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• W3169576657 abstract "Physical systems that dissipate, mix and develop turbulence also irreversibly transport statistical density. In statistical physics, however, laws for these processes have a mathematical form and tractability that depends on whether the description is classical or quantum mechanical. Here, using the techniques of nonlinear dynamics, we establish a theory for density transport in any classical dynamical system that is analogous to the density matrix formulation of quantum mechanics. Defining states in terms of a classical density matrix leads to generalizations of Liouville's theorem and Liouville's equation, establishing an alternative computationally-tractable foundation for nonequilibrium statistical mechanics. The formalism is complete with classical commutators and anti-commutators that embed measures of local instability and chaos and are directly related to Poisson brackets when the dynamics are Hamiltonian. It also recovers the traditional Liouville equation and the Liouville theorem by imposing trace preservation or Hamiltonian dynamics. Applying this formalism to models that are driven, transient, dissipative, regular, and chaotic, suggests the potential for broad applications to dynamical systems across physics." @default.
• W3169576657 created "2021-06-22" @default.
• W3169576657 creator A5048363389 @default.
• W3169576657 creator A5074833931 @default.
• W3169576657 date "2021-06-10" @default.
• W3169576657 modified "2023-09-27" @default.
• W3169576657 title "Density matrix formulation of dynamical systems" @default.
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• W3169576657 hasPublicationYear "2021" @default.
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