Information compressibility, entropy variation and approach to steady state in open systemsM. Di Ventra and Y. Dubi
Department of Physics, University of California - San Diego, La Jolla, CA 92093-0319, USA
received 13 November 2008; accepted in final form 28 January 2009; published February 2009
published online 19 February 2009
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. We also show analytically that for a two-level system in contact with external baths, the information compressibility is inversely proportional to the temperature measured at any given time by a probe that is coupled to the system, and whose temperature is adjusted so that the system dynamics is minimally perturbed. This concept, that applies to both classical and quantum open systems, thus provides insight into the properties of non-equilibrium steady states.
05.70.Ln - Nonequilibrium and irreversible thermodynamics.
05.70.Ce - Thermodynamic functions and equations of state.
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