Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Zeno's paradox and black hole information loss problem

Xian-Hui Ge

TL;DR

The paper draws an analogy between Zeno's paradox and the black hole information loss problem to motivate a limiting-procedure framework for observing finite information measures in black-hole evaporation. Building on the replica-wormhole paradigm in JT gravity, it develops a modular-thermodynamic description of evaporation, introducing modular entropy $S_m$, entanglement capacity $C_n$, and a relative-entropy-based generalized second law that together quantify irreversibility and information flow beyond strict unitarity. It clarifies that replicas are mathematical constructs (ensemble representations) rather than physical copies, thereby resolving apparent clashes with the no-cloning theorem and tying replica correlations to non-factorization and non-additivity akin to Tsallis statistics. The main contributions include a thermodynamic-like formalism for replica space, an $n$-dependent generalized second law, and a concrete interpretation of replica wormholes as a geometric realization of information correlations that restore the Page curve. The work provides a principled framework for understanding information preservation in quantum gravity with potential implications for gravitational path integrals and the fundamental organizing principles of black-hole evaporation.

Abstract

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.

Zeno's paradox and black hole information loss problem

TL;DR

The paper draws an analogy between Zeno's paradox and the black hole information loss problem to motivate a limiting-procedure framework for observing finite information measures in black-hole evaporation. Building on the replica-wormhole paradigm in JT gravity, it develops a modular-thermodynamic description of evaporation, introducing modular entropy , entanglement capacity , and a relative-entropy-based generalized second law that together quantify irreversibility and information flow beyond strict unitarity. It clarifies that replicas are mathematical constructs (ensemble representations) rather than physical copies, thereby resolving apparent clashes with the no-cloning theorem and tying replica correlations to non-factorization and non-additivity akin to Tsallis statistics. The main contributions include a thermodynamic-like formalism for replica space, an -dependent generalized second law, and a concrete interpretation of replica wormholes as a geometric realization of information correlations that restore the Page curve. The work provides a principled framework for understanding information preservation in quantum gravity with potential implications for gravitational path integrals and the fundamental organizing principles of black-hole evaporation.

Abstract

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.

Paper Structure

This paper contains 6 sections, 61 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Replica wormhole and wormhole saddle point
  3. Replica trick and quantum no-cloning theorem
  4. Modular entropy and entanglement capacity
  5. Relative entropy and generalized second law
  6. Summary and discussion

Figures (1)

  • Figure 1: Schematic diagram for the gravitational path integral. The indices $i$ and $j$ represent different states. The gravitational region is shown in blue and the EoW brane is shown in red: (a) The bodunary conditions for the purity \ref{['eq6']}; (b) and (c) are two different filling ways.