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Entropy examples9/5/2023 ![]() ![]() Have a look at Maxwell's Demon for one of the more slippery problems with entropy, which links it squarely to information. We also expect images with complicated spatial structure (like the questioner’s random noise example) to have higher information-entropy than images with simple spatial structure (like the questioner’s smooth gray-scale example). ![]() Osmosis, melting ice, and a clean room becoming dirty are all examples. Ice in water Consider putting some ice into a glass of water. Intuitively we might expect the Shannon information-entropy of an image to be independent of its orientation. Entropy can be thought of as the tendency for a system to become disordered, or random. Entropy is different: No conservation law the entropy change S associated with an irreversible process in a closed system is always greater than or equal to zero. Once you go to systems with order 10^23 coins the predictions how it will evolve get very strong. For example in a pendulum, energy continually goes to/from kinetic energy and potential energy. What is the most e cient way to encode the message The entropy of the random variable is 3 bits. ![]() In quantum terms, it is the movement from pure to mixed states, a highly correlated/concentrated state like, all the coins the same way up in a stack, to a mixed state, like each coin is randomly heads or tails spread over the floor. Entropy Entropy and Information Joint Entropy Conditional Entropy Entropy and Information Example: 8-sided die Suppose you wish to send the result of rolling the die. 2.1 Example 1 Entropy Entropy refers to the number of ways in which a system can be arranged. So, the entropy for the fair coin case comes out to be 1. So, the entropy of a fair coin is: Source: Author. In the case of a coin, we have heads (1) or tails (0). Here, c is the number of different classes you have. We can move order and disorder around, but in total the disorder increases.Īnother way to describe entropy is to say it's spreading out of energy, the most spread out usually being heat. The mathematical formula of Shannon’s entropy is: Source: Author. The Gini index has a maximum impurity is 0.5 and maximum purity is 0, whereas Entropy has a maximum impurity of 1 and maximum purity is 0. It's like the ordered bit is the cool part of the fridge - it can't cool the room as a whole, because the fins at the back are releasing a more than balancing amount of heat. For example, CART uses Gini ID3 and C4.5 use Entropy. Yes disorder was created to make the ordered cigarette or tube. Could you get them back, from those outputs? The key is the whole system. Consider these as closed systems, including the chemical energy involved in squeezing, the light radiated by smouldering. ![]()
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