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Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...
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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Physics
  • Complex Systems

Background:

  • Generalized Langevin equations (GLEs) model systems with memory effects.
  • Dissipationless systems present unique dynamic behaviors.
  • Power-law tails in inertial kernels (k(t) ~ t^-κ) influence system dynamics.

Purpose of the Study:

  • Analyze dynamic properties of dissipationless GLEs.
  • Investigate the impact of power-law inertial kernels on thermalization and particle motion.
  • Examine system behavior under external forces.

Main Methods:

  • Theoretical analysis of dissipationless generalized Langevin equations.
  • Investigation of systems with fluid inertial kernels k(t) ~ t^-κ.
  • Analysis of particle motion and velocity statistics for different κ values.

Main Results:

  • For κ>1, no thermalization occurs; particle motion is ballistic and non-ergodic.
  • For 0<κ<1, weak thermalization emerges with fluctuations and attractive potentials.
  • Absence of dissipation is confirmed by diverging particle velocity under constant force.

Conclusions:

  • System dynamics strongly depend on the exponent κ of the power-law kernel.
  • Dissipationless systems can exhibit non-ergodic behavior and unusual thermalization properties.
  • The absence of dissipation prevents asymptotic settling velocities under external forces.