Time and Space Bounds for Reversible Simulation

We prove a general upper bound on the tradeoff between time and space that suffices for the reversible simulation of irreversible computation. Previously, only simulations using exponential time or quadratic space were known. The tradeoff shows for the first time that we can simultaneously achieve subexponential time and subquadratic space. The boundary values are the exponential time with hardly any extra space required by the Lange-McKenzie-Tapp method and the ($\log 3$)th power time with square space required by the Bennett method. We also give the first general lower bound on the extra storage space required by general reversible simulation. This lower bound is optimal in that it is achieved by some reversible simulations.Comment: 11 pages LaTeX, Proc ICALP 2001, Lecture Notes in Computer Science, Vol xxx Springer-Verlag, Berlin, 200

The (absence of a) relationship between thermodynamic and logical reversibility

Landauer erasure seems to provide a powerful link between thermodynamics and information processing (logical computation). The only logical operations that require a generation of heat are logically irreversible ones, with the minimum heat generation being $kT \ln 2$ per bit of information lost. Nevertheless, it will be shown logical reversibility neither implies, nor is implied by thermodynamic reversibility. By examining thermodynamically reversible operations which are logically irreversible, it is possible to show that information and entropy, while having the same form, are conceptually different.Comment: 19 pages, 5 figures. Based on talk at ESF Conference on Philosophical and Foundational Issues in Statistical Physics, Utrecht, November 2003. Submitted to Studies in History and Philosophy of Modern Physic

Entropy Production and Heat Generation in Computational Processes

To make clear several issues relating with the thermodynamics of computations, we perform a simulation of a binary device using a Langevin equation. Based on our numerical results, we consider how to estimate thermodynamic entropy of computational devices. We then argue against the existence of the so-called residual entropy in frozen systems such as ice.Comment: 6 pages, 1 figure

Properties of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas II: The many point particles system

We study the stationary nonequilibrium states of N point particles moving under the influence of an electric field E among fixed obstacles (discs) in a two dimensional torus. The total kinetic energy of the system is kept constant through a Gaussian thermostat which produces a velocity dependent mean field interaction between the particles. The current and the particle distribution functions are obtained numerically and compared for small E with analytic solutions of a Boltzmann type equation obtained by treating the collisions with the obstacles as random independent scatterings. The agreement is surprisingly good for both small and large N. The latter system in turn agrees with a self consistent one particle evolution expected to hold in the limit of N going to infinity.Comment: 14 pages, 9 figure

Synthesis and Optimization of Reversible Circuits - A Survey

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table