Entropy production and the arrow of time: how to design an optimal Maxwell’s demon

The relationship between entropy production and irreversibility can be made quantitative using the Kullbak-Leibler divergence between a process and its time reversal. This relationship allows one to bound or estimate the energy transfer between a system and its surroundings just by measuring how irreversibly the system behaves. I will show two applications of this result. The first is a technique to detect if a stationary process is consuming energy or not, something of relevance in biophysics. The second is the design of optimal Maxwell’s demons, i.e., of protocols that, given some information of the state of a system, extract the maximum amount of energy in isothermal processes.