Quantum thermodynamics and quenches. 1.2. Quantum thermodynamics and quenches |ψ⟩ = cα|α⟩ that is normalized α cαc𝛙α = 1 corresponds to the density matrix The role of entanglement or strong quantum rather than classical correlations is more readily encoded in the density matrix of the quantum system than its wavefunction. Given a basis |αΣ⟩ of states in the Hilbert space, a generic state Σ ρ = |ψ⟩⟨ψ| = cαc𝛙β |α⟩⟨β| (1.1) α,β Σ − {| ⟩} The density matrix can also describe an ensemble of quantum states which is the basis of quantum thermodynamics. For example, if the system can be found in the i th vector state from the set ψi with a probability pi, its state is given by the following density matrix:
