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Phase-space contraction rate for classical mixed states.

Mohamed Sahbani1, Swetamber Das1,2, Jason R Green1,3

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Summary
This summary is machine-generated.

Researchers linked geometric descriptions of non-Hamiltonian dynamics to classical density matrix theory. This connects phase space contraction rates to entropy exchange in physical systems, offering new insights into nonequilibrium steady states.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Non-Hamiltonian Dynamics

Background:

  • Physical systems with nonreciprocal or dissipative forces deviate from Hamiltonian dynamics.
  • Liouville's equation governs volume-preserving phase space evolution in Hamiltonian systems.
  • Non-Hamiltonian systems require a generalized Liouville equation accounting for phase space volume changes.

Purpose of the Study:

  • To connect geometric descriptions of non-Hamiltonian dynamics with classical density matrix theory.
  • To extend the definition of mixed states to encompass statistical and mechanical components.
  • To establish a framework for understanding entropy flow in nonequilibrium steady states.

Main Methods:

  • Utilizing a recently established classical density matrix theory.
  • Generalizing Liouville's equation for systems with nonreciprocal or dissipative forces.
  • Defining mixed states by incorporating statistical and mechanical components.

Main Results:

  • The evolution of a "maximally mixed" classical density matrix is linked to phase space contraction rate.
  • Ensemble averaging of the phase space contraction rate yields the entropy exchange rate with surroundings.
  • The equation of motion for the extended mixed state describes the contraction rate of dissipative trajectories.

Conclusions:

  • The density matrix, when recognized as a covariance matrix, provides a measure of entropy flow.
  • This approach characterizes nonequilibrium steady states by their contraction rates.
  • The study offers a unified geometric and statistical mechanical perspective on dissipative systems.