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Microscopic theory of irreversible processes.

I Prigogine1, F Mayné, C George

  • 1Faculité des Sciences, Université Libre de Bruxelles, Campus Plaine U.L.B., CP.231, 1050, Brussels, Belgium.

Proceedings of the National Academy of Sciences of the United States of America
|October 1, 1977
PubMed
Summary

This study presents a microscopic theory of irreversible processes, combining dynamical and ensemble viewpoints. It introduces a Liapounov function for the second law, revealing microscopic entropy production in a universal form.

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Area of Science:

  • Statistical Mechanics
  • Theoretical Physics
  • Quantum Dynamics

Background:

  • Understanding irreversibility at a microscopic level is a fundamental challenge in physics.
  • Existing theories often struggle to reconcile deterministic microscopic laws with observed macroscopic irreversibility.

Purpose of the Study:

  • To develop a microscopic theory for irreversible processes.
  • To provide a dynamical interpretation of irreversibility by combining different theoretical viewpoints.
  • To establish a microscopic foundation for the second law of thermodynamics.

Main Methods:

  • Development of a nonunitary transformation theory based on Liouville equation symmetries.
  • Utilizing a continuous spectrum approach.
  • Application of the Friedrichs model as a field-theoretical example.

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Main Results:

  • A Liapounov function, a quadratic functional of the density operator, provides microscopic content to the second law.
  • A universal form for this functional is derived in a new dynamical representation.
  • A semi-group description is obtained, with its generator directly linked to microscopic entropy production.

Conclusions:

  • The theory offers a microscopic explanation for irreversibility and entropy production.
  • The Friedrichs model allows for explicit evaluation of entropy production and clarifies the meaning of lifetimes.
  • The framework discusses transitions from pure states to mixtures and the emergence of long tails in thermodynamic systems.