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  • 1Atomic and Laser Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK.

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Summary
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This study redefines thermal equilibrium for quantum systems by focusing on observable properties rather than the entire system state. This new approach, maximizing Shannon entropy for observables, offers experimentally accessible insights into thermalization.

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Area of Science:

  • Quantum statistical mechanics
  • Quantum information theory

Background:

  • The standard definition of thermal equilibrium in statistical mechanics relies on maximizing von Neumann entropy, which is experimentally challenging to probe.
  • Existing definitions are often inaccessible for direct experimental verification in quantum systems.

Purpose of the Study:

  • To propose a new, experimentally accessible notion of thermal equilibrium for quantum systems.
  • To characterize thermal equilibrium based on observable properties rather than the full quantum state.
  • To explore the connection between this new definition and established concepts like Gibbs ensembles and the Eigenstate Thermalization Hypothesis.

Main Methods:

  • Defining a new notion of thermal equilibrium through the maximization of Shannon entropy for arbitrary observables.
  • Analyzing the relationship between this observable-based equilibrium and traditional Gibbs ensembles.
  • Applying the framework to closed quantum systems to identify observables exhibiting thermal equilibrium properties.

Main Results:

  • A novel definition of thermal equilibrium is introduced, focusing on the Shannon entropy of observables.
  • The study demonstrates that a class of observables in closed quantum systems inherently exhibits thermal equilibrium properties.
  • Explicit recipes for constructing these observables are provided.

Conclusions:

  • The proposed observable-centric approach offers a practical alternative for probing thermal equilibrium in quantum experiments.
  • This work establishes a clear link between Shannon entropy maximization for observables and the Eigenstate Thermalization Hypothesis.
  • The findings provide new tools for understanding thermalization in quantum statistical mechanics.