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Intrinsic randomness and intrinsic irreversibility in classical dynamical systems
1Faculté des Sciences, Campus Plaine Université Libre de Bruxelles, Boulevard du Triomphe, 1050 Brussels, Belgium.
Summary
This study introduces "intrinsic irreversibility" in dynamic systems by reformulating the second law of thermodynamics. This selection rule breaks time-reversal symmetry, distinguishing possible from impossible initial conditions based on information content.
Area of Science:
- Statistical Mechanics
- Dynamical Systems Theory
- Thermodynamics
Background:
- Previous work established methods to derive dissipative Markov processes from dynamic intrinsically random systems.
- Unitary evolution in these systems can transform into two distinct Markov processes, leading to equilibrium at t → +∞ or t → -∞.
Purpose of the Study:
- To lift the degeneracy between forward and backward time evolution in intrinsically random systems.
- To formulate the second principle of thermodynamics as a selection rule applicable to these systems.
- To establish a microscopic formulation of the second law of thermodynamics.
Main Methods:
- Formulation of the second principle as a selection rule for intrinsically random systems.
- Exclusion of unrealizable states based on the selection rule.
- Characterization of admitted initial conditions by entropy, quantifying preparation information.
Main Results:
- The selection rule excludes states not invariant under velocity inversion, breaking time-reversal symmetry.
- This results in a property termed "intrinsic irreversibility" in the dynamical systems.
- Initial conditions selected by the second law require finite information for preparation, while rejected conditions require infinite information.
Conclusions:
- The proposed formulation provides a microscopic basis for the second law of thermodynamics in specific classes of dynamical systems.
- Intrinsic irreversibility emerges from the selection rule applied to intrinsically random systems.
- The concept of information required for state preparation is central to defining the directionality of time.
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