Information Theory and Thermodynamics

 Abstract. A communication theory for a transmitter broadcasting to many receivers presented.  In this case, energetic considerations cannot 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 for informatics systems that are not in thermal equilibrium and to calculate temperature, heat, and entropy with accordance to Clausius inequality.  It shown that for a binary file, the temperature is proportional to the bit energy and that information is thermodynamic entropy.  Equilibrium exists in random files that cannot compressed. Thermodynamic bounds on the computing power of a physical device, and the maximum information that an antenna can broadcast are calculated.Keywords. Information theory, Thermodynamics, Entropy.JEL. C62

Thermodynamical Cost of Accessing Quantum Information

Thermodynamics is a macroscopic physical theory whose two very general laws are independent of any underlying dynamical laws and structures. Nevertheless, its generality enables us to understand a broad spectrum of phenomena in physics, information science and biology. Recently, it has been realised that information storage and processing based on quantum mechanics can be much more efficient than their classical counterpart. What general bound on storage of quantum information does thermodynamics imply? We show that thermodynamics implies a weaker bound than the quantum mechanical one (the Holevo bound). In other words, if any post-quantum physics should allow more information storage it could still be under the umbrella of thermodynamics.Comment: 3 figure

A Resource Theory for Work and Heat

Several recent results on thermodynamics have been obtained using the tools of quantum information theory and resource theories. So far, the resource theories utilised to describe thermodynamics have assumed the existence of an infinite thermal reservoir, by declaring that thermal states at some background temperature come for free. Here, we propose a resource theory of quantum thermodynamics without a background temperature, so that no states at all come for free. We apply this resource theory to the case of many non-interacting systems, and show that all quantum states are classified by their entropy and average energy, even arbitrarily far away from equilibrium. This implies that thermodynamics takes place in a two-dimensional convex set that we call the energy-entropy diagram. The answers to many resource-theoretic questions about thermodynamics can be read off from this diagram, such as the efficiency of a heat engine consisting of finite reservoirs, or the rate of conversion between two states. This allows us to consider a resource theory which puts work and heat on an equal footing, and serves as a model for other resource theories.Comment: main text: 12 pages, 5 figure; appendix: 7 page