Tendency towards maximum complexity in a nonequilibrium isolated system

TLDR

The study focuses on the dynamical behavior of the López‑Ruiz‑Mancini‑Calbet complexity. The paper investigates the behavior of the López‑Ruiz‑Mancini‑Calbet complexity in the tetrahedral gas system. The authors derive the time‑evolution equations for a simplified isolated ideal gas, the “tetrahedral” gas. The study shows that complexity remains bounded between minimum and maximum values, disequilibrium decreases monotonically, and trajectories converge to the maximum‑complexity path as the system approaches equilibrium. © 1995, Phys.

Abstract

The time evolution equations of a simplified isolated ideal gas, the "tetrahedral" gas, are derived. The dynamical behavior of the López-Ruiz-Mancini-Calbet complexity [R. López-Ruiz, H. L. Mancini, and X. Calbet, Phys. Lett. A 209, 321 (1995)] is studied in this system. In general, it is shown that the complexity remains within the bounds of minimum and maximum complexity. We find that there are certain restrictions when the isolated "tetrahedral" gas evolves towards equilibrium. In addition to the well-known increase in entropy, the quantity called disequilibrium decreases monotonically with time. Furthermore, the trajectories of the system in phase space approach the maximum complexity path as it evolves toward equilibrium.