What Is Heat Energy?

Heat energy is a central element in both thermodynamics and radiative heat transfer. But what is in fact heat energy?

The 1st Law of Thermodynamics states that the total energy as kinetic energy plus (internal) heat energy remains constant in a system (without chemistry/fission/fusion) with no energy exchange with its surrounding. The 2nd Law of Thermodynamics states that transformation of kinetic energy into heat energy is irreversible. 

The Planck-Stefan-Boltzman Law (PSB Law) expresses that the transfer of heat energy by electromagnetic radiation from a warmer body of temperature $T_w$ to a colder body of temperature $T_c<T_w$ scales with $T_w^4 -T_c^4$. 

Computational Thermodynamics and Computational BlackBody Radiation present a new approach to uncover the mysteries of both the 2nd Law of Thermodynamics and the PSB Law based on a principle of finite precision computation/physics. In  this setting heat energy takes the form of small scale unordered kinetic motion.

In thermodynamics kinetic energy thus takes the form of large scale ordered motion and small scale unordered motion which is the result of turbulent dissipation into heat energy. The 2nd Law expresses that the process of turbulent dissipation is irreversible because in finite precision unordered small scale motion cannot be coordinated into large scale ordered motion. Heat energy here appears as "internal energy" with limits set by the 2nd Law as concerns transformation to "external energy" as large scale kinetic motion.

In radiative heat transfer the temperature of a body determines a cut-off frequency scaling with temperature with heat energy as atomic vibrations with only frequencies below cut-off appearing in synchronized ordered form capable to generating outgoing radiation. Here the finite precision limit thus scales with the inverse of the temperature and the heat transfer from a warm to a cold body consist only of the frequencies above cut-off for the colder and below cut-off for the warmer. 

In both cases heat energy is a result of an impossibility arising from finite precision computation. In thermodynamics heat energy is unresolvable unordered small scale kinetic motion. In thermodynamics a body absorbs heat energy as unordered kinetic motion for frequencies above cut-off. 

In short, heat energy emerges as a rest product of finite precision computation/physics meeting unresolvable scales of motion. 

Even if now heat energy is a form of rest product, it does not mean that it cannot be recycled into useful energy to some extent. In thermodynamics a gas expanding into a larger volume creates turbulence which is turned into heat energy, which can be used to do work when expanding into an even bigger volume. In radiative heat transfer a colder body when heating up by absorbing heat in unordered form from a warmer body, increases its cut-off and so can radiate higher frequencies in synchronised ordered form.