Entropy information theory11/25/2023 ![]() ![]() Building on his father's work, Sadi postulated the concept that "some caloric is always lost" in the conversion into work, even in his idealized reversible heat engine, which excluded frictional losses and other losses due to the imperfections of any real machine. In this book, Sadi visualized an ideal engine in which any heat (i.e., caloric) converted into work, could be reinstated by reversing the motion of the cycle, a concept subsequently known as thermodynamic reversibility. During the following year his son Sadi Carnot, having graduated from the École Polytechnique training school for engineers, but now living on half-pay with his brother Hippolyte in a small apartment in Paris, wrote Reflections on the Motive Power of Fire. This loss of moment of activity was the first-ever rudimentary statement of the second law of thermodynamics and the concept of 'transformation-energy' or entropy, i.e. From this Carnot drew the inference that perpetual motion was impossible. Over the next three decades, Carnot's theorem was taken as a statement that in any machine the accelerations and shocks of the moving parts all represent losses of moment of activity, i.e. Carnot saw through all the details of the mechanisms to develop a general discussion on the conservation of mechanical energy. This work includes a discussion on the efficiency of fundamental machines, i.e. In 1803, mathematician Lazare Carnot published a work entitled Fundamental Principles of Equilibrium and Movement. Since the mid-20th century the concept of entropy has found application in the field of information theory, describing an analogous loss of data in information transmission systems. Clausius continued to develop his ideas of lost energy, and coined the term entropy. In the early 1850s, Rudolf Clausius set forth the concept of the thermodynamic system and posited the argument that in any irreversible process a small amount of heat energy δQ is incrementally dissipated across the system boundary. ![]() Over the next two centuries, physicists investigated this puzzle of lost energy the result was the concept of entropy. Early heat-powered engines such as Thomas Savery's (1698), the Newcomen engine (1712) and the Cugnot steam tricycle (1769) were inefficient, converting less than two percent of the input energy into useful work output a great deal of useful energy was dissipated or lost. Resources and other perspectives on the field.The concept of entropy developed in response to the observation that a certain amount of functional energy released from combustion reactions is always lost to dissipation or friction and is thus not transformed into useful work. The notes close with a highly nonexhaustive list of references to Otherwise, proofs and intriguing tangents are referenced in liberally-sprinkledįootnotes. Only where the relevant techniques are illustrative of broader themes. More pithily, ``information theory makes common sense precise.'' Since theįocus of the notes is not primarily on technical details, proofs are provided ![]() Support natural theorems that sound ``obvious'' when translated into English. A recurring theme is that the definitions of information theory ![]() Weĭiscuss some of the main results, including the Chernoff bounds as aĬharacterization of the divergence Gibbs' Theorem and the Data Processing We take the Kullback-Leibler divergence as our most basicĬoncept, and then proceed to develop the entropy and mutual information. With elementary probability, including sample spaces, conditioning, andĮxpectations. The main mathematical prerequisite for the notes is comfort Interested in exploring potential connections between information theory and They are aimed at practicing systems scientists who are Outline some elements of the information-theoretic "way of thinking," byĬutting a rapid and interesting path through some of the theory's foundationalĬoncepts and results. With relatively little mathematical sophistication, while many others develop Many primers on information theory paint a broad picture With topics as diverse as artificial intelligence, statistical physics, andīiological evolution. Download a PDF of the paper titled Divergence, Entropy, Information: An Opinionated Introduction to Information Theory, by Philip Chodrow Download PDF Abstract: Information theory is a mathematical theory of learning with deep connections ![]()
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