# compute pressure command¶

## Syntax¶

compute ID group-ID pressure temp-ID keyword ...

• ID, group-ID are documented in compute command

• pressure = style name of this compute command

• temp-ID = ID of compute that calculates temperature, can be NULL if not needed

• zero or more keywords may be appended

• keyword = ke or pair or bond or angle or dihedral or improper or kspace or fix or virial or pair/hybrid

## Examples¶

compute 1 all pressure thermo_temp
compute 1 all pressure NULL pair bond
compute 1 all pressure NULL pair/hybrid lj/cut


## Description¶

Define a computation that calculates the pressure of the entire system of atoms. The specified group must be “all”. See the compute stress/atom command if you want per-atom pressure (stress). These per-atom values could be summed for a group of atoms via the compute reduce command.

The pressure is computed by the formula

$P = \frac{N k_B T}{V} + \frac{\sum_{i}^{N'} r_i \bullet f_i}{dV}$

where N is the number of atoms in the system (see discussion of DOF below), $$k_B$$ is the Boltzmann constant, T is the temperature, d is the dimensionality of the system (2 or 3 for 2d/3d), and V is the system volume (or area in 2d). The second term is the virial, equal to -dU/dV, computed for all pairwise as well as 2-body, 3-body, 4-body, many-body, and long-range interactions, where $$r_i$$ and $$f_i$$ are the position and force vector of atom i, and the black dot indicates a dot product. This is computed in parallel for each sub-domain and then summed over all parallel processes. Thus N’ necessarily includes atoms from neighboring sub-domains (so-called ghost atoms) and the position and force vectors of ghost atoms are thus included in the summation. Only when running in serial and without periodic boundary conditions is N’ = N = the number of atoms in the system. Fixes that impose constraints (e.g. the fix shake command) may also contribute to the virial term.

A symmetric pressure tensor, stored as a 6-element vector, is also calculated by this compute. The 6 components of the vector are ordered xx, yy, zz, xy, xz, yz. The equation for the I,J components (where I and J = x,y,z) is similar to the above formula, except that the first term uses components of the kinetic energy tensor and the second term uses components of the virial tensor:

$P_{IJ} = \frac{\sum_{k}^{N} m_k v_{k_I} v_{k_J}}{V} + \frac{\sum_{k}^{N'} r_{k_I} f_{k_J}}{V}$

If no extra keywords are listed, the entire equations above are calculated. This includes a kinetic energy (temperature) term and the virial as the sum of pair, bond, angle, dihedral, improper, kspace (long-range), and fix contributions to the force on each atom. If any extra keywords are listed, then only those components are summed to compute temperature or ke and/or the virial. The virial keyword means include all terms except the kinetic energy ke.

The pair/hybrid keyword means to only include contribution from a sub-style in a hybrid or hybrid/overlay pair style.

Details of how LAMMPS computes the virial efficiently for the entire system, including for many-body potentials and accounting for the effects of periodic boundary conditions are discussed in (Thompson).

The temperature and kinetic energy tensor is not calculated by this compute, but rather by the temperature compute specified with the command. If the kinetic energy is not included in the pressure, than the temperature compute is not used and can be specified as NULL. Normally the temperature compute used by compute pressure should calculate the temperature of all atoms for consistency with the virial term, but any compute style that calculates temperature can be used, e.g. one that excludes frozen atoms or other degrees of freedom.

Note that if desired the specified temperature compute can be one that subtracts off a bias to calculate a temperature using only the thermal velocity of the atoms, e.g. by subtracting a background streaming velocity. See the doc pages for individual compute commands to determine which ones include a bias.

Also note that the N in the first formula above is really degrees-of-freedom divided by d = dimensionality, where the DOF value is calculated by the temperature compute. See the various compute temperature styles for details.

A compute of this style with the ID of “thermo_press” is created when LAMMPS starts up, as if this command were in the input script:

compute thermo_press all pressure thermo_temp


where “thermo_temp” is the ID of a similarly defined compute of style “temp”. See the “thermo_style” command for more details.

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 Speed packages doc 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, USER-INTEL, KOKKOS, USER-OMP and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package doc 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 Speed packages doc page for more instructions on how to use the accelerated styles effectively.

## Output info¶

This compute calculates a global scalar (the pressure) and a global vector of length 6 (pressure tensor), which can be accessed by indices 1-6. These values can be used by any command that uses global scalar or vector values from a compute as input. See the Howto output doc page for an overview of LAMMPS output options.

The ordering of values in the symmetric pressure tensor is as follows: pxx, pyy, pzz, pxy, pxz, pyz.

The scalar and vector values calculated by this compute are “intensive”. The scalar and vector values will be in pressure units.

none

## Default¶

none

(Thompson) Thompson, Plimpton, Mattson, J Chem Phys, 131, 154107 (2009).