Perturbation theory is used to investigate the evolution of the von Neumann entropy of a subsystem of a bipartite quantum system under the action of a unitary matrix, in the limit where that matrix is close to the unit matrix. The physical context for such a process would be scattering with weak short-ranged interactions where the unitary matrix is the $S$ matrix. We find surprisingly simple criteria for the initial state and the $S$ matrix that guarantee that the subsystem entropy increases. The class of initial states that meet these criteria are more correlated than simple product states of the subsystems. They form a subclass of the set of all separable states, and they can therefore be assembled by classical processes alone.

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• Entanglement in field theory
• Perturbation theory
• Quantum field theory