7 research outputs found
Physical Foundations of Landauer's Principle
We review the physical foundations of Landauer's Principle, which relates the
loss of information from a computational process to an increase in
thermodynamic entropy. Despite the long history of the Principle, its
fundamental rationale and proper interpretation remain frequently
misunderstood. Contrary to some misinterpretations of the Principle, the mere
transfer of entropy between computational and non-computational subsystems can
occur in a thermodynamically reversible way without increasing total entropy.
However, Landauer's Principle is not about general entropy transfers; rather,
it more specifically concerns the ejection of (all or part of) some correlated
information from a controlled, digital form (e.g., a computed bit) to an
uncontrolled, non-computational form, i.e., as part of a thermal environment.
Any uncontrolled thermal system will, by definition, continually re-randomize
the physical information in its thermal state, from our perspective as
observers who cannot predict the exact dynamical evolution of the microstates
of such environments. Thus, any correlations involving information that is
ejected into and subsequently thermalized by the environment will be lost from
our perspective, resulting directly in an irreversible increase in total
entropy. Avoiding the ejection and thermalization of correlated computational
information motivates the reversible computing paradigm, although the
requirements for computations to be thermodynamically reversible are less
restrictive than frequently described, particularly in the case of stochastic
computational operations. There are interesting possibilities for the design of
computational processes that utilize stochastic, many-to-one computational
operations while nevertheless avoiding net entropy increase that remain to be
fully explored.Comment: 42 pages, 15 figures, extended postprint of a paper published in the
10th Conf. on Reversible Computation (RC18), Leicester, UK, Sep. 201
Games, puzzles, and computation
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 147-153).There is a fundamental connection between the notions of game and of computation. At its most basic level, this is implied by any game complexity result, but the connection is deeper than this. One example is the concept of alternating nondeterminism, which is intimately connected with two-player games. In the first half of this thesis, I develop the idea of game as computation to a greater degree than has been done previously. I present a general family of games, called Constraint Logic, which is both mathematically simple and ideally suited for reductions to many actual board games. A deterministic version of Constraint Logic corresponds to a novel kind of logic circuit which is monotone and reversible. At the other end of the spectrum, I show that a multiplayer version of Constraint Logic is undecidable. That there are undecidable games using finite physical resources is philosophically important, and raises issues related to the Church-Turing thesis. In the second half of this thesis, I apply the Constraint Logic formalism to many actual games and puzzles, providing new hardness proofs. These applications include sliding-block puzzles, sliding-coin puzzles, plank puzzles, hinged polygon dissections, Amazons, Kohane, Cross Purposes, Tip over, and others.(cont.) Some of these have been well-known open problems for some time. For other games, including Minesweeper, the Warehouseman's Problem, Sokoban, and Rush Hour, I either strengthen existing results, or provide new, simpler hardness proofs than the original proofs.by Robert Aubrey Hearn.Ph.D