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Area of Science:

  • Physics
  • Statistical Mechanics
  • Dynamical Systems

Background:

  • Deterministic active particles are crucial in modeling various physical phenomena.
  • Understanding their dynamics in external potentials is key to predicting system behavior.
  • Hamiltonian systems offer a framework for conservative dynamics, but their applicability to active particles requires investigation.

Purpose of the Study:

  • To analyze two models of deterministic active particles in an external potential.
  • To determine the conditions under which these models can be formulated as Hamiltonian systems.
  • To investigate the impact of particle identity on the conservation of phase volume.

Main Methods:

  • Formulation of active particle models in a fixed-speed limit.
  • Analysis of system dynamics using Hamiltonian mechanics.
  • Mathematical derivation of phase volume conservation for identical and non-identical particles.

Main Results:

  • Both models approximate a Hamiltonian system when particle speed is fixed and the potential is time-independent.
  • Identical particles exhibit conservative dynamics with conserved phase volume.
  • Non-identical particles demonstrate shrinking phase volume, even with time-independent potentials.

Conclusions:

  • The formulation of active particle systems as Hamiltonian systems is constrained by potential time-independence and particle identity.
  • Particle interactions significantly influence phase volume conservation.
  • The findings highlight fundamental differences in dynamics between identical and non-identical active particles.