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Geometric structure of thermal cones.

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The second law of thermodynamics defines a time

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Quantum Information Theory

Background:

  • The second law of thermodynamics dictates the directionality of time.
  • This asymmetry partitions a system's state space into past, future, and incomparable regions.
  • Thermal cones represent these regions of thermodynamic evolution.

Purpose of the Study:

  • To analyze the structure of thermal cones in classical systems.
  • To explicitly construct the past thermal cone and incomparable region for d-dimensional systems.
  • To generalize thermal cone construction for probabilistic transformations.

Main Methods:

  • Analysis of thermal cone structures for classical systems.
  • Explicit construction of past thermal cones and incomparable regions.
  • Utilizing thermodynamic monotones (volumes of thermal cones) for analysis.
  • Generalization to probabilistic transformations.

Main Results:

  • Explicit construction of the past thermal cone and incomparable region for d-dimensional classical systems.
  • Detailed analysis of thermal cone behavior using volumes as thermodynamic monotones.
  • Demonstrated applicability to majorization-based resource theories (entanglement, coherence).

Conclusions:

  • The study provides a clear geometric and quantitative understanding of thermodynamic arrows of time.
  • Findings offer insights into state transformations in thermodynamics and related resource theories.
  • The generalization accommodates probabilistic state transitions, broadening applicability.