Emergence of the 2nd Law in an Exactly Solvable Model of a Quantum Wire

TL;DR

This paper explores how the Second Law of Thermodynamics emerges in a quantum wire model through entropy production during Joule heating.

Contribution

The study introduces an exact solvable model showing that entropy production in quantum wires requires local measurements and decoherence.

Findings

Entropy production in a quantum wire does not occur automatically in exact microscopic descriptions.

Local measurements by thermoelectric probes inject entropy into the system.

Decoherence from inelastic processes is essential for entropy production due to Joule heating.

Abstract

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.

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