The physical impossibility of heat transfer under isothermal conditions implies that the classical expression for entropy ideal gas may not be compatible with internal energy itself. A corrected is derived here. It independent on volume. This result shown to at a variance statistical interpretations as quantity related number microstates macroscopic state system. also offers better understandin...

Statistical entropy was introduced by Shannon as a basic concept in information theory, measuring the average missing information on a random source. Extended into an entropy rate, it gives bounds in coding and compression theorems. I here present how statistical entropy and entropy rate relate to other notions of entropy, relevant either to probability theory (entropy of a discrete probability...

We consider the problem of finite sample corrections for entropy estimation. New estimates of the Shannon entropy are proposed and their systematic error (the bias) is computed analytically. We find that our results cover correction formulas of current entropy estimates recently discussed in literature. The trade-off between bias reduction and the increase of the corresponding statistical error...