Inherently Non-Gibbsian States

When one cools a system across a phase transition, long-range correlations develop through coarsening. More surprisingly, long-range information-theoretic correlations arise even when one heats a system across a phase transition. These information-theoretic correlations are captured by a length-scale called the Markov length, which is related to the decay of conditional mutual information. In the classical case the growing Markov length has a simple interpretation: the parent Hamiltonian of the state becomes increasingly nonlocal in time as it heats up. A similar nonlocality arises across the error correction threshold for topological quantum codes. I will discuss various properties of the Markov length: its stability under weak decoherence, its dynamics under thermalization, and the existence of information-theoretic "thermal" phase transitions between states that retain a Markov property under decoherence and those that do not.