James P. Crutchfield

TL;DR: In this paper, the authors critique the measure of complexity introduced by Shiner, Davison, and Landsberg and point out that it is over-universal, in the sense that it has the same dependence on disorder for structurally distinct systems.

TL;DR: It is shown that the quantum variable's size is generically smaller than the classical, according to two different measures---cardinality and entropy.

Abstract: Predictive equivalence in discrete stochastic processes have been applied with great success to identify randomness and structure in statistical physics and chaotic dynamical systems and to inferring hidden Markov models. We examine the conditions under which they can be reliably reconstructed from time-series data, showing that convergence of predictive states can be achieved from empirical samples in the weak topology of measures. Moreover, predictive states may be represented in Hilbert spaces that replicate the weak topology. We mathematically explain how these representations are particularly beneficial when reconstructing high-memory processes and connect them to reproducing kernel Hilbert spaces.

TL;DR: In this paper, a broad family of conditional fluctuation theorems that the component work distributions must satisfy are introduced, which encode the frequency of various mechanisms of both success and failure during computing, as well giving improved estimates of the total irreversibly dissipated heat.

TL;DR: In this article , the authors critique the measure of complexity introduced by Shiner, Davison, and Landsberg in Ref. [1] and point out that it is over-universal, in the sense that it has the same dependence on disorder for structurally distinct systems.