# Accession Number:

## AD0606146

# Title:

## LOWER BOUNDS FOR THE HELMHOLTZ FUNCTION.

# Descriptive Note:

## Technical rept. no. 10,

# Corporate Author:

## BRANDEIS UNIV WALTHAM MASS

# Personal Author(s):

# Report Date:

## 1964-09-15

# Pagination or Media Count:

## 8.0

# 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