This talk will take place in person at the Technion in Amado room #234 (note the unusual room!), and we will also broadcast the talk over Zoom.

We investigate Completely Positive Trace-Preserving (CPTP) maps and their density matrix fixed points, also known as steady states. Specifically, we focus on maps acting on many-body Hilbert spaces that admit a Kraus decomposition using local operators. These maps can be realized on quantum computers as a quantum analog of Markov processes. We address the question of when these fixed points describe Gibbs measures of a local Hamiltonian. By perturbatively interpolating from a 1-local map to a 2-local map, we demonstrate that the fixed-point Gibbs Hamiltonian perturbs into a quasi-local Hamiltonian, where the diameter of the Hamiltonian terms increases correspondingly with the perturbative order. This result is proved by introducing a framework of multi-parameter perturbations that respects the geometric structure of the system.