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Bridging Non-Equilibrium Problems: From the Fourier Law to Gene Expression

Final Report Summary - BRIDGES (Bridging Non-Equilibrium Problems: From the Fourier Law to Gene Expression)

There is, seemingly, a big gap between the language of mathematics, and the questions in humanities and biology. The aim of this ERC project was to work towards a possible connection between these two realms. Within the limits of time, this project has contributed to progress in bridging the two domains. The main outcome of the project is the idea that such research should be done, in order to enhance the mutual understanding of the two sides. The combination of techniques dealing with systems which are out of equilibrium and by studying particular instances of problems from linguistics and biology. The project enhances the conviction that the bridging is really possible:

- For the linguistics, a study of how words in dictionaries are linked together has shown us an unsuspected relation between these linkages and the evolution of concepts and vocabulary. In particular, these relations are not something which the dictionary-makers have put in but are hidden regularities which nobody willfully included in the dictionary.

- Similarly, in the theoretical study of evolution of proteins which perform mechanical functions, a close relationship between the evolution of the gene and the mechanical function has been established. It shows that there can be a feedback between function and evolution which one can be quantified.

- Similar ideas have been studied about the exchange of information when ants encounter each other. While the efficiency of such information exchange seems obvious to all, in fact, our study showed that in certain cases, the amount of information exchanged by ants is extremely low, and there is a subtle interplay of how, among this low information exchange, a common message can be filtered out. Here, again, the methods of mathematics (statistical mechanics) provide an answer.