Phase space contraction rate for classical mixed states
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916756088422400 |
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| author | Sahbani, Mohamed Das, Swetamber Green, Jason R. |
| author_facet | Sahbani, Mohamed Das, Swetamber Green, Jason R. |
| contents | Physical systems with non-reciprocal or dissipative forces evolve according to a generalization of Liouville's equation that accounts for the expansion and contraction of phase space volume. Here, we connect geometric descriptions of these non-Hamiltonian dynamics to a recently established classical density matrix theory. In this theory, the evolution of a ``maximally mixed'' classical density matrix is related to the well-known phase space contraction rate that, when ensemble averaged, is the rate of entropy exchange with the surroundings. Here, we extend the definition of mixed states to include statistical and mechanical components, describing both the deformations of local phase space regions and the evolution of ensembles within them. As a result, the equation of motion for this mixed state represents the rate of contraction for an ensemble of dissipative trajectories. Recognizing this density matrix as a covariance matrix, its contraction rate is another measure of entropy flow characterizing nonequilibrium steady states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09361 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Phase space contraction rate for classical mixed states Sahbani, Mohamed Das, Swetamber Green, Jason R. Statistical Mechanics Soft Condensed Matter Chaotic Dynamics Physical systems with non-reciprocal or dissipative forces evolve according to a generalization of Liouville's equation that accounts for the expansion and contraction of phase space volume. Here, we connect geometric descriptions of these non-Hamiltonian dynamics to a recently established classical density matrix theory. In this theory, the evolution of a ``maximally mixed'' classical density matrix is related to the well-known phase space contraction rate that, when ensemble averaged, is the rate of entropy exchange with the surroundings. Here, we extend the definition of mixed states to include statistical and mechanical components, describing both the deformations of local phase space regions and the evolution of ensembles within them. As a result, the equation of motion for this mixed state represents the rate of contraction for an ensemble of dissipative trajectories. Recognizing this density matrix as a covariance matrix, its contraction rate is another measure of entropy flow characterizing nonequilibrium steady states. |
| title | Phase space contraction rate for classical mixed states |
| topic | Statistical Mechanics Soft Condensed Matter Chaotic Dynamics |
| url | https://arxiv.org/abs/2502.09361 |