text: Fluid particle is the smallest unit (atoms or molecules) in the fluid phase (gas, liquid or plasma) without breaking any chemical bond. Energy of fluid particle is divided into potential, electronic, translational, vibrational, and rotational energies. The heat (thermal) energy storage in fluid particle is through the temperature-dependent particle motion (translational, vibrational, and rotational energies). The electronic energy is included only if temperature is high enough to ionize or dissociate the fluid particles or to include other electronic transitions. These quantum energy states of the fluid particles are found using their respective quantum Hamiltonian. These are H = −(ħ/2m)∇, H = −(ħ/2m)∇ + Γx/2 and H = −(ħ/2I)∇ for translational, vibrational and rotational modes. (Γ: spring constant, I: the moment of inertia for the molecule). From the Hamiltonian, the quantized fluid particle energy state E and partition functions Z [with the Maxwell–Boltzmann (MB) occupancy distribution] are found as
  * translational 
  * vibrational 
  * rotational 
  * total 
  Here, g is the degeneracy, n, l, and j are the transitional, vibrational and rotational quantum numbers, T is the characteristic temperature for vibration (= ħω/k, : vibration frequency), and T is the rotational temperature [= ħ/(2Ik)]. The average specific internal energy is related to the partition function through Z, 
  With the energy states and the partition function, the fluid particle specific heat capacity c is the summation of contribution from various kinetic energies (for non-ideal gas the potential energy is also added). Because the total degrees of freedom in molecules is determined by the atomic configuration, c has different formulas depending on the configuration,
  * monatomic ideal gas 
  * diatomic ideal gas 
  * nonlinear, polyatomic ideal gas 
  where R is the gas constant (= Nk, N: the Avogadro constant) and M is the molecular mass (kg/kmol). (For the polyatomic ideal gas, N is the number of atoms in a molecule.) In gas, constant-pressure specific heat capacity c has a larger value and the difference depends on the temperature T, volumetric thermal expansion coefficient β and the isothermal compressibility κ [c – c = Tβ/(ρκ), ρ : the fluid density].  For dense fluids that the interactions between the particles (the van der Waals interaction) should be included, and c and c would change accordingly.
  The net motion of particles (under gravity or external pressure) gives rise to the convection heat flux q = ρcuT. Conduction heat flux q for ideal gas is derived with the gas kinetic theory or the Boltzmann transport equations, and the thermal conductivity is
  where ⟨u⟩ is the RMS (root mean square) thermal velocity (3kT/m from the MB distribution function, m: atomic mass) and τ is the relaxation time (or intercollision time period) [(2π dn ⟨u⟩) from the gas kinetic theory, ⟨u⟩: average thermal speed (8kT/πm), d: the collision diameter of fluid particle (atom or molecule), n: fluid number density].
  k is also calculated using molecular dynamics (MD), which simulates physical movements of the fluid particles with the Newton equations of motion (classical) and force field (from ab initio or empirical properties). For calculation of k, the equilibrium MD with Green–Kubo relations, which express the transport coefficients in terms of integrals of time correlation functions (considering fluctuation), or nonequilibrium MD (prescribing heat flux or temperature difference in simulated system) are generally employed.
  Fluid particles can interact with other principal particles. Vibrational or rotational modes, which have relatively high energy, are excited or decay through the interaction with photons. Gas lasers employ the interaction kinetics between fluid particles and photons, and laser cooling has been also considered in CO gas laser. Also, fluid particles can be adsorbed on solid surfaces (physisorption and chemisorption), and the frustrated vibrational modes in adsorbates (fluid particles) is decayed by creating e-h pairs or phonons.  These interaction rates are also calculated through ab initio calculation on fluid particle and the Fermi golden rule.