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 many natural processes have been recognized to complete in non-polynomial time (NP). The irreversible process with three or more degrees of freedom is found intractable because, in terms of physics, flows of energy are inseparable from their driving forces. In computational terms, when solving problems in the class NP, decisions will affect subsequently available sets of decisions. The state space of a non-deterministic 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 of the NP problem itself is verifiable in polynomial time (P) because the corresponding state is stationary. Likewise the class P 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 class P set of states is inherently smaller than the set of class NP. Since the computational time to contract a given set is proportional to dissipation, the computational complexity class P is a subset of NP.Comment: 16, pages, 7 figure

A discrete, unitary, causal theory of quantum gravity

A discrete model of Lorentzian quantum gravity is proposed. The theory is completely background free, containing no reference to absolute space, time, or simultaneity. The states at one slice of time are networks in which each vertex is labelled with two arrows, which point along an adjacent edge, or to the vertex itself. The dynamics is specified by a set of unitary replacement rules, which causally propagate the local degrees of freedom. The inner product between any two states is given by a sum over histories. Assuming it converges (or can be Abel resummed), this inner product is proven to be hermitian and fully gauge-degenerate under spacetime diffeomorphisms. At least for states with a finite past, the inner product is also positive. This allows a Hilbert space of physical states to be constructed.Comment: 38 pages, 9 figures, v3 added to exposition and references, v4 expanded prospects sectio

On Dark Chemistry: What’s Dark Matter and How Mind Influences Brain Through Proactive Spin

Benjamin has written an article entitled “Dark Chemistry or Psychic Spin Pixel?” which promotes a “dark chemistry” model of mind and discuss the spin-mediated theory. This hypothetical chemistry is based on the hypothetical axion dark matter. Although Benjamin is commendable for boldly going where no one has gone before, he may find himself still in the “bright” territory instead of the “dark” side, if he is willing to use Occam’s razor to cut out “dark” things and replace them with non-local effects. Based on our recent experimental findings, our contentions are two-fold: (1) dark matter is likely the cosmological manifestation of quantum entanglement; and (2) the hypothetical axion dark matter is, therefore, replaceable by non-local effects mediated by the primordial spin processes. We also discuss the cause of apparent dark energy. In particular, we explore the issue how mind influences the brain through said spin processes. Our thoughts are that the manifestation of free will is intrinsically associated with the nuclear and/or electron spin processes inside the varying high electric voltage environment of the neural membranes and proteins which likely enable the said spin processes to be “proactive,” that is, being able to utilize non-local energy (potential) and quantum information to influence brain activities through spin chemistry and possibly other chemical/physical processes in defiance of the second law of thermodynamics

Phase transition in protocols minimizing work fluctuations

For two canonical examples of driven mesoscopic systems - a harmonically-trapped Brownian particle and a quantum dot - we numerically determine the finite-time protocols that optimize the compromise between the standard deviation and the mean of the dissipated work. In the case of the oscillator, we observe a collection of protocols that smoothly trade-off between average work and its fluctuations. However, for the quantum dot, we find that as we shift the weight of our optimization objective from average work to work standard deviation, there is an analog of a first-order phase transition in protocol space: two distinct protocols exchange global optimality with mixed protocols akin to phase coexistence. As a result, the two types of protocols possess qualitatively different properties and remain distinct even in the infinite duration limit: optimal-work-fluctuation protocols never coalesce with the minimal work protocols, which therefore never become quasistatic.Comment: 6 pages, 6 figures + SI as ancillary fil