Question

1.Which of the following best describes Maxwell's Demon?

A demon that knows everything and can predict anything

A demon that creates equilibrium

A demon that controls whether Schrodinger's Cat lives or dies

A demon that opens and closes a door for air molecules depending on their velocity 2. What makes living matter different from inorganic matter? It is organized in more complicated ways It carries electricity It has special chemical elements not present in inorganic matter It responds to a special magnetic force 3. Which problem is definitively unsolvable by computers? P=NP The Halting Problem Fermat's Last Theorem The Busy Beaver Problem

Answer 1

1. B

2.A

In the philosophy of thermal and statistical physics, Maxwell's demon is a thought experiment created by the physicist James Clerk Maxwell in 1867 in which he suggested how the second law of thermodynamics might hypothetically be violated. In the thought experiment, a demon controls a small door between two chambers of gas. As individual gas molecules approach the door, the demon quickly opens and shuts the door so that only fast molecules are passed into one of the chambers, while only slow molecules are passed into the other. Because faster molecules are hotter, the demon's behaviour causes one chamber to warm up and the other to cool down, thereby decreasing entropy and violating the second law of thermodynamics. This thought experiment has provoked debate and theoretical work on the relation between thermodynamics and information theoryextending to the present day, with a number of scientists arguing that theoretical considerations rule out any practical device violating the second law in this way.

3.A

The P versus NP problem is a major unsolved problem in computer science. It asks whether every problem whose solution can be quickly verified (technically, verified in polynomial time) can also be solved quickly (again, in polynomial time)

Ex: Consider Sudoku, a game where the player is given a partially filled-in grid of numbers and attempts to complete the grid following certain rules. Given an incomplete Sudoku grid, of any size, is there at least one legal solution? Any proposed solution is easily verified, and the time to check a solution grows slowly (polynomially) as the grid gets bigger. However, all known algorithms for finding solutions take, for difficult examples, time that grows exponentially as the grid gets bigger. So, Sudoku is in NP (quickly checkable) but does not seem to be in P (quickly solvable). Thousands of other problems seem similar, in that they are fast to check but slow to solve. Researchers have shown that many of the problems in NP have the extra property that a fast solution to any one of them could be used to build a quick solution to any other problem in NP, a property called NP-completeness. Decades of searching have not yielded a fast solution to any of these problems, so most scientists suspect that none of these problems can be solved quickly. This, however, has never been proven

An answer to the P = NP question would determine whether problems that can be verified in polynomial time, like Sudoku, can also be solved in polynomial time. If it turned out that P ≠ NP, it would mean that there are problems in NP that are harder to compute than to verify: they could not be solved in polynomial time, but the answer could be verified in polynomial time