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This Concept Map, created with IHMC CmapTools, has information related to: b8. History of Entropy, Atoms and molecules are ordered and have low entropy in a solid, less ordered in a liquid, and quite disordered with high entropy in a gas. ???? Consequently, scientists began to look upon a measurement of entropy as a measurement of the system’s degree of disorder., When there is a change from a solid to liquid to gas, there is an increase in entropy, and also a decrease in the orderly in the arrangement of constituent atoms (an increase in disorder). ???? Atoms and molecules are ordered and have low entropy in a solid, less ordered in a liquid, and quite disordered with high entropy in a gas., The tenth interpretation is that of information. In this sense, the number given by the equation is an information value that characterizes a particular group of probabilities. 1. High Entropy: Much information. 2. Low Entropy: Little information. ???? The information value is of so many bits. A relatively large number means a relatively large amount of information, and vice versa, The third common interpretation is in terms of probability. Boltzman’s probabilities dealt with particle motion, deviations from equilibrium, etc. 1. High Entropy: Equally probable events, low probability of a selected event. 2. Low Entropy: Preordained outcomes, high probability of a selected event. ???? Just as entropy is a maximum for disordered conditions, it is also a maximum for equally probable events. When all possible outcomes are equally likely, the probability of any one outcome is low, and entropy is high. When the outcome is fixed in advance, or far from probable, the outcomes are not equally probable, and the entropy is lowest., Energy is dissipated [unavailable], and entropy therefore increases with heat loss and other actions. 1. High Entropy: Disorder, disorganization, thorough mix. 2. Low Entropy: Order, high degree of organization, meticulous sorting or separation. ???? The third common interpretation is in terms of probability. Boltzman’s probabilities dealt with particle motion, deviations from equilibrium, etc. 1. High Entropy: Equally probable events, low probability of a selected event. 2. Low Entropy: Preordained outcomes, high probability of a selected event., Just as entropy is a maximum for disordered conditions, it is also a maximum for equally probable events. When all possible outcomes are equally likely, the probability of any one outcome is low, and entropy is high. When the outcome is fixed in advance, or far from probable, the outcomes are not equally probable, and the entropy is lowest. ???? Thus, there is an inverse relationship between entropy and probability., The seventh way of looking at entropy is freedom of choice or large numbers of possible outcomes or states. a. High Entropy: Freedom (wide variety) of choice, many possible outcomes b. Low Entropy: Narrowly constricted choice, few possible outcomes. ???? When constrained to one choice or outcome, there is no disorder, uncertainty or unpredictability. Probability is highest and entropy is lowest (zero), The first interpretation of entropy is Clausius’s interpretation, soon modified by others, to form the second interpretation. 1. High Entropy: Large proportion of energy is unavailable for work. 2. Low Entropy: Small proportion of energy is unavailable for work. ???? When there is a change from a solid to liquid to gas, there is an increase in entropy, and also a decrease in the orderly in the arrangement of constituent atoms (an increase in disorder)., The fifth interpretation of entropy is uncertainty. The uncertainty can pertain to the outcome of an experiment about to be run, or it can pertain to the state of a dynamical system. a. High Entropy: Great uncertainty. b. Low Entropy: Near certainty, high reliability. ???? The sixth idea is that of randomly distributed observations versus reliable predictability (in this sense random means unpredictability). a. High Entropy: Randomness or unpredictability. b. Low Entropy: Non-randomness, accurate forecasts., b8. History of Entropy ???? The first interpretation of entropy is Clausius’s interpretation, soon modified by others, to form the second interpretation. 1. High Entropy: Large proportion of energy is unavailable for work. 2. Low Entropy: Small proportion of energy is unavailable for work., The sixth idea is that of randomly distributed observations versus reliable predictability (in this sense random means unpredictability). a. High Entropy: Randomness or unpredictability. b. Low Entropy: Non-randomness, accurate forecasts. ???? The seventh way of looking at entropy is freedom of choice or large numbers of possible outcomes or states. a. High Entropy: Freedom (wide variety) of choice, many possible outcomes b. Low Entropy: Narrowly constricted choice, few possible outcomes., The seventh way of looking at entropy is freedom of choice or large numbers of possible outcomes or states. a. High Entropy: Freedom (wide variety) of choice, many possible outcomes b. Low Entropy: Narrowly constricted choice, few possible outcomes. ???? The eighth variation is diversity, suggested by the many possible outcomes of the seventh variation. High Entropy: Large diversity. Low Entropy: Small diversity., The third common interpretation is in terms of probability. Boltzman’s probabilities dealt with particle motion, deviations from equilibrium, etc. 1. High Entropy: Equally probable events, low probability of a selected event. 2. Low Entropy: Preordained outcomes, high probability of a selected event. ???? The fourth interpretation, based on the probability notion, is that of uniformity of distribution of data. a. High Entropy: Uniform distribution b. Low Entropy: Highly uneven distribution., The first interpretation of entropy is Clausius’s interpretation, soon modified by others, to form the second interpretation. 1. High Entropy: Large proportion of energy is unavailable for work. 2. Low Entropy: Small proportion of energy is unavailable for work. ???? Rudolf Clausius – 1865 Introduced entropy in his work on heat-producing engines It is impossible to direct all of a system’s energy into useful work, because some of that energy is not available for work (escapes, or lost to friction), The fifth interpretation of entropy is uncertainty. The uncertainty can pertain to the outcome of an experiment about to be run, or it can pertain to the state of a dynamical system. a. High Entropy: Great uncertainty. b. Low Entropy: Near certainty, high reliability. ???? When rolling a die, we really have no idea which number will appear, and our uncertainty is greatest. We can assume complete disarray, equal probabilities and a uniform distribution., The first interpretation of entropy is Clausius’s interpretation, soon modified by others, to form the second interpretation. 1. High Entropy: Large proportion of energy is unavailable for work. 2. Low Entropy: Small proportion of energy is unavailable for work. ???? Energy is dissipated [unavailable], and entropy therefore increases with heat loss and other actions. 1. High Entropy: Disorder, disorganization, thorough mix. 2. Low Entropy: Order, high degree of organization, meticulous sorting or separation., Some ecologist use Shannon’s equation, above, to model the number of species in a sample. However, high entropy in this variation can reflect not only large diversity, but also uniform distribution. ???? A single value of entropy does not distinguish between the two. A sample with only a few species, unevenly distributed can yield the same entropy as a large number of species, unevenly distributed.