Figure 2: Gibbs-preserving operations cooling maps.

Consider a parametric family of initial states , and a two-parameter family of final states , on a two-level system, with x,y,β real and non-negative. For each value of x, the corresponding region in the (y,β) plane represents part of the parametric state space that is reachable via Gibbs-preserving operations, but not via cooling maps (or thermal operations), from the initial state ρ(x).