{"product_id":"new-foundations-for-information-theory","title":"New Foundations For Information Theory :","description":"This monograph offers a new foundation for information theory that is based on the notion of information-as-distinctions, being directly measured by logical entropy, and on the re-quantification as Shannon entropy, which is the fundamental concept for the theory of coding and communications.\u003cdiv\u003e\n\u003cbr\u003e\u003cdiv\u003eInformation is based on distinctions, differences, distinguishability, and diversity. Information sets are defined that express the distinctions made by a partition, e.g., the inverse-image of a random variable so they represent the pre-probability notion of information. Then logical entropy is a probability measure on the information sets, the probability that on two independent trials, a distinction or \"dit\" of the partition will be obtained. \u003c\/div\u003e\n\u003cdiv\u003e\u003cbr\u003e\u003c\/div\u003e\n\u003cdiv\u003eThe formula for logical entropy is a new derivation of an old formula that goes back to the early twentieth century and has been re-derived many times in different contexts. As a probability measure, all the compound notions of joint, conditional, and mutual logical entropy are immediate. The Shannon entropy (which is not defined as a measure in the sense of measure theory)  and its compound notions are then derived from a non-linear dit-to-bit transform that re-quantifies the distinctions of a random variable in terms of bits-so the Shannon entropy is the average number of binary distinctions or bits necessary to make all the distinctions of the random variable. And, using a linearization method, all the set concepts in this logical information theory naturally extend to vector spaces in general-and to Hilbert spaces in particular-for quantum logical information theory which provides the natural measure of the distinctions made in quantum measurement.\u003c\/div\u003e\n\u003cbr\u003e\n\u003c\/div\u003e\u003cdiv\u003eRelatively short but dense in content, this work can be a reference to researchers and graduate students doing investigations in information theory,  maximum entropy methods in physics, engineering, and statistics, and to all those with a special interest in a new approach to  quantum information theory.\u003c\/div\u003e","brand":"MediaPlace","offers":[{"title":"Default Title","offer_id":57305183912318,"sku":"NW9783030865511","price":43.65,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1379\/1261\/files\/9783030865511.jpg?v=1778561876","url":"https:\/\/mediaplace.com\/products\/new-foundations-for-information-theory","provider":"MediaPlace","version":"1.0","type":"link"}