what is difference between entropy and randomness
First attested in 1867, as the translation of German Entropie, coined in 1865 by Rudolph Clausius in analogy to Energie (“energy”), replacing the root of Ancient Greek ἔργον (érgon, “work”) by Ancient Greek τροπή (tropḗ, “transformation”)).
- IPA(key): /ˈɛntɹəpi/
entropy (countable and uncountable, plural entropies)
- A measure of the disorder present in a system.
- Ludwig Boltzmann defined entropy as being directly proportional to the natural logarithm of the number of microstates yielding an equivalent thermodynamic macrostate (with the eponymous constant of proportionality). Assuming (by the fundamental postulate of statistical mechanics), that all microstates are equally probable, this means, on the one hand, that macrostates with higher entropy are more probable, and on the other hand, that for such macrostates, the quantity of information required to describe a particular one of its microstates will be higher. That is, the Shannon entropy of a macrostate would be directly proportional to the logarithm of the number of equivalent microstates (making it up). In other words, thermodynamic and informational entropies are rather compatible, which shouldn’t be surprising since Claude Shannon derived the notation ‘H’ for information entropy from Boltzmann’s H-theorem.
- (thermodynamics, countable) strictly thermodynamic entropy. A measure of the amount of energy in a physical system that cannot be used to do work.
- The thermodynamic free energy is the amount of work that a thermodynamic system can perform; it is the internal energy of a system minus the amount of energy that cannot be used to perform work. That unusable energy is given by the entropy of a system multiplied by the temperature of the system. (Note that, for both Gibbs and Helmholtz free energies, temperature is assumed to be fixed, so entropy is effectively directly proportional to useless energy.)
- The capacity factor for thermal energy that is hidden with respect to temperature .
- The dispersal of energy; how much energy is spread out in a process, or how widely spread out it becomes, at a specific temperature. 
- (statistics, information theory, countable) A measure of the amount of information and noise present in a signal.
- (uncountable) The tendency of a system that is left to itself to descend into chaos.
- bound entropy
- free entropy
- entropy in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.
- entropy in The Century Dictionary, New York, N.Y.: The Century Co., 1911.
- entropy at OneLook Dictionary Search
- Poynter, peryton
random + -ness
- IPA(key): /ˈɹændəmnəs/
randomness (usually uncountable, plural randomnesses)
- The property of all possible outcomes being equally likely.
- (mathematics) A type of circumstance or event that is described by a probability distribution.
- A measure of the lack of purpose, logic, or objectivity of an event.
- There was no randomness in the teacher’s selection of the class representative.
- algorithmic randomness
- statistical randomness
- at random