <run>` command with non-zero length.
   Similarly, the *volume*, *wiggle* and *variable* styles do not
   set a deformation rate during run initialization and are therefore
   not compatible with the "kick yes" option.

Additional parameters affecting the thermostat are specified by
keywords and values documented with the :doc:`fix nvt <fix_nh>`
command.  See, for example, discussion of the *temp* and *drag*
keywords.

This fix computes a temperature each timestep.  To do this, the fix
creates its own compute of style "temp" (if *peculiar* = *yes*) or
"temp/deform" (if *peculiar* = *no*), as if this command had been
issued:

.. code-block:: LAMMPS

   compute fix-ID_temp group-ID temp          # if peculiar = yes
   compute fix-ID_temp group-ID temp/deform   # if peculiar = no

See the :doc:`compute temp/deform <compute_temp_deform>` command for
details.  Note that the ID of the new compute is the fix-ID +
underscore + "temp", and the group for the new compute is the same as
the fix group.

Note that this is NOT the compute used by thermodynamic output (see
the :doc:`thermo_style <thermo_style>` command) with ID =
*thermo_temp*.  This means you can change the attributes of this fix's
temperature (e.g. its degrees-of-freedom) via the :doc:`compute_modify
<compute_modify>` command or print this temperature during
thermodynamic output via the :doc:`thermo_style custom <thermo_style>`
command using the appropriate compute-ID.  It also means that changing
attributes of *thermo_temp* will have no effect on this fix.

Like other fixes that perform thermostatting, this fix can be used
with :doc:`compute commands <compute>` that remove a "bias" from the
atom velocities.  E.g. to apply the thermostat only to atoms within a
spatial :doc:`region <region>`, or to remove the center-of-mass
velocity from a group of atoms, or to remove the x-component of
velocity from the calculation.

This is not done by default, but only if the :doc:`fix_modify
<fix_modify>` command is used to assign a temperature compute to this
fix that includes such a bias term.  See the doc pages for individual
:doc:`compute temp commands <compute>` to determine which ones include
a bias.  In this case, if *integrator* = *legacy* or *integrator* =
*reversible* and *peculiar* = *yes*, the thermostat works in the
following manner: bias is removed from each atom, thermostatting is
performed on the remaining thermal degrees of freedom, and the bias
is added back in.  If *integrator* = *reversible* and *peculiar* = *no*
the temperature compute MUST be of type :doc:`compute temp/deform <compute_temp_deform>`,
but it may use a user-specified internal temperature compute to achieve
the same effect.

If *integrator* = *reversible*, no bias is removed when applying
SLLOD to atom velocities when *peculiar* = *yes*, and only the
bias due to box deformation is removed when *peculiar* = *no*.
If *integrator* = *legacy*, all bias components (box deformation plus
any bias from the internal temperature compute of compute temp/deform)
are removed before applying SLLOD to the velocities.

----------

.. include:: accel_styles.rst

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

This fix writes the state of the Nose/Hoover thermostat to
:doc:`binary restart files <restart>`.  Similarly, it stores whether
or not the velocity kick has been applied so that it is not applied
a second time after a restart.  See the :doc:`read_restart
<read_restart>` command for info on how to re-specify a fix in an
input script that reads a restart file, so that the operation of the
fix continues in an uninterrupted fashion.

The :doc:`fix_modify <fix_modify>` *temp* option is supported by this
fix.  You can use it to assign a :doc:`compute <compute>` you have
defined to this fix which will be used in its thermostatting
procedure.  The *kick* option is also supported as described above.

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.  Note, this does NOT include the work done to
drive the flow, so those values are expected to change with time.
Details of the expected rate of change in *econserve* are discussed
in :ref:`(Sanderson and Searles) <Sanderson>`.

This fix computes the same global scalar and global vector of
quantities as does the :doc:`fix nvt <fix_nh>` command.

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
""""""""""""

This fix works best without Nose-Hoover chain thermostats, i.e. using
*tchain* = 1.  Setting *tchain* to larger values can result in poor
equilibration.

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

:doc:`fix nve <fix_nve>`, :doc:`fix nvt <fix_nh>`, :doc:`fix temp/rescale <fix_temp_rescale>`, :doc:`fix langevin <fix_langevin>`,
:doc:`fix_modify <fix_modify>`, :doc:`compute temp/deform <compute_temp_deform>`

Default
"""""""

Same as :doc:`fix nvt <fix_nh>`, except *tchain* = 1, *psllod* = *no*,
*peculiar* = *no*, *kick* = *yes*, *integrator* = *reversible*.

----------

.. _Evans3:

**(Evans and Morriss)** Evans and Morriss, Phys Rev A, 30, 1528 (1984).

.. _Daivis:

**(Daivis and Todd)** Daivis and Todd, J Chem Phys, 124, 194103 (2006).

.. _Todd-sllod:

**(Todd and Daivis)** Todd and Daivis, Nonequilibrium Molecular Dynamics (book),
Cambridge University Press, (2017) https://doi.org/10.1017/9781139017848.

.. _Tuckerman:

**(Tuckerman et al.)** Tuckerman, Mundy, Balasubramanian, and Klein, J Chem Phys 106, 5615 (1997).

.. _Edwards:

**(Edwards)** Edwards, Baig, and Keffer, J Chem Phys 124, 194104 (2006).

.. _Sanderson:

**(Sanderson and Searles)** Sanderson and Searles, arXiv preprint arXiv\:2512.01318, (2025) https://doi.org/10.48550/arXiv.2512.01318.

