INFORMATION AND PHYSICS – BETTER TOGETHER
Neri Merhav, Technion, Electrical Engineering Dept.
The interplay and the relationships between information theory and statistical physics have been widely recognized in the last few decades from a wide spectrum of aspects, both in the conceptual level and the technical level. The conceptual aspects are, first and foremost, about analogies between information measures and physical quantities, and between coding theorems and physical laws. They also concern phase transitions in both fields, as well as physical systems that include informational ingredients. The technical aspects are largely about mapping between mathematical formalisms in both fields and borrowing analysis techniques from one field to the other. I will try to highlight both the conceptual ingredient and the technical ingredient. While the former is interesting academically (at least in my view), as it provides new insights and perspectives, the latter turns out to be also very helpful for better analysis in concrete problems. A very well known example is the popular replica method, but one of the main take-home messages of my talk would be that the replica method is not the only idea that statistical physics has to offer to information theorists.
While in the fall of 2014, the “Better Together” campaign succeeded in keeping England and Scotland together, in the Spring of 2015, I am trying to call for keeping information theory and physics together…