LOWER BOUNDS FOR THE HELMHOLTZ FUNCTION.

Abstract

A mathematical theorem is established for traces of products of bounded Hermitian and definiteoperators. This theorem is applied to the equilibrium partition function by exploiting an infinite product representation of the exponential function of the sum of two operators. As a result, a set of inequalities is established which yields a set of upper bonds for the partition function. This result is invariant to the particle statistics of the system. A general argument yields the result that the classical Helmholtz free energy function serves as a lower bound to the corresponding quantum result. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 15, 1964
Accession Number
AD0606146

Entities

People

  • Sideny Golden

Organizations

  • Brandeis University

Tags

DTIC Thesaurus Topics

  • Data Science
  • Energy
  • Exponential Functions
  • Free Energy
  • Inequalities
  • Information Science
  • Mathematics
  • Particles
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Theoretical Analysis.

Technology Areas

  • Quantum Computing