Heat Transfer and Entropy Production as Applied to Planar Poiseuille Flow



Principal Investigator

Denis Evans

Research School of Chemistry


Gary Ayton

Research School of Chemistry


r61 - PC


The Second Law of thermodynamics states that spontaneous irreversible processes will generate entropy, but applies only to very large systems studied over microscopically long times. For small systems, for example molecular clusters, or for sub-regions as in a liquid/solid interface, the Second Law must be modified to include the possibility of spontaneous processes that involve entropy decreases over short measurement times.

This project is an extension of the examination of the origins of heat transport and viscous heating in narrow channel fluid flows. When a fluid is forced to flow between two stationary flat plates, viscous heating means that entropy is produced within the channel. As we understand the contributions to the heat flux in this system, we can now use this system as a template to examine the origins of localised entropy production in non-equilibrium steady state systems.




What are the results to date and the future of the work?

The results to date are twofold. Firstly, we have confirmed that in systems with spatially varying strain rates there are indeed contributions to the heat flux that do not originate from temperature variations, and that these contributions do not vanish in the weak flow limit. The results of this work are to be published in Molecular Physics.

Secondly, we have exploited hydrodynamics and irreversible thermodynamics to demonstrate the existence of a localised version of Second Law of Thermodynamics, known as the Localised Fluctuation Theorem (LFT). By meshing hydrodynamics and non-equilibrium molecular dynamics, we can now measure local entropy productions, and we find that, indeed, the Second Law of Thermodynamics becomes probabilistic for microscopically small regions examined for short times. The theoretical predictions of LFT have been confirmed by molecular dynamics simulation.

This result has profound consequences for any chemical or physical process that occurs over short times and in small regions; for example adsorption, and solvation. Any process that occurs over the time scale of entropy production fluctuations is intrinsically coupled to entropy increases, as well as entropy decreases. We are currently examining how entropy production fluctuations are correlated to short time molecular phenomena.

Appendix A -



What computational techniques are used?

Non-equilibrium molecular dynamics (NEMD) computer simulations, where an atomic fluid is placed between thermostatting walls, have been coupled with hydrodynamic (HYD) heat and entropy production calculations. Simulation development is ongoing, and the NEMD/HYD algorithm has been crucial in calculating weak field heat fluxes.


G. Ayton, O. G. Jepps and D. Evans, On the Validity of Fourier's Law in Systems with Spatially Varying Strain Rates, accepted to Molecular Physics.

G. Ayton, D. J. Searles and D. J. Evans, A Localised Fluctuation Theorem, submitted to Physical Review Letters and available at http://xxx.lanl.gov/abs/cond-mat/9901256.

- Appendix A