Overwriting information: Correlations, physical costs, and environment models

In this sequel to our previous study of the entropic and energetic costs of information erasure [N.G. Anderson, Phys. Lett. A 372 (2008) 5552], we consider direct overwriting of classical information encoded in a quantum-mechanical memory system interacting with a heat bath. Lower bounds on physical costs of overwriting – in both "single-shot" and "sequential" overwriting scenarios – are obtained from globally unitary quantum dynamics and entropic inequalities alone, all within a referential approach that grounds information content in correlations between physical system states. A heterogeneous environment model, required for consistent treatment of sequential overwriting, is introduced and used to establish and relate bounds for various cases. -- Highlights: ► Quantum dynamical description of overwriting in memory system coupled to heat bath. ► Classical source information physically instantiated in an external referent system. ► Minimum overwriting costs probed via quantum dynamics and entropic inequalities. ► Entropy and energy bounds established for single-shot and sequential overwriting.