Entropy Generation in Computation and the Second Law of Thermodynamics

Landauer discussed the minimum energy necessary for computation and stated that erasure of information is accompanied by heat generation to the amount of kT ln2/bit. Modifying the above statement, we claim that erasure of information is accompanied by entropy generation k ln2/bit. Some new concepts will be introduced in the field of thermodynamics that are implicitly included in our statement. The new concepts that we will introduce are ``partitioned state'', which corresponds to frozen state such as in ice, ``partitioning process'' and ``unifying process''. Developing our statement, i.e., our thermodynamics of computation, we will point out that the so-called ``residual entropy'' does not exist in the partitioned state. We then argue that a partioning process is an entropy decreasing process. Finally we reconsider the second law of thermodynamics especially when computational processes are involved.Comment: 5 pages, 2 figure

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

Statistics of level crossing intervals

ABSTRACT We present an analytic relation between the correlation function of dichotomous (taking two values, ±1) noise and the probability density function (PDF) of the zero crossing interval. The relation is exact if the values of the zero crossing interval τ are uncorrelated. It is proved that when the PDF has an asymptotic form L(τ ) = 1/τ c , the power spectrum density (PSD) of the dichotomous noise becomes S(f ) = 1/f β where β = 3 − c. On the other hand it has recently been found that the PSD of the dichotomous transform of Gaussian 1/f α noise has the form 1/f β with the exponent β given by β = α for 0 < α < 1 and β = (α + 1)/2 for 1 < α < 2. Noting that the zero crossing interval of any time series is equal to that of its dichotomous transform, we conclude that the PDF of level-crossing intervals of Gaussian 1/f α noise should be given by L(τ ) = 1/τ c , where c = 3 − α for 0 < α < 1 and c = (5 − α)/2 for 1 < α < 2. Recent experimental results seem to agree with the present theory when the exponent α is in the range 0.7 < ∼ α < 2 but disagrees for 0 < α < ∼ 0.7. The disagreement between the analytic and the numerical results will be discussed

Picture of the low-dimensional structure in chaotic dripping faucets

Chaotic dynamics of the dripping faucet was investigated both experimentally and theoretically. We measured continuous change in drop position and velocity using a high-speed camera. Continuous trajectories of a low-dimensional chaotic attractor were reconstructed from these data, which was not previously obtained but predicted in our fluid dynamic simulation. From the simulation, we further obtained an approximate potential function with only two variables, the drop mass and its position of the center of mass. The potential landscape helps one to understand intuitively how the dripping dynamics can exhibit low-dimensional chaos.Comment: 8 pages, 3 figure

Dynamical model of financial markets: fluctuating `temperature' causes intermittent behavior of price changes

We present a model of financial markets originally proposed for a turbulent flow, as a dynamic basis of its intermittent behavior. Time evolution of the price change is assumed to be described by Brownian motion in a power-law potential, where the `temperature' fluctuates slowly. The model generally yields a fat-tailed distribution of the price change. Specifically a Tsallis distribution is obtained if the inverse temperature is $\chi^{2}$-distributed, which qualitatively agrees with intraday data of foreign exchange market. The so-called `volatility', a quantity indicating the risk or activity in financial markets, corresponds to the temperature of markets and its fluctuation leads to intermittency.Comment: 9 pages including 2 figure