A curvature dependent bound for entanglement change in classically chaotic systems

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Using the Calogero-Moser model and the Nakamura equations for a multi-partite quantum system, we prove an inequality between the mean bi-partite entanglement rate of change under the variation of a critical parameter and the level-curvature. This provides an upper bound for the rate of production or distraction of entanglement induced dynamically. We then investigate the dependence of the upper bound on the degree of chaos of the system, which in turn, through the inequality, gives a measure of the stability of the entangled state. Our analytical results are supported with extensive numerical calculations.