Aiolli -Sistemi Informativi 2007/2008 55You have to be careful when thinking about this. Di Matematica Pura ed Applicata F. Entropy and Information Gain The entropy (very common in Information Theory) characterizes the (im)purityof an arbitrary collection of examples Information Gain is the expected reduction in entropy caused by partitioning the examples according to a given attribute Dip.

Generally, information entropy is the average amount of information conveyed by an event, when considering all possible. Because you don't know the answer, you can use a probability distribution: $p( ext$ bits or more.Two bits of entropy: In the case of two fair coin tosses, the information entropy in bits is the base-2 logarithm of the number of possible outcomes with two coins there are four possible outcomes, and two bits of entropy. For example: suppose you ask me a question to which the possible answers are 'yes' and 'no', and you have no idea what my answer will be.

'Entropy, as defined in information theory, is a measure of how random the message is.' Perhaps the writer means a measure of how unpredictable it is, and uses random as a synonym. But the only way its entropy can decrease is if we make a measurement, and this decrease in entropy is typically so small it can be neglected.If you would like to have a deep understanding of the relationship between Shannon entropy and thermodynamics, it is highly recommended that you read this long but awesome paper by Edwin Jaynes.* or, if we're thinking in terms of quantum mechanics rather than classical mechanics, it's the amount of information you would gain if you made a measurement such that the system was put into a pure state after the measurement.Just wanted to point out that the last comment may mislead people. This increases our uncertainty about the system, i.e. In general, the more certain or deterministic.The second law of thermodynamics arises because there are a lot of ways we can lose information about a system, for example if the motions of its particles become correlated with the motions of particles in its surroundings. It tells how much information there is in an event.

The act of figuring out what something means, the 'aha' or 'viola' moment, is information. Once the signals are completely decoded, putting aside any semantic content, they are entropy to the code breakers.Shannon's entropy is a byproduct of information, which, like happiness, is pursued. So if decoding cryptographic signals, the apparently random inputs are not entropy, but information. Information is found in unexpected signals, which is why newspapers will print an article about a man biting a dog, not the other way around. A sentence 'dog bites man' has more entropy than 'man bites dog,' because the latter is more unexpected.

Correspondingly, low entropy systems would have more information known regarding the microscopic state of the system.Thus I believe these are two different concepts, and should not be confused.However, these concepts are certainly deeply related (they do go by same names). This would thus correspond to little information known regarding which exact microscopic configuration the system is, given the macroscopic state of the system with its known macroscopic variables. Naturally for these states, more microscopic configurations with all macroscopic variables and the macroscopic state unchanged are possible than other macroscopic states (precisely why the macroscopic state is more probable). It happens that systems with high entropy turn out to be more 'random' states too, usually states of equilibrium. Entropy is then a measure of how probable the macroscopic state of the system is. Entropy, as defined in information theory, is a measure of how random the message is, which is precisely the information content of the message, as the more random a message is, the more information will be gained from decoding the message.In physics, I assume that information refers to information about the exact microscopic configuration (microstate) of the system.

Information Entropy