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Energy diagrams are important to understand the dynamics of a system. The topology of an energy diagram helps illustrate the equilibrium points of the system.
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The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or the other depending upon the temperature of the substance in question. Likewise, some chemical reactions can also exhibit temperature-dependent spontaneities. To illustrate this concept, the equation relating free energy change to the enthalpy and entropy changes for the process is considered:
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Related Experiment Video

Updated: Sep 26, 2025

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes
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Free-energy barriers in the Sherrington-Kirkpatrick model.

T Aspelmeier1, M A Moore2

  • 1Institute for Theoretical Physics, Georg-August-Universität Göttingen, D37077 Göttingen, Germany.

Physical Review. E
|April 16, 2022
PubMed
Summary

The Sherrington-Kirkpatrick (SK) model

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • The Sherrington-Kirkpatrick (SK) model describes a disordered magnetic system.
  • Understanding its free-energy landscape is crucial for explaining its complex behavior.

Purpose of the Study:

  • To analyze the free-energy landscape of the SK Ising spin glass using Thouless-Anderson-Palmer (TAP) equations.
  • To investigate the stability of different states and the associated free-energy barriers.

Main Methods:

  • Calculation of free-energy barriers between minima and associated saddle points.
  • Analysis of states with free energies above a critical threshold (f > f_c).
  • Examination of states with marginal stability (f < f_c) using scaling arguments.

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Main Results:

  • States with f > f_c have very small free-energy barriers, decreasing as 1/N^2, indicating instability.
  • These unstable states are rarely observed in large-scale numerical simulations.
  • Marginally stable states possess larger barriers (at least O(1)), consistent with numerical findings.

Conclusions:

  • Small free-energy barriers in unstable states explain their absence in numerical studies.
  • Marginal stability is key for states observed in simulations of the SK model.
  • For f < f_c, barriers may scale as N^(1/3), potentially aligning with Viana-Bray model observations.