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Generalized Landauer bound as a universal thermodynamic entropy in continuous phase transitions
M Cristina Diamantini1, Carlo A Trugenberger2
1NiPS Laboratory, INFN, and Dipartimento di Fisica, University of Perugia, via A. Pascoli, I-06100 Perugia, Italy.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 30, 2014
Summary
Continuous phase transitions can be viewed as information erasure, lowering the Landauer bound. This reveals a universal form for thermodynamic entropy in partially ordered systems, linking memory work to information erasure.
Area of Science:
- Thermodynamics
- Information Theory
- Statistical Mechanics
Background:
- The Landauer bound establishes a fundamental physical limit on the energy required to erase information.
- Information erasure is intrinsically linked to thermodynamic costs, particularly entropy production.
Purpose of the Study:
- To explore the connection between continuous phase transitions and information erasure.
- To derive a generalized Landauer bound applicable to systems with erasure errors.
- To demonstrate the universality of thermodynamic entropy in partially ordered phases.
Main Methods:
- Viewing continuous phase transitions as information erasure processes.
- Applying information-theoretic expressions for generalized Landauer bounds.
- Analyzing the Hopfield neural network model as a case study.
Main Results:
- Continuous phase transitions can be characterized as information erasure, reducing the Landauer bound.
- A universal form for thermodynamic entropy in partially ordered phases is derived from the generalized Landauer bound.
- Thermodynamic entropy in the Hopfield network precisely matches the information-theoretic expression in terms of error probability.
Conclusions:
- Continuous phase transitions provide a physical realization of information erasure with implications for the Landauer bound.
- The study unifies concepts from thermodynamics and information theory, showing entropy's universal form in partially ordered systems.
- The Landauer bound in this context limits the work required for information storage (remembering) rather than erasure (forgetting).
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