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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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Molecular Entanglement and Electrospinnability of Biopolymers
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Inverse spin glass and related maximum entropy problems.

Michele Castellana1, William Bialek2

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Summary

We introduce an inverse spin glass model where correlations are chosen from a distribution to infer coupling constants. This approach reveals block structures and offers solutions for complex statistical mechanics problems.

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Area of Science:

  • Statistical mechanics
  • Complex systems modeling
  • Machine learning

Background:

  • Ising models represent maximum entropy distributions for binary variables with pairwise correlations.
  • Understanding inhomogeneous systems requires novel approaches beyond standard correlation matrix analysis.

Purpose of the Study:

  • To develop an inverse spin glass model for inferring coupling constants from correlation distributions.
  • To explore the block structure in coupling constants and solve the inverse problem explicitly.
  • To generate a phase diagram for the distribution of correlations in inhomogeneous systems.

Main Methods:

  • Constraining the distribution of correlations rather than the full correlation matrix.
  • Inferring coupling constants by inverting the spin glass model.
  • Analyzing the emergent block structure in the coupling constant space.

Main Results:

  • An explicit solution for the inverse problem of inferring coupling constants from correlation distributions.
  • Identification of a block structure in the space of coupling constants.
  • Generation of a phase diagram based on measurable moments of the correlation distribution.

Conclusions:

  • The inverse spin glass model provides a framework for building models of complex systems, particularly in nonequilibrium statistical mechanics.
  • This approach is expected to be valuable for modeling networks of real neurons.
  • The method offers a new perspective on analyzing systems where correlations are drawn from a distribution.