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EEG Mu Rhythm in Typical and Atypical Development
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Statistical ensembles without typicality.

Paul Boes1, Henrik Wilming2, Jens Eisert2

  • 1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195, Berlin, Germany. pboes@zedat.fu-berlin.de.

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|March 11, 2018
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Summary
This summary is machine-generated.

This study derives maximum-entropy ensembles using an operational approach. It shows that possible system-environment transitions are those allowed by maximum-entropy states, independent of typicality.

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Area of Science:

  • Statistical mechanics
  • Thermodynamics
  • Information theory

Background:

  • Maximum-entropy ensembles are fundamental in statistical mechanics.
  • Existing justifications for their use lack full consensus.
  • A rigorous derivation is needed for operational applications.

Purpose of the Study:

  • To derive maximum-entropy ensembles from a strictly operational perspective.
  • To investigate the role of system-environment transitions under partial information.
  • To provide a novel justification for maximum-entropy ensembles.

Main Methods:

  • Investigated transitions between a system and its environment with partial information.
  • Analyzed the set of possible transitions, encoding thermodynamic laws.
  • Derived ensembles based on operational constraints.

Main Results:

  • The set of possible transitions is precisely that of maximum-entropy states for system and environment.
  • This result holds even with only partial information.
  • The derivation is independent of typicality or information-theoretic measures.

Conclusions:

  • Provides a novel operational derivation of maximum-entropy ensembles.
  • Justifies the widespread use of these ensembles in statistical mechanics.
  • Offers a new perspective on the foundations of statistical thermodynamics.