Information compressibility, entropy production and approach to steady state in open systems
Abstract
We introduce the concept of information compressibility, KI, which measures the relative change of number of available microstates of an open system in response to an energy variation. We then prove that at the time in which the system reaches a steady state, the second and third time derivatives of the information entropy are proportional to the corresponding time derivatives of the energy, the proportionality constant being KI. We argue that if two steady states with different but same-sign KI are dynamically connected in a non-adiabatic way it takes a longer time to reach the state with compressibility closer to zero than the reverse. This concept, that applies to both classical and quantum open systems, thus provides insight into the properties of non-equilibrium steady states.