1) The energy in the form of heat emitted by an object by virtue of its temperature.
2) The total potential and kinetic energies associated with the random motions of the
particles of a material. The quantity of thermal energy possessed by a body determines
its temperature. The thermal energy which is absorbed, given up, or transferred from
one material to another is heat.
3) The characteristic energy of → thermal neutrons
at room temperature, about 0.025 eV.

A particle belonging to the most energetic population of
→ cosmic rays with an
energy above ~ 10^{20} → electron-volts.
The UHECRs constitute a real challenge
for theoretical models, because their acceleration requires extreme conditions
hardly fulfilled by known astrophysical objects. See also
→ UHECR puzzle,
→ Greisen-Zatsepin-Kuzmin cutoff.

In particle physics the lowest energy allowed by field quantization when all fields are
in their → ground states. Vacuum energy is predicted to arise from
→ virtual particles that fluctuate in and out of existence,
as manifested by the → Casimir effect.
The cosmological → dark energy is postulated to be related
to vacuum fluctuations. There is however an enormous discrepancy with the predictions of
quantum field theory. In this theory the value of vacuum energy density is expected
to be roughly of the order
ρ_{v}≅ E_{max}^{4},
where E_{max} is the maximum energy at which the field theory is valid.
At energies of the order of the
→ Planck energy,
E_{Pl}≅ 10^{19} GeV, vacuum energy might be roughly:
ρ_{v}≅ E_{Pl}^{4}≅ 10^{76} GeV^{4}.
On the other hand, the vacuum energy density in standard cosmological model
is given by:
ρ_{Λ} = Ω_{Λ}.ρ_{crit}, where
Ω_{Λ} is the → density parameter for the
→ cosmological constant and ρ_{crit}
is the → critical density. More explicitly,
ρ_{Λ} = Ω_{Λ} . 3 H^{2}/(8πG).
Using
present-day values of Ω_{Λ} (0.7) and H (70) leads to
ρ_{Λ} = 10^{-46} GeV^{4}. Therefore,
the discrepancy between the prediction and the observed value is 122 orders
of magnitude.

The energy due to the vibration of the molecules making up atoms
(→ molecular vibration). A molecule in space can
have energies in various forms: → rotational energy,
vibrational energy, or electronic energy. These energies of
molecules are → quantized and a particular molecule
can exist in different rotational and vibrational
→ energy levels. The molecules
can move from one level to another level only by a jump
involving a finite amount of energy. → Quantum mechanics
predicts that any molecule can never have zero vibrational energy,
that is atoms can never be completely at rest relative to each other.
The harmonically oscillating molecules can undergo vibrational changes
determined by simple selection rules obtained from
→ Schrödinger equation.