The First Law: Q  W = dU.
However, the topological constraint of the first law is not limited to
equilibrium systems (which have a topological dimension 2).
The Second Law has to do with entropy increase. The third law is related to a conjecture that Absolute Zero is not achievable. In certain formulations, the idea of the third law states that by use of reversible processes, absolute zero cannot be reached in a finite number of steps. These ideas are not defined precisely by a mathematical formalism.
In this note a precise expression for the the Third Law of thermodynamics is
given as another topological statement expressing a cohomological constraint,
this time, the cohomology does not describe topological constraints on the
1forms of Heat and Work, but on their 3forms, Q^dQ and W^dW. Like the first
law, the Third Law is valid for equilibirium and nonequilibrium systems, and
for processes that are reversible or irreversiblw.
The Third Law: Q^dQ  W^dW = d(U dW). If the system is restricted to be an equilibrium system, then Q^dQ = 0 and W^dW = 0 in order to insure that the Pfaff topological dimension is not more than 2.
If a process is reversible, then Q^dQ = 0.
