Ground state cooling is not possible given initial system-thermal bath factorization

TL;DR

This paper proves that under common assumptions, it is fundamentally impossible to cool a quantum system to its ground state through unitary evolution if the initial system and bath are uncorrelated, highlighting a key limitation in quantum cooling.

Contribution

The paper establishes a fundamental no-go theorem showing that initial factorization prevents ground state cooling via unitary dynamics.

Findings

Cooling to the ground state is impossible under initial factorization.

The result applies to any pure target state, not just the ground state.

The assumption of initial factorization is critical for the no-go result.

Abstract

In this paper we prove that a fundamental constraint on the cooling dynamic implies that it is impossible to cool, via a unitary system-bath quantum evolution, a system that is embedded in a thermal environment down to its ground state, if the initial state is a factorized product of system and bath states. The latter is a crucial but artificial assumption often included in many descriptions of system-bath dynamics. The analogous conclusion holds for 'cooling' to any pure state of the system.