  Noise sources are ubiquitous in Nature and give rise to a description of
quantum systems in terms of stochastic Hamiltonians. Decoherence dominates the
noise-averaged dynamics and leads to dephasing and the decay of coherences in
the eigenbasis of the fluctuating operator. For energy-diffusion processes
stemming from fluctuations of the system Hamiltonian the characteristic
decoherence time is shown to be proportional to the heat capacity. We analyze
the decoherence dynamics of entangled CFTs and characterize the dynamics of the
purity, and logarithmic negativity, that are shown to decay monotonically as a
function of time. The converse is true for the quantum Renyi entropies. From
the short-time asymptotics of the purity, the decoherence rate is identified
and shown to be proportional to the central charge. The fixed point
characterizing long times of evolution depends on the presence degeneracies in
the energy spectrum. We show how information loss associated with decoherence
can be attributed to its leakage to an auxiliary environment and discuss how
gravity duals of decoherence dynamics in holographic CFTs looks like in
AdS/CFT. We find that the inner horizon region of eternal AdS black hole is
highly squeezed due to decoherence.
