Pilitron thermodynamics

Pilitron thermodynamics is the pilitron physics description of temperature. Like everything else in pilitron physics, temperature is quantized.

Notation & Laws
The temperature of a system is called the temperature parameter and is denoted by $$\bar{T}$$. The difference between the temperature of 2 systems is the temperature difference parameter, and is denoted by $$\Delta\bar{T}$$.

The pilitron laws of thermodynamics are based on the classical laws of thermodynamics, but extended to account for pilitrons.

Zeroth Law
The zeroth law of pilitron thermodynamics states (like classical thermodynamics) that when systems A and B are in thermal equilibrium with system C, then they must be in thermal equilibrium with each other.

First Law
The first law of pilitron thermodynamics states that heat is a transfer of energy, ie. work. Temperature of a system is exactly proportional to work and the temperature factor and reversely proportional to volume:


 * $$\bar{T} = \frac{W\tau}{\bar{v}}$$

As the volume approaches the size of the Universe, the error in temperature approaches infinity:


 * $$\lim_{\bar{v} \to \Omega} \mbox{E}\bar{T} = \infty$$

And as the volume approaches 1 (the volume of a pilitron), the error approaches 0:


 * $$\lim_{\bar{v} \to 1} \mbox{E}\bar{T} = 0$$

Additionally, since no work can be performed by a single pilitron without the presence of other pilitrons, then a volume of 1 means that temperature is 0.

Second Law
The second law of pilitron thermodynamics states that the temperature factor of isolated systems not in thermal equilibrium almost always increases in respect to time:


 * $$\mbox{d}\dot{\tau} \geq 0$$

The exception is the impossible equilibrium state, when one system passing heat to another becomes colder than it, meaning that the systems will always exchange some heat (n being the number of systems):


 * $$\bar{T}\mod n \neq 0$$

In this case, the temperature factor will still remain constant:


 * $$\tau = \frac{\bar{T}\bar{v}}{\bar{T}\mod n}$$

And in a system whose sub-systems have thermal equilibrium, the temperature factor is:


 * $$\tau = \frac{\bar{T}\bar{v}}{W}$$

Third Law
The third law of pilitron thermodynamics states that the temperature factor is 0 in a system where $$\bar{T}=0$$. In such a system, all sub-systems must be in thermal equilibrium, and no work is performed, so:


 * $$\tau = \frac{\bar{T}\bar{v}}{W} = \frac{0 \times n}{0} = \frac{0}{0} = 0$$

Units & Quantization
According to the first law of pilitron thermodynamics, stating that $$\bar{T} = WS/\bar{v}$$, a good unit of temperature is J/m. This means that the temperature factor comes in quanta of 1/Pilipczuk's constant, meaning that a quantum of temperature must be:


 * $$T_0 = \frac{\epsilon}{\eta\ell_P^3} \approx 1.41 \times 10^{-64} \mbox{J}/\mbox{m}^3$$

Thermal energy
Thermal energy can be explained as internal work in a system, which leads to disorder in that system. The work is performed by electromagnetism - low-energy photons are exchanged by particles in the system. Relative temperature of a particle can therefore by given as:


 * $$\Delta\bar{T} = \bar{q}\Psi$$

Where $$\bar{q}$$ is the charge of the particle, and $$\Psi$$ is the product of surrounding electromagnetic force.