https://doi.org/10.1140/epjp/s13360-023-04000-6
Regular Article
On stability of thermodynamic systems: a fluctuation theory perspective
1
INFN-Laboratori Nazionali di Frascati, Via E. Fermi 40, 00044, Frascati (Rome), Italy
2
Avantika University, 456006, Ujjain, India
a
bhupendray2.tiwari.phd@iitkalumni.org
Received:
9
December
2022
Accepted:
23
February
2023
Published online:
13
June
2023
In this paper, we study the stability analysis of thermodynamic configurations in the space of matrices, arising from an embedding of real thermodynamic spaces under fluctuations of the model parameters. The model parameters under the present consideration are the thermal expansion parameter, and the isothermal and/or adiabatic compressibilities. Under parametric fluctuations, we examine the matrix valued Fourier series and Fourier transforms by invoking the limiting local and global stability structures. The resulting embeddings are taken as the specific heat capacity at a constant pressure and that of at a constant volume, their ratio, and Mayer’s relation. In conclusion, by examining the Fourier series and Fourier transforms in the space of regular matrices, we have explicated the stability properties of such configurations under fluctuations of experimentally measurable quantities. To be specific, our method determines positions of the underling critical phenomena such as the phase transition points/ curves, bifurcations, cross-overs and others. Indeed, we provide highlights for possible geometric extensions by discussing the standing notions, such as the Onsager region, local stability structures and global parameter space invariants, and others. Moreover, an extension of our approach for the thermodynamic systems away from attractor fixed points may be examined for moduli space configurations through certain geometric and algebraic techniques. Finally, we have discussed prospective research directions toward the existence of the series representations of matrix valued functions, series expansions with discontinuities, integral kernels, and their multi-matrix extensions in the light of thermodynamic (in)stabilities under fluctuations of the system parameters.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
