Quantum diffusion and entropy production: An exactly solvable model

M. Esposito, P. Gaspard

Wim Magnus, K. Nelissen

Marco A. Jimenez-Valencia, Charles A. Stafford

As remarked by Boltzmann, the Second Law of Thermodynamics is notable for the fact that it is readily proved using elementary statistical arguments, but becomes harder and harder to verify the more precise the microscopic description of a system. In this article, we investigate one particular realization of the 2nd Law, namely Joule heating in a wire under electrical bias. We analyze the production of entropy in an exactly solvable model of a quantum wire wherein the conserved flow of entropy under unitary quantum evolution is taken into account using an exact formula for the entropy current of a system of independent quantum particles. In this exact microscopic description of the quantum dynamics, the entropy production due to Joule heating does not arise automatically. Instead, we show that the expected entropy production is realized in the limit of a large number of local measurements by a series of floating thermoelectric probes along the length of the wire, which inject entropy into the system as a result of the information obtained via their continuous measurements of the system. The decoherence resulting from inelastic processes introduced by the local measurements is essential to the phenomenon of entropy production due to Joule heating, and would be expected to arise due to inelastic scattering in real systems of interacting particles.

Morozov, GERD RÖPKE

We present analytical results for the time-dependent information entropy in exactly solvable two-state (qubit) models.The first model describes dephasing (decoherence) in a qubit coupled to a bath of harmonic oscillators.The entropy production for this model in the regimes of "complete" and "incomplete" decoherence is discussed.As another example, we consider the damped Jaynes-Cummings model describing a spontaneous decay of a two-level system into the field vacuum.It is shown that, for all strengths of coupling, the open system passes through the mixed state with the maximum information entropy.

V. P. Belavkin

Massimiliano Esposito, Katja Lindenberg, Christian Van den Broeck

We derive an exact (classical and quantum) expression for the entropy production of a finite system placed in contact with one or several finite reservoirs, each of which is initially described by a canonical equilibrium distribution. Although the total entropy of system plus reservoirs is conserved, we show that system entropy production is always positive and is a direct measure of system–reservoir correlations and/or entanglements. Using an exactly solvable quantum model, we illustrate our novel interpretation of the Second Law in a microscopically reversible finite-size setting, with strong coupling between the system and the reservoirs. With this model, we also explicitly show the approach of our exact formulation to the standard description of irreversibility in the limit of a large reservoir.