Basic Ideas of Information Thermodynamics – Pages 6-26

Basic Ideas of Information Thermodynamics

Pages 6-26

Bohdan Hejna

Department of Mathematics, Institute of Chemical Technology Prague, Studentská 6, 166 28 Prague 6, Czech Republic

Abstract: We apply a certain unifying physical description of the results of Information Theory. Assuming that heat entropy is a thermodynamic realization of information entropy, we construct a cyclical, thermodynamic, average-value model of an information transfer chain as a general heat engine, in particular a Carnot engine, reversible or irreversible. A working medium of the cycle (a thermodynamic system transforming input heat energy) can be considered as a thermodynamic, average-value model or, as such, as a realization of an information transfer channel. We show that for a model realized in this way the extended II. Principle of Thermodynamics is valid and we formulate its information form.

In addition we solve the problem of a proof of II. Principle of Thermodynamics. We state the relation between the term of information entropy, introduced by C. Shannon (1948), and thermodynamic entropy, introduced by R. Clausius (1850) and, further, explain the Gibbs paradox. Our way to deal with the given topic is a connection of both the mathematical definitions of information entropies and their mutual relations within a system of stochastic quantities, especially with thermodynamic entropies defined on an isolated system in which a realization of our (repeatable) observation is performed [it is a (cyclic) transformation of heat energy of an observed, measured system].

We use the information description to analyze the Gibbs paradox, reasoning it as a property of such observation, measuring an (equilibrium) thermodynamic system. We state a logical proof of the II. P.T. as a derivation of relations among the entropies of a system of stochastic variables, realized physically, and, the Equivalence Principle of the I., II. and III. Principle of Thermodynamics is formulated.

Keywords: Carnot cycle, I., II., III. Principle of Thermodynamics, Heat entropy, Observation, Information entropy, Transfer channel, Transinformation, Noise.