ThermodynamicQuantities

class hoomd.md.compute.ThermodynamicQuantities(filter)

Bases: Compute

Compute thermodynamic properties of a subset of the system.

Parameters:

filter (hoomd.filter) – Particle filter to compute thermodynamic properties for.

ThermodynamicQuantities acts on a subset of particles in the system and calculates thermodynamic properties of those particles. Add a ThermodynamicQuantities instance to a logger to save these quantities to a file, see hoomd.logging.Logger for more details.

Note

For compatibility with hoomd.md.constrain.Rigid, ThermodynamicQuantities performs all sums $\sum_{i \in \mathrm{filter}}$ over free particles and rigid body centers - ignoring constituent particles to avoid double counting.

Examples:

f = filter.Type("A")
compute.ThermodynamicQuantities(filter=f)

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Members inherited from AutotunedObject:

property kernel_parameters

Kernel parameters. Read more...

property is_tuning_complete

Check if kernel parameter tuning is complete. Read more...

tune_kernel_parameters()

Start tuning kernel parameters. Read more...

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Members defined in ThermodynamicQuantities:

property degrees_of_freedom

Number of degrees of freedom in the subset $N_{\mathrm{dof}}$.

$$N_\mathrm{dof} = N_\mathrm{dof, translational} + N_\mathrm{dof, rotational}$$

See also

hoomd.State.update_group_dof describes when $N_{\mathrm{dof}}$ is updated.

(Loggable: category=”scalar”)

property kinetic_energy

Total kinetic energy $K$ of the subset $[\mathrm{energy}]$.

$$K = K_\mathrm{rotational} + K_\mathrm{translational}$$

(Loggable: category=”scalar”)

property kinetic_temperature

Instantaneous thermal energy $kT_k$ of the subset $[\mathrm{energy}]$.

$$kT_k = 2 \cdot \frac{K}{N_{\mathrm{dof}}}$$

(Loggable: category=”scalar”)

property num_particles

Number of particles $N$ in the subset.

(Loggable: category=”scalar”)

property potential_energy

Potential energy $U$ that the subset contributes to the system $[\mathrm{energy}]$.

$$U = U_{\mathrm{net},\mathrm{additional}} + \sum_{i \in \mathrm{filter}} U_{\mathrm{net},i},$$

where the net energy terms are computed by hoomd.md.Integrator over all of the forces in hoomd.md.Integrator.forces.

(Loggable: category=”scalar”)

property pressure

Instantaneous pressure $P$ of the subset $[\mathrm{pressure}]$.

$$P = \frac{ 2 \cdot K_{\mathrm{translational}} + W_\mathrm{isotropic} }{D \cdot V},$$

where $D$ is the dimensionality of the system, $V$ is the volume of the simulation box (or area in 2D), and $W_\mathrm{isotropic}$ is the isotropic virial:

W_\mathrm{isotropic} = & \left( W_{\mathrm{net},\mathrm{additional}}^{xx} + W_{\mathrm{net},\mathrm{additional}}^{yy} + W_{\mathrm{net},\mathrm{additional}}^{zz} \right) \\ + & \sum_{i \in \mathrm{filter}} \left( W_\mathrm{{net},i}^{xx} + W_\mathrm{{net},i}^{yy} + W_\mathrm{{net},i}^{zz} \right)

where the net virial terms are computed by hoomd.md.Integrator over all of the forces in hoomd.md.Integrator.forces and $W^{zz}=0$ in 2D simulations.

(Loggable: category=”scalar”)

property pressure_tensor

Instantaneous pressure tensor of the subset $[\mathrm{pressure}]$.

The six components of the pressure tensor are given in the order: ($P^{xx}$, $P^{xy}$, $P^{xz}$, $P^{yy}$, $P^{yz}$, $P^{zz}$):

$$P^{kl} = \frac{1}{V} \left( W_{\mathrm{net},\mathrm{additional}}^{kl} + \sum_{i \in \mathrm{filter}} m_i \cdot v_i^k \cdot v_i^l + W_{\mathrm{net},i}^{kl} \right),$$

where the net virial terms are computed by hoomd.md.Integrator over all of the forces in hoomd.md.Integrator.forces, $v_i^k$ is the k-th component of the velocity of particle $i$ and $V$ is the total simulation box volume (or area in 2D).

(Loggable: category=”sequence”)

property rotational_degrees_of_freedom

Number of rotational degrees of freedom in the subset $N_\mathrm{dof, rotational}$.

Integration methods (hoomd.md.methods) determine the number of degrees of freedom they give to each particle. Each integration method operates on a subset of the system $\mathrm{filter}_m$ that may be distinct from the subset from the subset given to ThermodynamicQuantities.

When hoomd.md.Integrator.integrate_rotational_dof is False, $N_\mathrm{dof, rotational} = 0$. When it is True, the given degrees of freedom depend on the dimensionality of the system.

In 2D:

$$N_\mathrm{dof, rotational} = \sum_{m \in \mathrm{methods}} \; \sum_{i \in \mathrm{filter} \cup \mathrm{filter}_m} \left[ I_{z,i} > 0 \right]$$

where $I$ is the particles’s moment of inertia.

In 3D:

$$N_\mathrm{dof, rotational} = \sum_{m \in \mathrm{methods}} \; \sum_{i \in \mathrm{filter} \cup \mathrm{filter}_m} \left[ I_{x,i} > 0 \right] + \left[ I_{y,i} > 0 \right] + \left[ I_{z,i} > 0 \right]$$

See also

hoomd.State.update_group_dof describes when $N_{\mathrm{dof, rotational}}$ is updated.

(Loggable: category=”scalar”)

property rotational_kinetic_energy

Rotational kinetic energy $K_\mathrm{rotational}$ of the subset $[\mathrm{energy}]$.

$$K_\mathrm{rotational,d} = \frac{1}{2} \sum_{i \in \mathrm{filter}} \begin{cases} \frac{L_{d,i}^2}{I_{d,i}} & I^d_i > 0 \\ 0 & I^d_i = 0 \end{cases} K_\mathrm{rotational} = K_\mathrm{rotational,x} + K_\mathrm{rotational,y} + K_\mathrm{rotational,z}$$

$I$ is the moment of inertia and $L$ is the angular momentum in the (diagonal) reference frame of the particle.

(Loggable: category=”scalar”)

property translational_degrees_of_freedom

Number of translational degrees of freedom in the subset $N_{\mathrm{dof, translational}}$.

When using a single integration method on all particles that is momentum conserving, the center of mass motion is conserved and the number of translational degrees of freedom is:

$$N_\mathrm{dof, translational} = DN - D\frac{N}{N_\mathrm{particles}} - N_\mathrm{constraints}(\mathrm{filter})$$

where $D$ is the dimensionality of the system and $N_\mathrm{constraints}(\mathrm{filter})$ is the number of degrees of freedom removed by constraints (hoomd.md.constrain) in the subset. The fraction $\frac{N}{N_\mathrm{particles}}$ distributes the momentum conservation constraint evenly when ThermodynamicQuantities is applied to multiple subsets.

Note

When using rigid bodies (hoomd.md.constrain.Rigid), $N$ is the number of rigid body centers plus free particles selected by the filter and $N_\mathrm{particles}$ is total number of rigid body centers plus free particles in the whole system.

When hoomd.md.Integrator.rigid is not set, $N$ is the total number of particles selected by the filter and $N_\mathrm{particles}$ is the total number of particles in the system, regardless of their body value.

When using multiple integration methods, a single integration method on fewer than all particles, or a single integration method that is not momentum conserving, hoomd.md.Integrator assumes that linear momentum is not conserved and counts the center of mass motion in the degrees of freedom:

$$N_{\mathrm{dof, translational}} = DN - N_\mathrm{constraints}(\mathrm{filter})$$

(Loggable: category=”scalar”)

property translational_kinetic_energy

Translational kinetic energy $K_{\mathrm{translational}}$ of the subset $[\mathrm{energy}]$.

$$K_\mathrm{translational} = \frac{1}{2} \sum_{i \in \mathrm{filter}} m_i v_i^2$$

(Loggable: category=”scalar”)

property volume

Volume $V$ of the simulation box (area in 2D) $[\mathrm{length}^{D}]$.

(Loggable: category=”scalar”)