Steady shear flow thermodynamics based on a canonical distribution approach
| dc.creator | Taniguchi, Tooru | |
| dc.creator | Morriss, Gary P. | |
| dc.date | 2003-12-10 | |
| dc.date.accessioned | 2026-07-07T02:55:19Z | |
| dc.date.available | 2026-07-07T02:55:19Z | |
| dc.description | 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 $dE = T dS - Q dγ$ relating infinitesimal changes in energy $E$, entropy $S$ and shear rate $γ$ 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. | |
| dc.description | 23 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0312241 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0312241 | |
| dc.identifier | Phys. Rev. E 70, 056124 (2004) | |
| dc.identifier | doi:10.1103/PhysRevE.70.056124 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/22897 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Chaotic Dynamics | |
| dc.title | Steady shear flow thermodynamics based on a canonical distribution approach | |
| dc.type | text |