Statistical mechanics
Thermodynamics Kinetic theory
Particle statistics Spin–statistics theorem Indistinguishable particles Maxwell–Boltzmann Bose–Einstein Fermi–Dirac Parastatistics Anyonic statistics Braid statistics
Thermodynamic ensembles NVE Microcanonical NVT Canonical µVT Grand canonical NPH Isoenthalpic–isobaric NPT Isothermal–isobaric
Models Debye Einstein Ising Potts
Potentials Internal energy Enthalpy Helmholtz free energy Gibbs free energy Grand potential / Landau free energy
Scientists Maxwell Boltzmann Bose Gibbs Einstein Ehrenfest von Neumann Tolman Debye Fermi

The isoenthalpic-isobaric ensemble (constant enthalpy and constant pressure ensemble) is a statistical mechanical ensemble that maintains constant enthalpy ${\displaystyle H\,}$ and constant pressure ${\displaystyle P\,}$ applied. It is also called the ${\displaystyle NPH}$-ensemble, where the number of particles ${\displaystyle N\,}$ is also kept as a constant. It was developed by physicist H. C. Andersen in 1980.^[1] The ensemble adds another degree of freedom, which represents the variable volume ${\displaystyle V\,}$ of a system to which the coordinates of all particles are relative. The volume ${\displaystyle V\,}$ becomes a dynamical variable with potential energy and kinetic energy given by ${\displaystyle PV\,}$.^[2] The enthalpy ${\displaystyle H=E+PV\,}$ is a conserved quantity.^[3] Using isoenthalpic-isobaric ensemble of Lennard-Jones fluid, it was shown ^[4] that the Joule–Thomson coefficient and inversion curve can be computed directly from a single molecular dynamics simulation. A complete vapor-compression refrigeration cycle and a vapor–liquid coexistence curve, as well as a reasonable estimate of the supercritical point can be also simulated from this approach. NPH simulation can be carried out using GROMACS and LAMMPS.

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