Energy equipartitioning

According to the energy equipartition theorem of classical physics, the three translational kinetic energy modes each acquire average thermal energy kT (where k = R/NA is Boltzmann s constant),... 

Hendrik Antoon Lorentz, from Leyden (Holland), presided the conference, whose general theme was the Theory of Radiation and the Quanta. The conference5 was opened with speeches by Lorentz and Jeans, one on Applications of the Energy Equipartition Theorem to Radiation, the other on the Kinetic Theory of Specific Heat according to Maxwell and Boltzmann. In their talks, the authors explored the possibility of reconciling radiation theory with the principles of statistical mechanics within the classical frame. Lord Rayleigh, in a letter read to the... 

This result implies that the energy equipartition relationship of Eq. (2.S) applies as well as the general definitions of Chapter I. Note that for Af m the variable turns out to be coupled weakly to the thermal bath. This condition generates that time-scale separation which is indispensable for recovering an exponential time decay. To recover the standard Brownian motion we have therefore to assiune that the Brownian particle be given a macroscopic size. In the linear case, when M = w we have no chance of recovering the properties of the standard Brownian motion. In the next two sections we shall show that microscopic nonlinearity, on the contrary, may allow that the Markov characters of the standard Brownian motion be recovered with increasing temperature. 

J.E. Straub, M. Karplus, Energy equipartitioning in the classical time-dependent Hartree approximation, J. Chem. Phys. 94 (1991), 6737... 

Harvey SC, Tan RK-Z, Cheatham TE III (1998) The flying ice cube velocity rescaling in molecular dynamics leads to violation of energy equipartition. J Comput Chem 19 726-740 Lundberg M, Nishimoto Y, Irle S (2012) Delocalization errors in a Hubbard-like model consequences for density-functional tight-binding calculations of molecular systems. Int J Quant Chem 112 1701-1711... 

The particles comprising the molecule arc in equilibrium so that, in the mean, they have similar kinetic energies (equipartition). 

At low E where the motion of both ions and gas molecules is thermal, energy equipartition yields... 

Is Granular Temperature Existent Or Lack of Energy Equipartition ... 

Lu et al, 2001 Rahaman et al, 2003). Ny is scaled by di ttittyg considering that Ny varies greatly with the Enskog factor. Three surfaces intersect at line 9i = 9j, about which both our results and Rahaman s results are symmetric. That is consistent with theoretical analysis as discussed above, while Huilin s result fails. Furthermore, we can observe that our surfaces are higher than the Huilin s prediction and lower than Rahaman s when 9i<9y This is expected as the Huilin s profile can only be applied in energy equipartition system, which may underestimate the collision frequencies, whereas Rahaman s hypothesis implies aU the collisions happen in a 2D plane, which obviously overestimates the collision frequency. 

Chen Y, Evesque P, Hou M Breakdown of energy equipartition in vibro-fluidized granular media in micro-gravity. Chin Phys Lett 29 074501, 2012. 

Feitosa K, Menon N Breakdown of energy equipartition in a 2D binary vibrated granular... 

For the atomic case, for example of a nucleus of mass (M) and an electron of mass (/w), once the energy equipartition (as in the classical mechanics) is accepted, then the (quantum) energies of the two particles become equal ... 

In this section a relationship between the equilibrium value of H and entropy, S, is derived [20] (p. 78). For a gas at uniform steady state, the H(t) quantity defined by (2.235) can be expressed in terms of n and T. By use of the absolute Maxwellian distribution (2.243) and the energy equipartition theorem yields ... 

The average kinetic energy is considered proportional to temperature through the kinetic energy equipartition theorem. 

In kinetic theory, in accordance with the kinetic energy equipartition theorem, the kinetic temperature T of a gas at a uniform state at rest or in uniform translation is defined directly in terms of the average peculiar speeds of the molecules, by the three dimensional relation m C )M = kT obtained from (2.200) and (2.199). In accordance with (2.200) and (2.192) the static pressure p of a. gas in equilibrium is given hy p = 3px = nm C )M = nm C )M = knT. Considering the mass M of gas contained in a volume V, the number of mono-atomic molecules N in the mass M is M/m, and the number density n is therefore N/ V. The thermodynamic pressure is then given by pV = NkT. Alternatively one can write N = nNa, where n is the number of moles of gas present and is Avogadro s number. Then, the ideal gas law, yields ... 

K. Feitosa and N. Menon. Breakdown of energy equipartition in a 2d binary vibrated granular gas. Physical Review Letters, 88 198301, April 2002. 

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