We review the notions of the dissipation function and T-mixing for noninvariant measures, recently introduced for nonequilibrium molecular dynamics models. We provide a dynamical-systems interpretation for the dissipation function and related results, providing new perspectives into results such as the second-law inequality. We then consider the problem of relaxation within this framework—the convergence of time averages along single phase– space trajectories, as opposed to the convergence of ensemble averages. As a first step in this direction, we observe that T-mixing implies convergence to a unique asymptotic ensemble, independent on the initial ensemble. In particular, the initial ensemble can be concentrated arbitrarily closely to any point in phase–space.
A dynamical-systems interpretation of the dissipation function, T-mixing and their relation to thermodynamic relaxation / Jepps, Owen G; Rondoni, Lamberto. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - STAMPA. - 49:15/154002(2016), pp. 1-20. [10.1088/1751-8113/49/15/154002]
A dynamical-systems interpretation of the dissipation function, T-mixing and their relation to thermodynamic relaxation
RONDONI, Lamberto
2016
Abstract
We review the notions of the dissipation function and T-mixing for noninvariant measures, recently introduced for nonequilibrium molecular dynamics models. We provide a dynamical-systems interpretation for the dissipation function and related results, providing new perspectives into results such as the second-law inequality. We then consider the problem of relaxation within this framework—the convergence of time averages along single phase– space trajectories, as opposed to the convergence of ensemble averages. As a first step in this direction, we observe that T-mixing implies convergence to a unique asymptotic ensemble, independent on the initial ensemble. In particular, the initial ensemble can be concentrated arbitrarily closely to any point in phase–space.File | Dimensione | Formato | |
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https://hdl.handle.net/11583/2637519
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