Abstract

Using the mapping of a Fokker-Planck description of classical stochastic dynamics into a quantum Hamiltonian, we argue that a classical dynamical glass transition must have a precise definition in terms of a quantum phase transition. At the static level, the transition affects the ground state wavefunction: while in some cases it could be picked up by the expectation value of a local operator, in others the order may be non-local, and impossible to be determined with any local probe. In general, even in the absence of a local order parameter, the transition can be detected via the quantum fidelity of the ground state wavefunction, which we show translates directly into a singularity in the heat capacity of the classical system. The entanglement entropy is another probe that can detect exotic quantum phase transitions, even those without local order parameters. We show that the von Neumann entropy in these quantum models has a clear correspondence with thermodynamic properties of subsystems of the classical system.