The Indefinite Logarithm, Logarithmic Units, and the Nature of Entropy

We define the indefinite logarithm [log x] of a real number x>0 to be a mathematical object representing the abstract concept of the logarithm of x with an indeterminate base (i.e., not specifically e, 10, 2, or any fixed number). The resulting indefinite logarithmic quantities naturally play a mathematical role that is closely analogous to that of dimensional physical quantities (such as length) in that, although these quantities have no definite interpretation as ordinary numbers, nevertheless the ratio of two of these entities is naturally well-defined as a specific, ordinary number, just like the ratio of two lengths. As a result, indefinite logarithm objects can serve as the basis for logarithmic spaces, which are natural systems of logarithmic units suitable for measuring any quantity defined on a logarithmic scale. We illustrate how logarithmic units provide a convenient language for explaining the complete conceptual unification of the disparate systems of units that are presently used for a variety of quantities that are conventionally considered distinct, such as, in particular, physical entropy and information-theoretic entropy.Comment: Manuscript of a 15 pp. review article. Suggestions for additional appropriate references to relevant prior work are solicited from the communit

Isometric Tensor Network States in Two Dimensions

Tensor network states (TNS) are a promising but numerically challenging tool for simulating two-dimensional (2D) quantum many-body problems. We introduce an isometric restriction of the TNS ansatz that allows for highly efficient contraction of the network. We consider two concrete applications using this ansatz. First, we show that a matrix-product state representation of a 2D quantum state can be iteratively transformed into an isometric 2D TNS. Second, we introduce a 2D version of the time-evolving block decimation algorithm (TEBD$^2$) for approximating the ground state of a Hamiltonian as an isometric TNS, which we demonstrate for the 2D transverse field Ising model.Comment: 5 pages, 4 figure

Stated Choice Experiments with Complex Ecosystem Changes: The Effect of Information Formats on Estimated Variances and Choice Parameters

Stated choice experiments about ecosystem changes involve complex information. This study examines whether the format in which ecosystem information is presented to respondents affects stated choice outcomes. Our analysis develops a utility-maximizing model to describe respondent behavior. The model shows how alternative questionnaire formats alter respondents’ use of filtering heuristics and result in differences in preference estimates. Empirical results from a large-scale stated choice experiment confirm that different format presentations of the same information lead to different preference parameter estimates and error variances. A tabular format results in choice parameter estimates with statistically smaller variances than parameters estimated from data obtained with a text-based format. A text-based format also appears to induce greater use of decision heuristics than does a tabular format.choice experiments, heuristics, stated preference, valuation, web surveys, wetland mitigation, Crop Production/Industries, Demand and Price Analysis,

A SPLIT-SAMPLE TEST OF EXPERIMENTAL DESIGNS FOR STATED CHOICE MODELS OF ENVIRONMENTAL VALUATION

A stated choice model is used to estimate wetland mitigation preferences. In a split sample mail survey, a main effects design is compared to a randomized design. Although randomized designs estimate main effects less efficiently, several policy relevant interactions were found to be significant, suggesting some merits of randomized designs.Environmental Economics and Policy,