Physical portrayal of computational complexity

Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because information requires physical representations and because many natural processes have been recognized to complete in non-deterministic polynomial time ( ). The irreversible process with three or more degrees of freedom is found intractable when, in terms of physics, flows of energy are inseparable from their driving forces. In computational terms, when solving a problem in the class , decisions among alternatives will affect subsequently available sets of decisions. The state space of a nondeterministic finite automaton is evolving due to the computation itself hence it cannot be efficiently contracted using a deterministic finite automaton that will arrive at a solution in super-polynomial time. The solution itself is verifiable in polynomial time ( ) because the accepting state of computation is stationary. Conversely when solving problems in the class , the set of states does not depend on computational history hence it can be efficiently contracted to the accepting state by a deterministic sequence of dissipative transformations. Thus it is concluded that the state set of class is inherently smaller than the set of class . Since the computational time to contract a given set is proportional to dissipation, the computational complexity class is a proper (strict) subset of .