![]() (But this happens only in the $N \to \infty$ limit as discussed e.g. In phase transitions as common as freezing/melting entropy is even discontinuous thus the criterion. for a complete set of extensive parameter $A_i$ we have $S(\lambda A_1. Generally, information entropy is the average amount of information conveyed by an event, when considering all possible outcomes. This randomness is often collected from hardware sources, either pre-existing ones such as mouse movements or specially provided randomness generators. Entropy is homogeneous in the parameters defined by physical criteria as "extensive". In computing, entropy is the randomness collected by an operating system or application for use in cryptography or other uses that require random data.Entropy has a finite difference between any two points in the macro parameter space.if it is not it might also be because the list of parameters is not complete.) Entropy is a single-valued function of the full set of macroscopic parameters.Then the strongest we can say is the following: Let's say our the physical motivation is paramount. So the answer would be: If a well developed model predicting quantitatively the entropy exists and it is confirmed by thorough testing, the entropy qualifies as the unique entropy of the system.Īdditional note: Observed mathematical conditions Instead we define entropic terms based on macroscopic variables of a system, like the followings (examples among the usual ones):įor a perfect gas one can write the entropy per atom of N atoms in volume V as: $$S_ $$īut also a lot of other response coefficient involving temperature as specified e.g. But of course we almost never use this exact form of entropy in studying real systems, as it is impossible to count the microstates by any means. Where $\Omega$, can be the partition function in an ensemble, or simply the number of microstates within a given macrostate. Limiting the discussion to physics, when studying a physical system, can be a box filled with an ideal gas, a melt of polymers or the state of rods/molecules in a liquid crystalline system, in all such scenarios, there are specific entropic terms that we define in describing the evolution of the system (by including it in the free energy expression).įrom a statistical mechanics point of view, we use Boltzmann's definition of: $$S=k_B \ln\Omega$$ The concept of entropy is very ubiquitous, we learn about its uses starting from Information Theory ( Shannon entropy) up to its basic definition in statistical mechanics in terms of number of micro-states.
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