182,454 research outputs found
The approach towards equilibrium in a reversible Ising dynamics model -- an information-theoretic analysis based on an exact solution
We study the approach towards equilibrium in a dynamic Ising model, the Q2R
cellular automaton, with microscopic reversibility and conserved energy for an
infinite one-dimensional system. Starting from a low-entropy state with
positive magnetisation, we investigate how the system approaches equilibrium
characteristics given by statistical mechanics. We show that the magnetisation
converges to zero exponentially. The reversibility of the dynamics implies that
the entropy density of the microstates is conserved in the time evolution.
Still, it appears as if equilibrium, with a higher entropy density is
approached. In order to understand this process, we solve the dynamics by
formally proving how the information-theoretic characteristics of the
microstates develop over time. With this approach we can show that an estimate
of the entropy density based on finite length statistics within microstates
converges to the equilibrium entropy density. The process behind this apparent
entropy increase is a dissipation of correlation information over increasing
distances. It is shown that the average information-theoretic correlation
length increases linearly in time, being equivalent to a corresponding increase
in excess entropy.Comment: 15 pages, 2 figure
OPTIMAL USE OF COMMUNICATION RESOURCES
We study a repeated game with asymmetric information about a dynamic state of nature. In the course of the game, the better informed player can communicate some or all of his information with the other. Our model covers costly and/or bounded communication. We characterize the set of equilibrium payoffs, and contrast these with the communication equilibrium payoffs, which by definition entail no communication costs.Repeated games, communication, entropy
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Excess-entropy scaling of dynamics for a confined fluid of dumbbell-shaped particles
We use molecular simulation to study the ability of excess entropy scaling relationships to describe the kinetic properties of a confined molecular system. We examine a model for a confined fluid consisting of dumbbell-shaped molecules that interact with atomistically detailed pore walls via a Lennard-Jones potential. We obtain kinetic, thermodynamic, and structural properties of the system at three wall-fluid interaction strengths and over a temperature range that includes sub-and super-critical conditions. Four dynamic properties are considered: translational and rotational diffusivities, a characteristic relaxation time for rotational motion, and a collective relaxation time stemming from analysis of the coherent intermediate scattering function. We carefully consider the reference state used to define the excess entropy of a confined fluid. Three ideal-gas reference states are considered, with the cases differentiated by the extent to which one-body spatial and orientational correlations are accounted for in the reference state. Our results indicate that a version of the excess entropy that includes information related to the one-body correlations in a confined fluid serves as the best scaling variable for dynamic properties. When adopting such a definition for the reference state, to a very good approximation, bulk and confined data for a specified dynamic property at a given temperature collapse onto a common curve when plotted against the excess entropy.National Science Foundation CBET-0828979Welch Foundation F-1696David and Lucile Packard FoundationChemical Engineerin
Information Theory and Knowledge-Gathering
It is assumed that human knowledge-building depends on a discrete sequential decision-making process subjected to a stochastic information transmitting environment. This environment randomly transmits Shannon type information-packets to the decision-maker, who examines each of them for relevancy and then determines his optimal choices. Using this set of relevant information-packets, the decision-maker adapts, over time, to the stochastic nature of his environment, and optimizes the subjective expected rate-of-growth of knowledge. The decision-maker’s optimal actions, lead to a decision function that involves his view of the subjective entropy of the environmental process and other important parameters at each stage of the process. Using this model of human behavior, one could create psychometric experiments using computer simulation and real decision-makers, to play programmed games to measure the resulting human performance.decision-making; dynamic programming; entropy; epistemology; information theory; knowledge; sequential processes; subjective probability
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