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# fix nvt/sllod command

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

## Syntax

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

- ID, group-ID are documented in fix command

- nvt/sllod = style name of this fix command

- zero or more keyword/value pairs may be appended

      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 fix nvt command can be appended

## Examples

    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 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

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 (Evans and Morriss)), were proven to be equivalent to Newton’s equations of motion for shear flow by (Evans and Morriss). 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 (Daivis and Todd).

Changed in version 8Feb2023.

For the default (psllod = no), the LAMMPS implementation adheres to the standard SLLOD equations of motion, as defined by (Evans and Morriss). The option psllod = yes invokes the slightly different SLLOD variant first introduced by (Tuckerman et al.) as g-SLLOD and later by (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 fix nvt command.

Note

A recent (2017) book by (Todd and Daivis) 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.

Changed in version 11Feb2026.

With integrator = reversible (the default), the numerical integration scheme closely follows the one described by (Sanderson and Searles), 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, 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 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 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 fix deform), it can be queued up by using the fix_modify command. Note, the kick will be applied even when using `run 0`, which can be useful to first remove the current streaming velocity and then apply a new one. For example:

    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

    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 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 fix_modify immediately before the next 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 fix nvt 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:

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

See the 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 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 compute_modify command or print this temperature during thermodynamic output via the thermo_style custom 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 compute commands that remove a “bias” from the atom velocities. E.g. to apply the thermostat only to atoms within a spatial 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 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 compute temp commands 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 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.

Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed on the Accelerator packages page. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.

These accelerated styles are part of the GPU, INTEL, KOKKOS, OPENMP, and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package page for more info.

You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.

See the Accelerator packages page for more instructions on how to use the accelerated styles effectively.

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

This fix writes the state of the Nose/Hoover thermostat to binary restart files. 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 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 fix_modify temp option is supported by this fix. You can use it to assign a 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 thermodynamic output keywords ecouple and econserve. See the 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 (Sanderson and Searles).

This fix computes the same global scalar and global vector of quantities as does the fix nvt command.

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

This fix is not invoked during energy minimization.

## 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

fix nve, fix nvt, fix temp/rescale, fix langevin, fix_modify, compute temp/deform

## Default

Same as fix nvt, except tchain = 1, psllod = no, peculiar = no, kick = yes, integrator = reversible.

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

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

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

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

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

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