[AntonioLao]

There are 3 fundamental laws for classical thermodynamics. These study the conversion of energy from one form to another, the flow of heat energy (Q) in a particular direction, and the sustainability of mechanical energy (V or W) for an applied force along the same direction as the local spacetime displacement. If the mechanical forces are in static or dynamic equilibrium then V or W is called virtual work. The 3rd main form of energy is the internal energy (U) as the total kinetic and scalar potential (V) energy of the atoms and molecules comprising an isolated system. U is usually measured as heat transfer (ΔQ) between closed systems or open systems. Therefore, thermodynamics properly excludes electric, magnetic, chemical, or nuclear energy description.

For an adiabatic (Q=0) closed system with constant mass then ΔU=W. By convention, W is positive if work is done on the system and negative if done by the system in question. For nonadiabatic (Q>0) closed systems with constant mass: ΔU=Q+W. This is equivalent to the law of conservation of energy and is commonly known as the 1st law of thermodynamics. Natural processes obeying the strong form of this law are reversible. Those obeying the weak form are irreversible. The direction that a natural process takes is measurable by a parameter called the entropy (S). its increase or decrease depends on the parameter called temperature (T) such that work seems to be always at the expense of a closed system and now ΔU=TΔS-W where ΔQ= TΔS and ∆S=∆Q/T is known as the 2nd law of thermodynamics that asserts entropy always increases. However, the 3rd law says that the change in entropy (∆S) can absolutely be zero: ∆S=0 where and when the spacetime domain is at absolute zero temperature: T=0. This is classically nonsense. However, quantum mechanically, it makes sense if and only if one and only one quantum state of energy exists. This can be the square of zero point energy of the quantum vacuum. Furthermore, it was proved succinctly by Pauli that (1) the lowest state is not degenerate; (2) the lowest state is sufficiently separated from the next to lowest state.

General covariance exists between the Hamiltonian function and the 1st law, the Lagrangian function and the 2nd law. Their product becomes a general covariance for the 3rd law with a difference of squares: (Q+W)(Q-W)=Q-W. This implies that if Q=W or Q=-W then (Q+W) and (Q-W) cannot both be zero simultaneously. That is, either the Hamiltonian is zero or the Lagrangian but not both at the same space and time.