Quantum memory at nonzero temperature in a thermodynamically trivial system Yifan Hong, Jinkang Guo, and Andrew Lucas have shown that certain families of constant-rate classical and quantum low-density parity-check (LDPC) codes do not exhibit thermodynamic phase transitions at nonzero temperature, but still display ergodicity-breaking dynamical transitions. These codes, despite lacking thermodynamic phase transitions, enable fault-tolerant passive quantum error correction using finite-depth circuits. This approach is suitable for measurement-free quantum error correction and may offer a practical alternative to conventional error correction methods. The study explores the relationship between error correction and thermodynamics, highlighting how passive error correction can protect logical information in quantum systems. Classical LDPC codes, which are thermodynamically trivial, exhibit linear confinement and energy barriers that prevent thermal equilibration, leading to slow Gibbs sampling. Similarly, quantum LDPC codes, such as hypergraph product (HGP) codes, also show no thermodynamic phase transitions but can still protect logical qubits through self-correction. The research demonstrates that thermodynamic phase transitions are not necessary for passive error correction in both classical and quantum systems. Classical LDPC codes, with their thermodynamic triviality, can protect logical information through deep energy minima, while quantum LDPC codes, such as HGP codes, achieve similar results without phase transitions. These findings have implications for quantum error correction, particularly in measurement-free quantum error correction (MFQEC), where the system can be corrected using local feedback and finite-depth circuits. The study also discusses the practical implementation of these codes, noting that neutral-atom quantum computing platforms are well-suited for MFQEC due to their ability to perform nonlocal operations efficiently. The results suggest that passive decoding can be implemented without the need for global syndrome measurements, making it a promising approach for quantum error correction in the future. The research highlights the importance of understanding the connection between thermodynamics and error correction, showing that passive error correction can be achieved without thermodynamic phase transitions.Quantum memory at nonzero temperature in a thermodynamically trivial system Yifan Hong, Jinkang Guo, and Andrew Lucas have shown that certain families of constant-rate classical and quantum low-density parity-check (LDPC) codes do not exhibit thermodynamic phase transitions at nonzero temperature, but still display ergodicity-breaking dynamical transitions. These codes, despite lacking thermodynamic phase transitions, enable fault-tolerant passive quantum error correction using finite-depth circuits. This approach is suitable for measurement-free quantum error correction and may offer a practical alternative to conventional error correction methods. The study explores the relationship between error correction and thermodynamics, highlighting how passive error correction can protect logical information in quantum systems. Classical LDPC codes, which are thermodynamically trivial, exhibit linear confinement and energy barriers that prevent thermal equilibration, leading to slow Gibbs sampling. Similarly, quantum LDPC codes, such as hypergraph product (HGP) codes, also show no thermodynamic phase transitions but can still protect logical qubits through self-correction. The research demonstrates that thermodynamic phase transitions are not necessary for passive error correction in both classical and quantum systems. Classical LDPC codes, with their thermodynamic triviality, can protect logical information through deep energy minima, while quantum LDPC codes, such as HGP codes, achieve similar results without phase transitions. These findings have implications for quantum error correction, particularly in measurement-free quantum error correction (MFQEC), where the system can be corrected using local feedback and finite-depth circuits. The study also discusses the practical implementation of these codes, noting that neutral-atom quantum computing platforms are well-suited for MFQEC due to their ability to perform nonlocal operations efficiently. The results suggest that passive decoding can be implemented without the need for global syndrome measurements, making it a promising approach for quantum error correction in the future. The research highlights the importance of understanding the connection between thermodynamics and error correction, showing that passive error correction can be achieved without thermodynamic phase transitions.