Information compressibility, entropy production and approach to steady state in open systems

Abstract

We introduce the concept of {\em information compressibility}, $K_I$, 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 $K_I$. We argue that if two steady states with different but same-sign $K_I$ 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.

6 pages, 1 figure. Accepted for publication in Europhysics Letters

References in corpus (4)

• Entropy production and time asymmetry in nonequilibrium fluctuations
• Theory of non-equilibrium thermoelectric effects in nanoscale junctions
• Transport in nanoscale systems: the microcanonical versus grand-canonical picture
• Approach to steady state transport in nanoscale conductors

Cited by in corpus (8)

• Fourier's Law: insight from a simple derivation
• Local temperatures of strongly-correlated quantum dots out of equilibrium
• Local Temperatures Out of Equilibrium
• Quantum Shock Waves and Population Inversion in Collisions of Ultracold Atomic Clouds
• Local and Effective Temperatures of Quantum Driven Systems
• Reconstructing Fourier's law from disorder in quantum wires
• The thermodynamic meaning of local temperature of nonequilibrium open quantum systems
• Local heat current flow in ballistic phonon transport of graphene nanoribbons