@article{2902fb808f93473f8585bdcaef21bdee,
title = "Theory of cross phenomena and their coefficients beyond Onsager theorem",
abstract = "Cross phenomena, representing responses of a system to external stimuli, are ubiquitous from quantum to macro scales. The Onsager theorem is often used to describe them, stating that the coefficient matrix of cross phenomena connecting the driving forces and the fluxes of internal processes is symmetric. Here we show that this matrix is intrinsically diagonal when the driving forces are chosen from the gradients of potentials that drive the fluxes of their respective conjugate molar quantities in the combined law of thermodynamics including the contributions from internal processes. Various cross phenomena are discussed in terms of the present theory.",
author = "Liu, {Zi Kui}",
note = "Funding Information: The author is grateful for financial supports from many funding agencies in the United States as listed in the cited references and previous overview paper [1], plus some more recent ones including the National Science Foundation [NSF CMMI-2050069], the Department of Energy [DE-AR0001435, DE-NE0008945], and Office of Naval Research [N00014-21-1-2608]. The high-performance computing facilities include the Roar supercomputer at the Pennsylvania State University{\textquoteright}s Institute for Computational and Data Sciences (ICDS), the National Energy Research Scientific Computing Center (NERSC) supported by the US Department of Energy Office of Science User Facility operated under [DE-AC02-05CH11231], and the Extreme Science and Engineering Discovery Environment (XSEDE) supported by NSF [ACI-1548562]. The author feels privileged to work with all his current and former students and numerous collaborators over the years at Penn State and around the world as reflected in the references cited in this paper and previous overview paper [1]. He would like to particularly thank Yi Wang, Shun-Li Shang, and Jorge Sofo for simulating discussions on cross phenomena and superconductivity. The author would like to thank Johnn {\AA}gren, Graeme Murch, and Irina Belova for many stimulating discussions on cross phenomena, John Mauro, Digby MacDonald, and Susan Sinnott for critical reading of the manuscript, and inspiring communications with Graeme Ackland, Alan Allnatt, Ping Ao, H.K.D.H. Bhadeshia, Dieter Braun, Nigel Goldenfeld, Martin Gruebele, Christopher Jarzynski, Werner K{\"o}hler, Manfred Martin, Piergiulio Tempesta, Anton Van Der Ven, George Verros, and Han-Ill Yoo. Publisher Copyright: {\textcopyright} 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.",
year = "2022",
doi = "10.1080/21663831.2022.2054668",
language = "English (US)",
volume = "10",
pages = "393--439",
journal = "Materials Research Letters",
issn = "2166-3831",
publisher = "Taylor and Francis Ltd.",
number = "7",
}