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Motivated by the growing importance of strong system-bath coupling in severalbranches of quantum information and related technological applications, weanalyze and compare two strategies currently used to obtain (approximately)steady states in strong coupling. The first strategy is based on perturbativeexpansions while the second one uses reaction coordinate mapping. Focusing onthe widely used spin-boson model, we show that, as expected and hoped, thepredictions of these two strategies coincide for some parameter regions. Thisconfirms and strengthens the relevance of both techniques. Beyond that, it isalso crucial to know precisely their respective range of validity. In thatperspective, thanks to their different limitations, we use one to benchmark theother. We introduce and successfully test some very simple validity criteriafor both strategies, bringing some answers to the question of the validityrange.

Steady state in strong system-bath coupling: mean force Gibbs state versus reaction coordinate