Zeno's paradox and black hole information loss problem

We develop a conceptual parallel between the black hole information problem and Zeno's paradox, highlighting the role of limiting procedures that turn formally infinite constructions into finite physical observables. Building on the replica--wormhole paradigm, we move beyond unitarity restoration to formulate a quantitative notion of irreversibility in Hawking radiation. Our main result is a modular thermodynamic framework for black-hole evaporation, in which modular entropy, entanglement capacity, and relative entropy assume thermodynamic roles. The monotonicity of relative entropy furnishes a generalized second law that determines the arrow of evolution in replica space. We further resolve the apparent tension between the replica method and the quantum no-cloning theorem by interpreting replicas as ensemble representations rather than physical copies of an unknown state, thereby clarifying the operational meaning of gravitational path integrals. A key message of this work is that non-additivity in Tsallis statistics provides an information-theoretic analogue of the correlations induced by replica wormholes.