We describe our recent attempts toward statistical mechanics and thermodynamics for nonequilibrium steady states (NESS) realized, e.g., in a heat conducting system. Our first result is a simple expression of the probability distribution (of microscopic states) of a NESS. Our second result is a natural extension of the thermodynamic Clausius relation and a definition of an accompanying entropy in NESS. This entropy coincides with the normalization constant appearing in the above mentioned microscopic expression of NESS, and has an expression similar to the Shannon entropy (with a further symmetrization). The NESS entropy proposed here is a clearly defined measurable quantity even in a system with a large degrees of freedom. We numerically measure the NESS entropy in hardsphere fluid systems with a heat current, by observing energy exchange between the system and the heat baths when the temperatures of the baths are changed according to specified protocols.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-005-04
Acknowledgements: We wish to thank H. Watanabe for helpful advices on numerical simulations ofhardsphere systems. Our simulation code was developed based on the 2D hard-diskcode of T. Ishiwata.15) This work was partially supported by the Global ResearchPartnership of King Abdullah University of Science and Technology (KUK-I1-005-04)(TSK,NI), by grants Nos. 19540392 (NN), 19540394 (SS) and 21015005 (SS) from theMinistry of Education, Science, Sports and Culture of Japan, and also by YukawaInternational Program for Quark-Hadron Sciences (YIPQS).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.