NVE/NVT/NPT/NHT

Below is an overview of the common integration fixes in LAMMPS often referred to by their statistical ensemble abbreviations: NVE, NVT, NPT, and sometimes NHT (Nose-Hoover Thermostat). The acronyms indicate what thermodynamic variables are being held constant (or tightly controlled):

---

1. NVE (Microcanonical Ensemble)

• Acronym:
  • N = Number of particles
  • V = Volume (of the simulation box)
  • E = Energy (total energy, kinetic + potential)
• LAMMPS Command:fix nve \texttt{fix nve}
• Key Idea:
  • The system evolves with no thermostat or barostat (i.e., no energy added or removed).
  • The integrator simply updates positions and velocities using Newton’s equations of motion (Velocity Verlet scheme by default in LAMMPS).
• When to Use:
  • When you want to simulate an isolated system with no temperature or pressure control.
  • Typical for microcanonical ensemble or certain nonequilibrium dynamics where you do not want external coupling.

---

2. NVT (Canonical Ensemble)

• Acronym:
  • N = Number of particles
  • V = Volume (held fixed)
  • T = Temperature (maintained at a target value)
• LAMMPS Command:fix nvt \texttt{fix nvt}
• Key Idea:
  • Uses a thermostat (commonly Nose-Hoover) to regulate the temperature.
  • The volume is constant; no barostat is applied.
  • The total energy of the extended system can fluctuate because the thermostat exchanges energy with the system to maintain the target temperature.
• When to Use:
  • When you want your system to sample the canonical ensemble (constant T, constant V).
  • Typical for equilibration at a given temperature without changing volume.

---

3. NPT (Isothermal-Isobaric Ensemble)

• Acronym:
  • N = Number of particles
  • P = Pressure (maintained at a target value)
  • T = Temperature (maintained at a target value)
• LAMMPS Command:fix npt \texttt{fix npt}
• Key Idea:
  • Combines a thermostat (e.g., Nose-Hoover) and a barostat (e.g., also Nose-Hoover style) so that both temperature and pressure are controlled.
  • The simulation box volume can change to maintain the specified pressure.
  • The total enthalpy of the extended system is conserved, but the system’s volume and total energy can fluctuate.
• When to Use:
  • When you want your system to sample the isothermal-isobaric ensemble (constant T, constant P).
  • Commonly used for equilibrating the system at certain temperature and pressure conditions.

---

4. NHT (Nosé-Hoover Thermostat)

• Acronym / Meaning:
  • NHT is not a standard ensemble label like NVE, NVT, NPT, but rather shorthand for “Nose-Hoover Thermostat.”
  • Strictly speaking, it refers to the type of thermostat used in many LAMMPS fixes (such as fix nvt or the thermostat component of fix npt).
• Where it Appears in LAMMPS:
  • LAMMPS’s fix nvt and fix npt use Nose-Hoover chains for temperature control by default. You might see references to “Nose-Hoover thermostats” or “Nose-Hoover chain thermostats.”
• Summary:
  • “NHT” is not a separate fix in LAMMPS but rather the mathematical approach used under the hood by those fixes.
  • If you see references to “NHT,” it indicates the specific flavor of thermostat (Nose-Hoover).
  • For barostats (pressure control), LAMMPS also uses the extended formalism of Nose-Hoover (or sometimes other methods).

---

Additional Notes

1. fix nph:
   • If you only want to control (or let fluctuate) the pressure while leaving temperature unregulated, you can use fix nph (NPH ensemble).
   • This changes the box volume to maintain pressure, but does not thermostat the system.
2. Implementation Details in LAMMPS:
   • fix nve, fix nvt, fix npt, and fix nph are all time-integration fixes. You typically use one time-integration fix on each group of atoms so you don’t “double integrate” the same atoms.
   • Under the hood, LAMMPS implements Nose-Hoover or other thermostats/barostats by adding extra “thermostat variables” or “barostat variables” to the equations of motion.
3. Choice of Thermostat or Barostat:
   • Nose-Hoover is common, but LAMMPS also supports Langevin (fix langevin) or Berendsen thermostats (fix temp/berendsen), among others.
   • For barostats, in addition to Nose-Hoover (fix npt, fix press/berendsen) are available.

---

Quick Comparison Table

Fix (Ensemble) DoF Controlled Volume Change? Typical Use Case

fix nve (NVE)	Energy no, Temp no, Press no	No	Isolated system, no T or P control
fix nvt (NVT)	Temperature yes (Nose-Hoover), Pressure no	No	Constant volume, set T
fix npt (NPT)	Temperature yes, Pressure yes	Yes	Equilibrate at given T, P
fix nph (NPH)	Pressure yes, Temperature no	Yes	Let T float, but control P

---

References in LAMMPS Documentation

• fix nve: LAMMPS manual: fix nve
• fix nvt: LAMMPS manual: fix nvt
• fix npt: LAMMPS manual: fix npt
• fix nph: LAMMPS manual: fix nph

Reading these pages will give you the precise details of how LAMMPS implements the various thermostats (Nose-Hoover chain, etc.) and barostats (also Nose-Hoover style), as well as important usage notes (e.g., how to choose damping parameters).

---

Summary

• NVE = microcanonical ensemble (no thermostat, no barostat).
• NVT = canonical ensemble (thermostat only).
• NPT = isothermal-isobaric ensemble (thermostat + barostat).
• NHT refers to the Nose-Hoover Thermostat method, which LAMMPS employs in fix nvt and as part of fix npt.

These are the foundational concepts for statistical ensembles in molecular dynamics, controlling which thermodynamic variables remain constant during a simulation.