# fix npt/cauchy command

## Syntax

    fix ID group-ID style_name keyword value ...

-   ID, group-ID are documented in [fix](fix) command

-   style_name = *npt/cauchy*

-   one or more keyword/value pairs may be appended

-   keyword = *temp* or *iso* or *aniso* or *tri* or *x* or *y* or *z*
    or *xy* or *yz* or *xz* or *couple* or *tchain* or *pchain* or *mtk*
    or *tloop* or *ploop* or *nreset* or *drag* or *dilate* or *scalexy*
    or *scaleyz* or *scalexz* or *flip* or *alpha* or *continue* or
    *fixedpoint*

        *temp* values = Tstart Tstop Tdamp
          Tstart,Tstop = external temperature at start/end of run
          Tdamp = temperature damping parameter (time units)
        *iso* or *aniso* or *tri* values = Pstart Pstop Pdamp
          Pstart,Pstop = scalar external pressure at start/end of run (pressure units)
          Pdamp = pressure damping parameter (time units)
        *x* or *y* or *z* or *xy* or *yz* or *xz* values = Pstart Pstop Pdamp
          Pstart,Pstop = external stress tensor component at start/end of run (pressure units)
          Pdamp = stress damping parameter (time units)
        *couple* = *none* or *xyz* or *xy* or *yz* or *xz*
        *tchain* value = N
          N = length of thermostat chain (1 = single thermostat)
        *pchain* values = N
          N length of thermostat chain on barostat (0 = no thermostat)
        *mtk* value = *yes* or *no* = add in MTK adjustment term or not
        *tloop* value = M
          M = number of sub-cycles to perform on thermostat
        *ploop* value = M
          M = number of sub-cycles to perform on barostat thermostat
        *nreset* value = reset reference cell every this many timesteps
        *drag* value = Df
          Df = drag factor added to barostat/thermostat (0.0 = no drag)
        *dilate* value = dilate-group-ID
          dilate-group-ID = only dilate atoms in this group due to barostat volume changes
        *scalexy* value = *yes* or *no* = scale xy with ly
        *scaleyz* value = *yes* or *no* = scale yz with lz
        *scalexz* value = *yes* or *no* = scale xz with lz
        *flip* value = *yes* or *no* = allow or disallow box flips when it becomes highly skewed
        *alpha* value = strength of Cauchy stress control parameter
        *continue* value = *yes* or *no* = whether of not to continue from a previous run
        *fixedpoint* values = x y z
          x,y,z = perform barostat dilation/contraction around this point (distance units)

## Examples

``` LAMMPS
fix 1 water npt/cauchy temp 300.0 300.0 100.0 iso 0.0 0.0 1000.0 alpha 0.001
```

## Description

This command performs time integration on Nose-Hoover style
non-Hamiltonian equations of motion which are designed to generate
positions and velocities sampled from the isothermal-isobaric (npt)
ensembles. This updates the position and velocity for atoms in the group
each timestep and the box dimensions.

The thermostatting and barostatting is achieved by adding some dynamic
variables which are coupled to the particle velocities (thermostatting)
and simulation domain dimensions (barostatting). In addition to basic
thermostatting and barostatting, this fix can also create a chain of
thermostats coupled to the particle thermostat, and another chain of
thermostats coupled to the barostat variables. The barostat can be
coupled to the overall box volume, or to individual dimensions,
including the *xy*, *xz* and *yz* tilt dimensions. The external pressure
of the barostat can be specified as either a scalar pressure (isobaric
ensemble) or as components of a symmetric stress tensor (constant stress
ensemble). When used correctly, the time-averaged temperature and stress
tensor of the particles will match the target values specified by
Tstart/Tstop and Pstart/Pstop.

The equations of motion used are those of Shinoda et al in
[(Shinoda)](nc-Shinoda), which combine the hydrostatic equations of
Martyna, Tobias and Klein in [(Martyna)](nc-Martyna) with the strain
energy proposed by Parrinello and Rahman in
[(Parrinello)](nc-Parrinello). The time integration schemes closely
follow the time-reversible measure-preserving Verlet and rRESPA
integrators derived by Tuckerman et al in [(Tuckerman)](nc-Tuckerman).

------------------------------------------------------------------------

The thermostat parameters are specified using the *temp* keyword. Other
thermostat-related keywords are *tchain*, *tloop* and *drag*, which are
discussed below.

The thermostat is applied to only the translational degrees of freedom
for the particles. The translational degrees of freedom can also have a
bias velocity removed before thermostatting takes place; see the
description below. The desired temperature at each timestep is a ramped
value during the run from *Tstart* to *Tstop*. The *Tdamp* parameter is
specified in time units and determines how rapidly the temperature is
relaxed. For example, a value of 10.0 means to relax the temperature in
a timespan of (roughly) 10 time units (e.g. $\tau$ or fs or ps - see the
[units](units) command). The atoms in the fix group are the only ones
whose velocities and positions are updated by the velocity/position
update portion of the integration.

:::: note
::: title
Note
:::

A Nose-Hoover thermostat will not work well for arbitrary values of
*Tdamp*. If *Tdamp* is too small, the temperature can fluctuate wildly;
if it is too large, the temperature will take a very long time to
equilibrate. A good choice for many models is a *Tdamp* of around 100
timesteps. Note that this is NOT the same as 100 time units for most
[units](units) settings.
::::

------------------------------------------------------------------------

The barostat parameters are specified using one or more of the *iso*,
*aniso*, *tri*, *x*, *y*, *z*, *xy*, *xz*, *yz*, and *couple* keywords.
These keywords give you the ability to specify all 6 components of an
external stress tensor, and to couple various of these components
together so that the dimensions they represent are varied together
during a constant-pressure simulation.

Other barostat-related keywords are *pchain*, *mtk*, *ploop*, *nreset*,
*drag*, and *dilate*, which are discussed below.

Orthogonal simulation boxes have 3 adjustable dimensions (x,y,z).
Triclinic (non-orthogonal) simulation boxes have 6 adjustable dimensions
(x,y,z,xy,xz,yz). The [create_box](create_box), [read data](read_data),
and [read_restart](read_restart) commands specify whether the simulation
box is orthogonal or non-orthogonal (triclinic) and explain the meaning
of the xy,xz,yz tilt factors.

The target pressures for each of the 6 components of the stress tensor
can be specified independently via the *x*, *y*, *z*, *xy*, *xz*, *yz*
keywords, which correspond to the 6 simulation box dimensions. For each
component, the external pressure or tensor component at each timestep is
a ramped value during the run from *Pstart* to *Pstop*. If a target
pressure is specified for a component, then the corresponding box
dimension will change during a simulation. For example, if the *y*
keyword is used, the y-box length will change. If the *xy* keyword is
used, the xy tilt factor will change. A box dimension will not change if
that component is not specified, although you have the option to change
that dimension via the [fix deform](fix_deform) command.

Note that in order to use the *xy*, *xz*, or *yz* keywords, the
simulation box must be triclinic, even if its initial tilt factors are
0.0.

For all barostat keywords, the *Pdamp* parameter operates like the
*Tdamp* parameter, determining the time scale on which pressure is
relaxed. For example, a value of 10.0 means to relax the pressure in a
timespan of (roughly) 10 time units (e.g. $\tau$ or fs or ps - see the
[units](units) command).

:::: note
::: title
Note
:::

A Nose-Hoover barostat will not work well for arbitrary values of
*Pdamp*. If *Pdamp* is too small, the pressure and volume can fluctuate
wildly; if it is too large, the pressure will take a very long time to
equilibrate. A good choice for many models is a *Pdamp* of around 1000
timesteps. However, note that *Pdamp* is specified in time units, and
that timesteps are NOT the same as time units for most [units](units)
settings.
::::

Regardless of what atoms are in the fix group (the only atoms which are
time integrated), a global pressure or stress tensor is computed for all
atoms. Similarly, when the size of the simulation box is changed, all
atoms are re-scaled to new positions, unless the keyword *dilate* is
specified with a *dilate-group-ID* for a group that represents a subset
of the atoms. This can be useful, for example, to leave the coordinates
of atoms in a solid substrate unchanged and controlling the pressure of
a surrounding fluid. This option should be used with care, since it can
be unphysical to dilate some atoms and not others, because it can
introduce large, instantaneous displacements between a pair of atoms
(one dilated, one not) that are far from the dilation origin. Also note
that for atoms not in the fix group, a separate time integration fix
like [fix nve](fix_nve) or [fix nvt](fix_nh) can be used on them,
independent of whether they are dilated or not.

------------------------------------------------------------------------

The *couple* keyword allows two or three of the diagonal components of
the pressure tensor to be \"coupled\" together. The value specified with
the keyword determines which are coupled. For example, *xz* means the
*Pxx* and *Pzz* components of the stress tensor are coupled. *Xyz* means
all 3 diagonal components are coupled. Coupling means two things: the
instantaneous stress will be computed as an average of the corresponding
diagonal components, and the coupled box dimensions will be changed
together in lockstep, meaning coupled dimensions will be dilated or
contracted by the same percentage every timestep. The *Pstart*, *Pstop*,
*Pdamp* parameters for any coupled dimensions must be identical. *Couple
xyz* can be used for a 2d simulation; the *z* dimension is simply
ignored.

------------------------------------------------------------------------

The *iso*, *aniso*, and *tri* keywords are simply shortcuts that are
equivalent to specifying several other keywords together.

The keyword *iso* means couple all 3 diagonal components together when
pressure is computed (hydrostatic pressure), and dilate/contract the
dimensions together. Using \"iso Pstart Pstop Pdamp\" is the same as
specifying these 4 keywords:

    x Pstart Pstop Pdamp
    y Pstart Pstop Pdamp
    z Pstart Pstop Pdamp
    couple xyz

The keyword *aniso* means *x*, *y*, and *z* dimensions are controlled
independently using the *Pxx*, *Pyy*, and *Pzz* components of the stress
tensor as the driving forces, and the specified scalar external
pressure. Using \"aniso Pstart Pstop Pdamp\" is the same as specifying
these 4 keywords:

    x Pstart Pstop Pdamp
    y Pstart Pstop Pdamp
    z Pstart Pstop Pdamp
    couple none

The keyword *tri* means *x*, *y*, *z*, *xy*, *xz*, and *yz* dimensions
are controlled independently using their individual stress components as
the driving forces, and the specified scalar pressure as the external
normal stress. Using \"tri Pstart Pstop Pdamp\" is the same as
specifying these 7 keywords:

    x Pstart Pstop Pdamp
    y Pstart Pstop Pdamp
    z Pstart Pstop Pdamp
    xy 0.0 0.0 Pdamp
    yz 0.0 0.0 Pdamp
    xz 0.0 0.0 Pdamp
    couple none

------------------------------------------------------------------------

In some cases (e.g. for solids) the pressure (volume) and/or temperature
of the system can oscillate undesirably when a Nose/Hoover barostat and
thermostat is applied. The optional *drag* keyword will damp these
oscillations, although it alters the Nose/Hoover equations. A value of
0.0 (no drag) leaves the Nose/Hoover formalism unchanged. A non-zero
value adds a drag term; the larger the value specified, the greater the
damping effect. Performing a short run and monitoring the pressure and
temperature is the best way to determine if the drag term is working.
Typically a value between 0.2 to 2.0 is sufficient to damp oscillations
after a few periods. Note that use of the drag keyword will interfere
with energy conservation and will also change the distribution of
positions and velocities so that they do not correspond to the nominal
NVT, NPT, or NPH ensembles.

An alternative way to control initial oscillations is to use chain
thermostats. The keyword *tchain* determines the number of thermostats
in the particle thermostat. A value of 1 corresponds to the original
Nose-Hoover thermostat. The keyword *pchain* specifies the number of
thermostats in the chain thermostatting the barostat degrees of freedom.
A value of 0 corresponds to no thermostatting of the barostat variables.

The *mtk* keyword controls whether or not the correction terms due to
Martyna, Tuckerman, and Klein are included in the equations of motion
[(Martyna)](nc-Martyna). Specifying *no* reproduces the original Hoover
barostat, whose volume probability distribution function differs from
the true NPT and NPH ensembles by a factor of 1/V. Hence using *yes* is
more correct, but in many cases the difference is negligible.

The keyword *tloop* can be used to improve the accuracy of integration
scheme at little extra cost. The initial and final updates of the
thermostat variables are broken up into *tloop* sub-steps, each of
length *dt*/\*tloop\*. This corresponds to using a first-order
Suzuki-Yoshida scheme [(Tuckerman)](nc-Tuckerman). The keyword *ploop*
does the same thing for the barostat thermostat.

The keyword *nreset* controls how often the reference dimensions used to
define the strain energy are reset. If this keyword is not used, or is
given a value of zero, then the reference dimensions are set to those of
the initial simulation domain and are never changed. If the simulation
domain changes significantly during the simulation, then the final
average pressure tensor will differ significantly from the specified
values of the external stress tensor. A value of *nstep* means that
every *nstep* timesteps, the reference dimensions are set to those of
the current simulation domain.

The *scaleyz*, *scalexz*, and *scalexy* keywords control whether or not
the corresponding tilt factors are scaled with the associated box
dimensions when barostatting triclinic periodic cells. The default
values *yes* will turn on scaling, which corresponds to adjusting the
linear dimensions of the cell while preserving its shape. Choosing *no*
ensures that the tilt factors are not scaled with the box dimensions.
See below for restrictions and default values in different situations.
In older versions of LAMMPS, scaling of tilt factors was not performed.
The old behavior can be recovered by setting all three scale keywords to
*no*.

The *flip* keyword allows the tilt factors for a triclinic box to exceed
half the distance of the parallel box length, as discussed below. If the
*flip* value is set to *yes*, the bound is enforced by flipping the box
when it is exceeded. If the *flip* value is set to *no*, the tilt will
continue to change without flipping. Note that if applied stress induces
large deformations (e.g. in a liquid), this means the box shape can tilt
dramatically and LAMMPS will run less efficiently, due to the large
volume of communication needed to acquire ghost atoms around a
processor\'s irregular-shaped subdomain. For extreme values of tilt,
LAMMPS may also lose atoms and generate an error.

The *fixedpoint* keyword specifies the fixed point for barostat volume
changes. By default, it is the center of the box. Whatever point is
chosen will not move during the simulation. For example, if the lower
periodic boundaries pass through (0,0,0), and this point is provided to
*fixedpoint*, then the lower periodic boundaries will remain at (0,0,0),
while the upper periodic boundaries will move twice as far. In all
cases, the particle trajectories are unaffected by the chosen value,
except for a time-dependent constant translation of positions.

------------------------------------------------------------------------

:::: note
::: title
Note
:::

Using a barostat coupled to tilt dimensions *xy*, *xz*, *yz* can
sometimes result in arbitrarily large values of the tilt dimensions,
i.e. a dramatically deformed simulation box. LAMMPS allows the tilt
factors to grow a small amount beyond the normal limit of half the box
length (0.6 times the box length), and then performs a box \"flip\" to
an equivalent periodic cell. See the discussion of the *flip* keyword
above, to allow this bound to be exceeded, if desired.
::::

The flip operation is described in more detail in the page for [fix
deform](fix_deform). Both the barostat dynamics and the atom
trajectories are unaffected by this operation. However, if a tilt factor
is incremented by a large amount (1.5 times the box length) on a single
timestep, LAMMPS can not accommodate this event and will terminate the
simulation with an error. This error typically indicates that there is
something badly wrong with how the simulation was constructed, such as
specifying values of *Pstart* that are too far from the current stress
value, or specifying a timestep that is too large. Triclinic
barostatting should be used with care. This also is true for other
barostat styles, although they tend to be more forgiving of insults. In
particular, it is important to recognize that equilibrium liquids can
not support a shear stress and that equilibrium solids can not support
shear stresses that exceed the yield stress.

One exception to this rule is if the first dimension in the tilt factor
(x for xy) is non-periodic. In that case, the limits on the tilt factor
are not enforced, since flipping the box in that dimension does not
change the atom positions due to non-periodicity. In this mode, if you
tilt the system to extreme angles, the simulation will simply become
inefficient due to the highly skewed simulation box.

:::: note
::: title
Note
:::

Unlike the [fix temp/berendsen](fix_temp_berendsen) command which
performs thermostatting but NO time integration, this fix performs
thermostatting/barostatting AND time integration. Thus you should not
use any other time integration fix, such as [fix nve](fix_nve) on atoms
to which this fix is applied. Likewise, fix npt/cauchy should not
normally be used on atoms that also have their temperature controlled by
another fix - e.g. by [fix langevin](fix_nh) or [fix
temp/rescale](fix_temp_rescale) commands.
::::

See the [Howto thermostat](Howto_thermostat) and [Howto
barostat](Howto_barostat) doc pages for a discussion of different ways
to compute temperature and perform thermostatting and barostatting.

------------------------------------------------------------------------

This fix compute a temperature and pressure each timestep. To do this,
the fix creates its own computes of style \"temp\" and \"pressure\", as
if one of these sets of commands had been issued:

``` LAMMPS
compute fix-ID_temp all temp
compute fix-ID_press all pressure fix-ID_temp
```

The group for both the new temperature and pressure compute is \"all\"
since pressure is computed for the entire system. See the [compute
temp](compute_temp) and [compute pressure](compute_pressure) commands
for details. Note that the IDs of the new computes are the fix-ID +
underscore + \"temp\" or fix_ID + underscore + \"press\".

Note that these are NOT the computes used by thermodynamic output (see
the [thermo_style](thermo_style) command) with ID = *thermo_temp* and
*thermo_press*. This means you can change the attributes of these fix\'s
temperature or pressure via the [compute_modify](compute_modify)
command. Or you can print this temperature or pressure during
thermodynamic output via the [thermo_style custom](thermo_style) command
using the appropriate compute-ID. It also means that changing attributes
of *thermo_temp* or *thermo_press* will have no effect on this fix.

Like other fixes that perform thermostatting, this fix can be used with
[compute commands](compute) that remove a \"bias\" from the atom
velocities. E.g. to apply the thermostat only to atoms within a spatial
[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 [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 [compute
temp commands](compute) to determine which ones include a bias. In this
case, 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.

------------------------------------------------------------------------

This fix can be used with either the *verlet* or *respa*
[integrators](run_style). When using this fix with *respa*, LAMMPS uses
an integrator constructed according to the following factorization of
the Liouville propagator (for two rRESPA levels):

$$\begin{aligned}
\exp \left(\mathrm{i} L \Delta t \right) = & \hat{E}
\exp \left(\mathrm{i} L_{\rm T\textrm{-}baro} \frac{\Delta t}{2} \right)
\exp \left(\mathrm{i} L_{\rm T\textrm{-}part} \frac{\Delta t}{2} \right)
\exp \left(\mathrm{i} L_{\epsilon , 2} \frac{\Delta t}{2} \right)
\exp \left(\mathrm{i} L_{2}^{(2)} \frac{\Delta t}{2} \right) \\
&\times \left[
\exp \left(\mathrm{i} L_{2}^{(1)} \frac{\Delta t}{2n} \right)
\exp \left(\mathrm{i} L_{\epsilon , 1} \frac{\Delta t}{2n} \right)
\exp \left(\mathrm{i} L_1 \frac{\Delta t}{n} \right)
\exp \left(\mathrm{i} L_{\epsilon , 1} \frac{\Delta t}{2n} \right)
\exp \left(\mathrm{i} L_{2}^{(1)} \frac{\Delta t}{2n} \right)
\right]^n \\
&\times
\exp \left(\mathrm{i} L_{2}^{(2)} \frac{\Delta t}{2} \right)
\exp \left(\mathrm{i} L_{\epsilon , 2} \frac{\Delta t}{2} \right)
\exp \left(\mathrm{i} L_{\rm T\textrm{-}part} \frac{\Delta t}{2} \right)
\exp \left(\mathrm{i} L_{\rm T\textrm{-}baro} \frac{\Delta t}{2} \right) \\
&+ \mathcal{O} \left(\Delta t^3 \right)
\end{aligned}$$

This factorization differs somewhat from that of Tuckerman et al, in
that the barostat is only updated at the outermost rRESPA level, whereas
Tuckerman\'s factorization requires splitting the pressure into pieces
corresponding to the forces computed at each rRESPA level. In theory,
the latter method will exhibit better numerical stability. In practice,
because Pdamp is normally chosen to be a large multiple of the outermost
rRESPA timestep, the barostat dynamics are not the limiting factor for
numerical stability. Both factorizations are time-reversible and can be
shown to preserve the phase space measure of the underlying
non-Hamiltonian equations of motion.

:::: note
::: title
Note
:::

Under NPT dynamics, for a system with zero initial total linear
momentum, the total momentum fluctuates close to zero. It may
occasionally undergo brief excursions to non-negligible values, before
returning close to zero. Over long simulations, this has the effect of
causing the center-of-mass to undergo a slow random walk. This can be
mitigated by resetting the momentum at infrequent intervals using the
[fix momentum](fix_momentum) command.
::::

------------------------------------------------------------------------

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

This fix writes the state of all the thermostat and barostat variables
to [binary restart files](restart). See the [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 [fix_modify](fix_modify) *temp* and *press* options are supported by
this fix. You can use them to assign a [compute](compute) you have
defined to this fix which will be used in its thermostatting or
barostatting procedure, as described above. If you do this, note that
the kinetic energy derived from the compute temperature should be
consistent with the virial term computed using all atoms for the
pressure. LAMMPS will warn you if you choose to compute temperature on a
subset of atoms.

:::: note
::: title
Note
:::

If both the *temp* and *press* keywords are used in a single
thermo_modify command (or in two separate commands), then the order in
which the keywords are specified is important. Note that a [pressure
compute](compute_pressure) defines its own temperature compute as an
argument when it is specified. The *temp* keyword will override this
(for the pressure compute being used by fix npt), but only if the *temp*
keyword comes after the *press* keyword. If the *temp* keyword comes
before the *press* keyword, then the new pressure compute specified by
the *press* keyword will be unaffected by the *temp* setting.
::::

The cumulative energy change in the system imposed by this fix, due to
thermostatting and/or barostatting, is included in the [thermodynamic
output](thermo_style) keywords *ecouple* and *econserve*. See the
[thermo_style](thermo_style) page for details.

This fix computes a global scalar which can be accessed by various
[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 also computes a global vector of quantities, which can be
accessed by various [output commands](Howto_output). Rhe vector values
are \"intensive\".

The vector stores internal Nose/Hoover thermostat and barostat
variables. The number and meaning of the vector values depends on which
fix is used and the settings for keywords *tchain* and *pchain*, which
specify the number of Nose/Hoover chains for the thermostat and
barostat. If no thermostatting is done, then *tchain* is 0. If no
barostatting is done, then *pchain* is 0. In the following list,
\"ndof\" is 0, 1, 3, or 6, and is the number of degrees of freedom in
the barostat. Its value is 0 if no barostat is used, else its value is 6
if any off-diagonal stress tensor component is barostatted, else its
value is 1 if *couple xyz* is used or *couple xy* for a 2d simulation,
otherwise its value is 3.

The order of values in the global vector and their meaning is as
follows. The notation means there are tchain values for eta, followed by
tchain for eta_dot, followed by ndof for omega, etc:

-   eta\[tchain\] = particle thermostat displacements (unitless)
-   eta_dot\[tchain\] = particle thermostat velocities (1/time units)
-   omega\[ndof\] = barostat displacements (unitless)
-   omega_dot\[ndof\] = barostat velocities (1/time units)
-   etap\[pchain\] = barostat thermostat displacements (unitless)
-   etap_dot\[pchain\] = barostat thermostat velocities (1/time units)
-   PE_eta\[tchain\] = potential energy of each particle thermostat
    displacement (energy units)
-   KE_eta_dot\[tchain\] = kinetic energy of each particle thermostat
    velocity (energy units)
-   PE_omega\[ndof\] = potential energy of each barostat displacement
    (energy units)
-   KE_omega_dot\[ndof\] = kinetic energy of each barostat velocity
    (energy units)
-   PE_etap\[pchain\] = potential energy of each barostat thermostat
    displacement (energy units)
-   KE_etap_dot\[pchain\] = kinetic energy of each barostat thermostat
    velocity (energy units)
-   PE_strain\[1\] = scalar strain energy (energy units)

This fix can ramp its external temperature and pressure over multiple
runs, using the *start* and *stop* keywords of the [run](run) command.
See the [run](run) command for details of how to do this.

This fix is not invoked during [energy minimization](minimize).

------------------------------------------------------------------------

## Restrictions

This fix is part of the EXTRA-FIX package. It is only enabled if LAMMPS
was built with that package. See the [Build package](Build_package) page
for more info.

*X*, *y*, *z* cannot be barostatted if the associated dimension is not
periodic. *Xy*, *xz*, and *yz* can only be barostatted if the simulation
domain is triclinic and the second dimension in the keyword (\*y\*
dimension in *xy*) is periodic. *Z*, *xz*, and *yz*, cannot be
barostatted for 2D simulations. The [create_box](create_box), [read
data](read_data), and [read_restart](read_restart) commands specify
whether the simulation box is orthogonal or non-orthogonal (triclinic)
and explain the meaning of the xy,xz,yz tilt factors.

For the *temp* keyword, the final Tstop cannot be 0.0 since it would
make the external T = 0.0 at some timestep during the simulation which
is not allowed in the Nose/Hoover formulation.

The *scaleyz yes* and *scalexz yes* keyword/value pairs can not be used
for 2D simulations. *scaleyz yes*, *scalexz yes*, and *scalexy yes*
options can only be used if the second dimension in the keyword is
periodic, and if the tilt factor is not coupled to the barostat via
keywords *tri*, *yz*, *xz*, and *xy*.

The *alpha* keyword modifies the barostat as per Miller et al.
(Miller)\_\"#nc-Miller\" so that the Cauchy stress is controlled.
*alpha* is the non-dimensional parameter, typically set to 0.001 or 0.01
that determines how aggressively the algorithm drives the system towards
the set Cauchy stresses. Larger values of *alpha* will modify the system
more quickly, but can lead to instabilities. Smaller values will lead to
longer convergence time. Since *alpha* also influences how much the
stress fluctuations deviate from the equilibrium fluctuations, it should
be set as small as possible.

A *continue* value of *yes* indicates that the fix is subsequent to a
previous run with the npt/cauchy fix, and the intention is to continue
from the converged stress state at the end of the previous run. This may
be required, for example, when implementing a multi-step
loading/unloading sequence over several fixes.

Setting *alpha* to zero is not permitted. To \"turn off\" the cauchystat
control and thus restore the equilibrium stress fluctuations, two
subsequent fixes should be used. In the first, fix npt/cauchy is used
and the simulation box equilibrates to the correct shape for the desired
stresses. In the second, [fix npt](fix_nh) is used instead which uses
the original Parrinello-Rahman algorithm, but now with the corrected
simulation box shape from using fix npt/cauchy.

This fix can be used with dynamic groups as defined by the
[group](group) command. Likewise it can be used with groups to which
atoms are added or deleted over time, e.g. a deposition simulation.
However, the conservation properties of the thermostat and barostat are
defined for systems with a static set of atoms. You may observe odd
behavior if the atoms in a group vary dramatically over time or the atom
count becomes very small.

## Related commands

[fix nve](fix_nve), [fix_modify](fix_modify), [run_style](run_style)

## Default

The keyword defaults are tchain = 3, pchain = 3, mtk = yes, tloop =
ploop = 1, nreset = 0, drag = 0.0, dilate = all, couple = none,
cauchystat = no, scaleyz = scalexz = scalexy = yes if periodic in second
dimension and not coupled to barostat, otherwise no.

------------------------------------------------------------------------

::: {#nc-Martyna}
**(Martyna)** Martyna, Tobias and Klein, J Chem Phys, 101, 4177 (1994).
:::

::: {#nc-Parrinello}
**(Parrinello)** Parrinello and Rahman, J Appl Phys, 52, 7182 (1981).
:::

::: {#nc-Tuckerman}
**(Tuckerman)** Tuckerman, Alejandre, Lopez-Rendon, Jochim, and Martyna,
J Phys A: Math Gen, 39, 5629 (2006).
:::

::: {#nc-Shinoda}
**(Shinoda)** Shinoda, Shiga, and Mikami, Phys Rev B, 69, 134103 (2004).
:::

::: {#nc-Miller}
**(Miller)** Miller, Tadmor, Gibson, Bernstein and Pavia, J Chem Phys,
144, 184107 (2016).
:::