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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
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Landauer Bound and Continuous Phase Transitions.

Maria Cristina Diamantini1

  • 1NiPS Laboratory, INFN and Dipartimento di Fisica e Geologia, University of Perugia, Via A. Pascoli, I-06100 Perugia, Italy.

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|July 29, 2023
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Summary
This summary is machine-generated.

Information erasure is linked to continuous phase transitions, where system ordering acts as erasure. This connection extends the Landauer bound to analog computing, setting work limits for memory systems.

Keywords:
Landauer boundanalog computingcontinuous phase transitions

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Area of Science:

  • Thermodynamics
  • Information Theory
  • Computational Science

Background:

  • Continuous phase transitions are characterized by an order parameter ranging from 0 (disordered) to 1 (ordered).
  • Information erasure, such as resetting bits, can be viewed as a process of ordering a system.
  • The Landauer bound relates the minimum energy required for information erasure to thermodynamic principles.

Purpose of the Study:

  • To establish a relationship between information erasure and continuous phase transitions.
  • To generalize the Landauer bound for information erasure to analog computing systems.
  • To explore the implications of this relationship for associative memory models.

Main Methods:

  • Analyzing the order parameter in continuous phase transitions.
  • Applying information-theoretic expressions for the generalized Landauer bound.
  • Demonstrating the relationship using the Hopfield neural network model.
  • Extending the bound to analog systems by considering analog variable erasure.

Main Results:

  • A direct relation is established between information erasure and continuous phase transitions.
  • The thermodynamic entropy in partially ordered phases is described by a generalized Landauer bound.
  • The Landauer bound is shown to limit the work required for 'remembering' in associative memory.
  • The bound is extended to analog computing, with entropy production related to configurational volume.

Conclusions:

  • Information erasure and continuous phase transitions are fundamentally linked.
  • The Landauer bound can be extended to analog computing systems.
  • This framework provides insights into the physical limits of computation and memory.