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This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1977.

Statistical mechanics relies on the maximization of entropy in a system at thermal equilibrium. However, an isolated quantum many-body system initialized in a pure state remains pure during Schrödinger evolution, and in this sense it has static, zero entropy. We experimentally studied the emergence of statistical mechanics in a quantum state and observed the fundamental role of quantum entanglement in facilitating this emergence. Microscopy of an evolving quantum system indicates that the full quantum state remains pure, whereas thermalization occurs on a local scale. We directly measured entanglement entropy, which assumes the role of the thermal entropy in thermalization. The entanglement creates local entropy that validates the use of statistical physics for local observables. Our measurements are consistent with the eigenstate thermalization hypothesis.

We study the conditional distribution of GDP growth as a function of economic and financial conditions. Deteriorating financial conditions are associated with an increase in the conditional volatility and a decline in the conditional mean of GDP growth, leading the lower quantiles of GDP growth to vary with financial conditions and the upper quantiles to be stable over time. Upside risks to GDP growth are low in most periods while downside risks increase as financial conditions become tighter. We argue that amplification mechanisms in the financial sector generate the observed growth vulnerability dynamics.

The description of the non-equilibrium dynamics of isolated quantum many-body systems within the framework of statistical mechanics is a fundamental open question. Conventional thermodynamical ensembles fail to describe the large class of systems that exhibit nontrivial conserved quantities, and generalized ensembles have been predicted to maximize entropy in these systems. We show experimentally that a degenerate one-dimensional Bose gas relaxes to a state that can be described by such a generalized ensemble. This is verified through a detailed study of correlation functions up to 10th order. The applicability of the generalized ensemble description for isolated quantum many-body systems points to a natural emergence of classical statistical properties from the microscopic unitary quantum evolution.

This study assesses whether the accrual-generating process is adequately described by a linear model with respect to a range of underlying determinants examined by prior literature. We document substantial departures from linearity across the distributions of accrual determinants, including measures of size, performance, and growth. To incorporate non-linear relations, we employ a recently developed multivariate matching approach (entropy balancing) to adjust for determinants in place of relying on a linear model. Entropy balancing identifies weights for the control sample to equalize the distribution of determinants across treatment and control samples. In simulations drawing random samples from deciles where a linear model displays poor fit, we find that entropy balancing significantly improves accrual model specification by reducing coefficient bias relative to linear and propensity-score matched models. Consistent with entropy balancing retaining sufficient power, we find that its estimates detect seeded accrual manipulations and explain variation in accruals around equity issuances.

Artificial biochemical circuits are likely to play as large a role in biological engineering as electrical circuits have played in the engineering of electromechanical devices. Toward that end, nucleic acids provide a designable substrate for the regulation of biochemical reactions. However, it has been difficult to incorporate signal amplification components. We introduce a design strategy that allows a specified input oligonucleotide to catalyze the release of a specified output oligonucleotide, which in turn can serve as a catalyst for other reactions. This reaction, which is driven forward by the configurational entropy of the released molecule, provides an amplifying circuit element that is simple, fast, modular, composable, and robust. We have constructed and characterized several circuits that amplify nucleic acid signals, including a feedforward cascade with quadratic kinetics and a positive feedback circuit with exponential growth kinetics.

The main emphasis of this work is the mathematical theory of quantum channels and their entropic and information characteristics.Quantum information theory is one of the key research areas, since it leads the way to vastly increased computing speeds by using quantum systems to store and process information.

We design new approximation algorithms for the problems of optimizing submodular and supermodular functions subject to a single matroid constraint. Specifically, we consider the case in which we wish to maximize a monotone increasing submodular function or minimize a monotone decreasing supermodular function with a bounded total curvature c . Intuitively, the parameter c represents how nonlinear a function f is: when c = 0, f is linear, while for c = 1, f may be an arbitrary monotone increasing submodular function. For the case of submodular maximization with total curvature c , we obtain a (1 − c/e )-approximation—the first improvement over the greedy algorithm of of Conforti and Cornuéjols from 1984, which holds for a cardinality constraint, as well as a recent analogous result for an arbitrary matroid constraint. Our approach is based on modifications of the continuous greedy algorithm and nonoblivious local search, and allows us to approximately maximize the sum of a nonnegative, monotone increasing submodular function and a (possibly negative) linear function. We show how to reduce both submodular maximization and supermodular minimization to this general problem when the objective function has bounded total curvature. We prove that the approximation results we obtain are the best possible in the value oracle model, even in the case of a cardinality constraint. We define an extension of the notion of curvature to general monotone set functions and show a (1 − c )-approximation for maximization and a 1/(1 − c )-approximation for minimization cases. Finally, we give two concrete applications of our results in the settings of maximum entropy sampling, and the column-subset selection problem.

In this paper, we propose a novel image encryption algorithm based on a hybrid model of deoxyribonucleic acid (DNA) masking, a Secure Hash Algorithm SHA-2 and the Lorenz system. Our study uses DNA sequences and operations and the chaotic Lorenz system to strengthen the cryptosystem. The significant advantages of this approach are improving the information entropy which is the most important feature of randomness, resisting against various typical attacks and getting good experimental results. The theoretical analysis and experimental results show that the algorithm improves the encoding efficiency, enhances the security of the ciphertext and has a large key space and a high key sensitivity, and it is able to resist against the statistical and exhaustive attacks.

This article reviews the recent work on the high-entropy alloys (HEAs) in our group and others. HEAs usually contain five or more elements, and thus, the phase diagram of HEAs is often not available to be used to design the alloys. We have proposed that the parameters of δ and Ω can be used to predict the phase formation of HEAs, namely Ω ≥ 1.1 and δ  ≤ 6.6%, which are required to form solid-solution phases. To test this criterion, alloys of TiZrNbMoV x and CoCrFeNiAlNb x were prepared. Their microstructures mainly consist of simple body-centered cubic solid solutions at low Nb contents. TiZrNbMoV x alloys possess excellent mechanical properties. Bridgman solidification was also used to control the microstructure of the CoCrFeNiAl alloy, and its plasticity was improved to be about 30%. To our surprise, the CoCrFeNiAl HEAs exhibit no apparent ductile-to-brittle transition even when the temperatures are lowered from 298 K to 77 K.