Enhancing Variational Informational Principles: A Complexified Approach with Arbitrary Order Norms

D. Bernal-Casas () and José M. Oller
Additional contact information
D. Bernal-Casas: Department of Information and Communication Technologies, Universitat Pompeu Fabra, 08018 Barcelona, Spain
José M. Oller: Department of Genetics, Microbiology and Statistics, Faculty of Biology, Universitat de Barcelona, 08028 Barcelona, Spain

Mathematics, 2025, vol. 13, issue 19, 1-15

Abstract: This paper offers an innovative exploration of variational informational principles by incorporating complexification and studying norms of arbitrary order, thereby surpassing the limitations of the conventional L 2 norm. For years, variational principles have been vital for deriving fundamental results in both physics and information theory; however, our proposed framework represents a significant advancement by utilizing complex variables to enhance our understanding of information measures. By employing complex numbers, we introduce a sophisticated structure that captures phase information, thereby significantly improving the potential applicability and scope of variational principles. The inclusion of norms of arbitrary order further expands the scope of optimization problems in information theory, leading to the potential for more creative solutions. Our findings indicate that this extended framework not only maintains the essential characteristics of traditional variational principles but also reveals valuable insights into the complex interplay between complexity, information, and optimization. We conclude with a thoughtful discussion of potential applications and future research directions, emphasizing the transformative impact that complexified variational principles, together with norms of arbitrary order, could have on the study of quantum dynamics.

Keywords: Fisher information; variational principles; L p norms; information theory; Schrödinger equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/19/3160/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/19/3160/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:19:p:3160-:d:1763702

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().