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Limits of information flow between classically interacting particles.

Miles Miller-Dickson1, Christopher Rose1

  • 1Brown University, School of Engineering, Providence, Rhode Island 02906, USA.

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|April 18, 2026
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Summary
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We propose a new measure for information flow in physical systems, crucial for stochastic thermodynamics and quantum information science. This measure, derived from mutual information, acts as a lower bound on channel capacity, offering insights into the physical nature of information.

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Area of Science:

  • Physics
  • Information Science
  • Thermodynamics

Background:

  • Understanding information flow in physical interactions is key to stochastic thermodynamics and quantum information science.
  • Accurate accounting of bits and qubits deepens the understanding of information's physical nature.

Purpose of the Study:

  • Propose a novel measure for quantifying information flow in physical systems.
  • Establish a lower bound on channel capacity between a particle and its environment.
  • Interpret this bound using communication theory as a signal-to-noise ratio.

Main Methods:

  • Utilizing a saddle-point solution of mutual information to define the information flow measure.
  • Calculating the measure as P₀/2E₀ (nats/sec) in a zero average momentum frame.
  • Applying a communication theory framework to interpret the bound.

Main Results:

  • The proposed measure provides a lower bound on channel capacity.
  • The measure is interpretable as a signal-to-noise ratio.
  • This quantification is effective for early-time information flow in particle-thermal bath interactions.

Conclusions:

  • The developed measure offers a new perspective on information flow in physical systems.
  • This approach bridges concepts from thermodynamics and information theory.
  • The findings have implications for both stochastic thermodynamics and quantum information science.