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Steady shear flow thermodynamics based on a canonical distribution approach | | Tooru Taniguchi
; Gary P. Morriss
; | | Date: |
10 Dec 2003 | | Journal: | Phys. Rev. E 70, 056124 (2004) DOI: 10.1103/PhysRevE.70.056124 | | Subject: | Statistical Mechanics; Chaotic Dynamics | cond-mat.stat-mech nlin.CD | | Abstract: | A non-equilibrium steady state thermodynamics to describe shear flows is developed using a canonical distribution approach. We construct a canonical distribution for shear flow based on the energy in the moving frame using the Lagrangian formalism of the classical mechanics. From this distribution we derive the Evans-Hanley shear flow thermodynamics, which is characterized by the first law of thermodynamics $dE = T dS - Q dgamma$ relating infinitesimal changes in energy $E$, entropy $S$ and shear rate $gamma$ with kinetic temperature $T$. Our central result is that the coefficient $Q$ is given by Helfand’s moment for viscosity. This approach leads to thermodynamic stability conditions for shear flow, one of which is equivalent to the positivity of the correlation function of $Q$. We emphasize the role of the external work required to sustain the steady shear flow in this approach, and show theoretically that the ensemble average of its power $dot{W}$ must be non-negative. A non-equilibrium entropy, increasing in time, is introduced, so that the amount of heat based on this entropy is equal to the average of $dot{W}$. Numerical results from non-equilibrium molecular dynamics simulation of two-dimensional many-particle systems with soft-core interactions are presented which support our interpretation. | | Source: | arXiv, cond-mat/0312241 | | Other source: | [GID 144850] pmid15600709 | | Services: | Forum | Review | PDF | Favorites | |
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