Existence proof for orthogonal dynamics and the Mori-Zwanzig formalism |
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| Authors: | Email author" target="_blank">Dror?GivonEmail author Raz?Kupferman Ole?H?Hald |
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| Institution: | (1) Institute of Mathematics, The Hebrew University of Jerusalem Givat Ram, 91904 Jerusalem, Israel;(2) Department of Mathematics, Lawrence Berkeley Laboratory, 94720 Berkeley, CA, USA;(3) Department of Mathematics, University of California, 94720 Berkeley, CA, USA |
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| Abstract: | We study the existence of solutions to the orthogonal dynamics equation, which arises in the Mori-Zwanzig formalism in irreversible
statistical mechanics. This equation generates the random noise associated with a reduction in the number of variables. IfL is the Liouvillian, or Lie derivative associated with a Hamiltonian system, andP an orthogonal projection onto a closed subspace ofL
2, then the orthogonal dynamics is generated by the operator (I −P)L. We prove the existence of classical solutions for the case whereP has finite-dimensional range. In the general case, we prove the existence of weak solutions. |
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