The paper explores the relationship between error correction and thermodynamics, focusing on the passive error correction mechanism. It demonstrates that certain families of classical and quantum low-density parity-check (LDPC) codes exhibit ergodicity-breaking dynamical transitions at nonzero temperatures, even though they do not have thermodynamic phase transitions. This means that below a critical temperature, the mixing time of local Gibbs sampling diverges in the thermodynamic limit, enabling fault-tolerant passive quantum error correction using finite-depth circuits. This approach is particularly suitable for measurement-free quantum error correction and may offer a desirable experimental alternative to conventional quantum error correction methods. The study also highlights the connection between quantum error-correcting codes and recent models of ergodicity breaking in statistical physics, providing insights into the dynamics of these systems.The paper explores the relationship between error correction and thermodynamics, focusing on the passive error correction mechanism. It demonstrates that certain families of classical and quantum low-density parity-check (LDPC) codes exhibit ergodicity-breaking dynamical transitions at nonzero temperatures, even though they do not have thermodynamic phase transitions. This means that below a critical temperature, the mixing time of local Gibbs sampling diverges in the thermodynamic limit, enabling fault-tolerant passive quantum error correction using finite-depth circuits. This approach is particularly suitable for measurement-free quantum error correction and may offer a desirable experimental alternative to conventional quantum error correction methods. The study also highlights the connection between quantum error-correcting codes and recent models of ergodicity breaking in statistical physics, providing insights into the dynamics of these systems.