Thermodynamics and entropy

The relationships between thermodynamic entropy and Shannon s information-theoretic entropy and between physics and computation have been explored and hotly debated ever since. It is now well known, for example, that computers can, in principle, provide an arbitrary amount of reliable computation per kT of dissipated energy ([benu73], [fredkin82] see also the discussion in section 6.4). Whether a dissipationless computer can be built in practice, remains an open problem. We must also remember that computers are themselves physical (and therefore, ultimately, quantum) devices, so that any exploration of the limitations of computation will be inextricably linked with the fundamental limitations imposed by the laws of physics. 

Physical information is a function of (1) structural organization, (2) thermodynamic entropy, and/or (3) the amount of useful work required to create it. 

These indices encode information on the molecule entropy (thermodynamic entropy) and are useful in modeUing physico-chemical properties related to entropy and symmetry. 

We have noted the close connection between thermodynamic entropy and accessible phase space volume. Because of this connection Eq. (A.6) may be recast as... 

Gladyshew. G.P. On thermodynamics, entropy and evolution of biological systems What is life from a physical chemist s viewpoint. Entropy 1999. L 9-20. 

Our paper is arranged as a sequence of successive step>s, definitions and derivations (4)-(12) and interpretations (82)-(86) especially, stating gradually, the relation between combinatorial definition of Shannon (information) entropy and Boltzman and Clausius (thermodynamic) entropy, and, finally, resulting in (87) and (88). Although we combined the known facts about heat transformations and the Shannon s concept of an information transfer chain, this combination presented has not been used yet by another else, as far as the author of the pap>er is informed. 

We can now shed some additional light on the relation between statistical entropy and thermodynamic entropy, and also on the identification of the parameter fi with 1 /k T. Using the definition of the statistical entropy in Eq. (26.1-1) and replacing In(f ) by its largest term, In(Wmp), we obtain... 

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