Dynamics and thermodynamics of linear quantum open systems

TL;DR

This paper studies the dynamics and thermodynamics of linear quantum oscillator networks coupled to environments, revealing how thermodynamic laws emerge and constraining environmental spectral densities, with implications for quantum refrigeration.

Contribution

It provides an analytical solution for the dynamics of quantum networks and explores the emergence of thermodynamic laws, highlighting the necessity of non-linearity for quantum refrigerators.

Findings

Quantum states follow a local master equation with an analytical solution.

The second law restricts the design of quantum refrigerators without moving parts.

The third law constrains the low-frequency behavior of environmental spectral densities.

Abstract

We analyze the behavior of a network of quantum oscillators coupled with a number of external environments. We show that the dynamics is such that the quantum state of the network always obeys a local master equation with a simple analytical solution. We use this to study the emergence of thermodynamical laws in the stationary regime, achieved for sufficiently long times if the environments are dissipative. We show that the validity of the second law implies the impossibility of building a quantum refrigerator without moving parts (therefore, a quantum absorption refrigerators requires non-linearity as an crucial ingredient, as recently proposed by Kosloff and others cite{Kosloff1,Kosloff2}). We also show that the third law imposes strong constraints on the low frequency behavior of the environmental spectral densities.