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Tendency towards maximum complexity in a nonequilibrium isolated system.

X Calbet1, R López-Ruiz

  • 1Instituto de Astrofísica de Canarias Vía Láctea, s/n, E-38200 La Laguna, Tenerife, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 21, 2001
PubMed
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The study derives equations for a "tetrahedral" gas and analyzes its complexity. It finds that while complexity stays within bounds, disequilibrium decreases as the gas approaches equilibrium.

Area of Science:

  • Statistical Mechanics
  • Theoretical Physics
  • Thermodynamics

Background:

  • The López-Ruiz-Mancini-Calbet complexity is a measure of a system's deviation from equilibrium.
  • Understanding the behavior of simplified gas models provides insights into fundamental thermodynamic principles.

Purpose of the Study:

  • To derive the time evolution equations for a simplified isolated ideal gas, termed the "tetrahedral" gas.
  • To investigate the dynamical behavior of the López-Ruiz-Mancini-Calbet complexity within this system.
  • To analyze the relationship between complexity, entropy, and disequilibrium during the gas's evolution towards equilibrium.

Main Methods:

  • Derivation of time evolution equations for the "tetrahedral" gas model.
  • Analysis of the López-Ruiz-Mancini-Calbet complexity using the derived equations.

Related Experiment Videos

  • Examination of system trajectories in phase space.

    • Main Results:

    • The López-Ruiz-Mancini-Calbet complexity generally remains within its theoretical minimum and maximum bounds.
    • Specific restrictions are identified for the evolution of the isolated "tetrahedral" gas towards equilibrium.
    • A monotonic decrease in disequilibrium is observed over time, accompanying the expected increase in entropy.
    • System trajectories in phase space converge towards the maximum complexity path during equilibration.

    Conclusions:

    • The "tetrahedral" gas model exhibits constrained complexity dynamics during its approach to equilibrium.
    • The study confirms that disequilibrium is a monotonically decreasing function of time in this isolated system.
    • Phase space trajectories indicate a tendency towards maximum complexity as the system reaches equilibrium.