Phase space view of quantum mechanical systems and Fisher information

Nagy, Á.

doi:10.1016/j.physleta.2016.05.006

Physics Letters A

2016

DOI: 10.1016/j.physleta.2016.05.006

|View full text |Cite

Phase space view of quantum mechanical systems and Fisher information

Á. Nagy

Abstract: Pennini and Plastino showed that the form of the Fisher information generated by the canonical distribution function reflects the intrinsic structure of classical mechanics. Now, a quantum mechanical generalization of the Pennini -Plastino theory is presented based on the thermodynamical transcription of the density functional theory. Comparing to the classical case, the phase-space Fisher information contains an extra term due to the position dependence of the temperature.However, for the special case of cons… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2017

2018

Publication Types

Select...

Article3

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Steric charge

Liu

et al. 2018

Phys. Chem. Chem. Phys.

View full text Add to dashboard Cite

The steric effect is one of the most widely used chemical concepts in chemistry, yet a generally accepted implementation of its formulation and quantification from a theoretical viewpoint, if even possible, is still an unaccomplished task. Based on the energetics viewpoint of our earlier proposal using the Weizsäcker kinetic energy as a quantification of the energy contribution from the steric effect as well as our recent work using steric force as a reliable local descriptor to account for the origin of the stereoselective propensity in chemical reactions, in this work, we systematically examine the local behavior and general applicability of another closely related quantity, steric charge. To this end, its physical origin and physiochemical properties are formalized and highlighted, and are shown with numerical illustrations and verifications. To showcase its usefulness in appreciating chemical reactivity, we present three case studies of steric charge in this work. In the case of ethane flexible rotation, we found that the eclipsed conformer is more sterically charged than the staggered conformer, leading to the reduced stability and higher energy of the former. For the case of S2 reactions, a remarkable linear correlation has been obtained between the steric charge on the central atom in the transition state and the reaction barrier height of S2 reactions, in good agreement with experimental findings. In the case of stereoselectivity properties for the nucleophilic addition of carbonyl compounds, we found that steric charge is equally applicable as steric force to justify the stereoselective origin for the nucleophilic attack to the carbonyl carbon atom with different substituent groups. Put together, our results from the present study should pave the way towards the general use of steric charge, together with steric energy and steric force, as an insightful global and local descriptor to appreciate and quantify chirality and stereoselectivity related phenomena in chemical processes and transformations.

show abstract

Steric charge

Liu

et al. 2018

Phys. Chem. Chem. Phys.

View full text Add to dashboard Cite

show abstract

Quantification and origin of cooperativity: insights from density functional reactivity theory

Rong

Zhao

et al. 2018

Phys. Chem. Chem. Phys.

View full text Add to dashboard Cite

Cooperativity is a widely used chemical concept whose existence is ubiquitous in chemical and biological systems but whose quantification is still controversial and origin much less appreciated. In this work, using the interaction energy of a molecular system, which is composed of multiple copies of a building block, we propose a quantitative measurement to evaluate the cooperativity effect. This quantification approach is then applied to six molecular systems, i.e., water cluster, argon cluster, protonated water cluster, zinc atom cluster, water cluster on top of a graphene sheet, and alpha helix of glycine amino acids, each with up to 20 copies of the building block. Cooperativity is seen in all these systems. Both positive and negative cooperativity effects are observed. Employing the two energy partition schemes in density functional theory and the information-theoretic quantities such as Shannon entropy, Fisher information, information gain, etc., we then examine the origin of the cooperativity effect for these systems. Strong linear correlations between the cooperativity measure and some of these theoretical quantities have been unveiled. With these correlations, we are able to quantitatively account for their origin of cooperativity. Our results show that the interactions governing the existence and validity of the cooperativity effect are complicated. An opposite mechanism in enthalpy-entropy compensation for positive and negative cooperativity has been unveiled. These results should provide new insights and understandings from a different viewpoint about the nature and origin of cooperativity to appreciate this vastly important chemical concept.

show abstract

Fisher information and topological pressure

Godó

Nagy

2017

Journal of Mathematical Physics

View full text Add to dashboard Cite

The relationship between the Fisher information and the topological pressure is explored. The new concept of topological Fisher information is introduced and the relation between the topological pressure and the topological Fisher information is derived. In the special case of expanding maps, a relation between the topological and the dimensional Fisher information is obtained. Relations between the Legendre transforms of the topological and the dimensional Fisher information are also formulated.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Phase space view of quantum mechanical systems and Fisher information

Cited by 3 publications

References 23 publications

Steric charge

Steric charge

Quantification and origin of cooperativity: insights from density functional reactivity theory

Fisher information and topological pressure

Contact Info

Product

Resources

About