Axiomatic Information Thermodynamics

An axiomatic foundation for continuum thermodynamics

Constantin Carathéodory and the axiomatic thermodynamics

The birth, raise, development and fortunes of a fundamental theory in thermodynamics, the axiomatic thermodynamics, a creation of Constantin Carathéodory, is thoroughly presented together with a summary of Carathéodory’s biography. Axiomatic thermodynamics is centered around some interesting properties of Pfaffian differential equations, which are here introduced and used for some well-known ca...

Axiomatic Characterizations of Information Measures

Axiomatic characterizations of Shannon entropy, Kullback I-divergence, and some generalized information measures are surveyed. Three directions are treated: (A) Characterization of functions of probability distributions suitable as information measures. (B) Characterization of set functions on the subsets of {1, . . . , N} representable by joint entropies of components of an N -dimensional rand...

Thermodynamics of Information Retrieval

In this work, we suggest a parameterized statistical model (the gamma distribution) for the frequency of word occurrences in long strings of english text and use this model to build a corresponding thermodynamic picture by constructing the partition function. We then use our partition function to compute thermodynamic quantities such as the free energy and the specific heat. In this approach, t...

Information theory and Thermodynamics

A communication theory for a transmitter broadcasting to many receivers is presented. In this case energetic considerations cannot be neglected as in Shannon theory. It is shown that, when energy is assigned to the information bit, information theory complies with classical thermodynamic and is part of it. To provide a thermodynamic theory of communication it is necessary to define equilibrium ...