Journal of Mathematical Physics

Derivation of a Lower Bound on the Free Energy

Robert H. T. Yeh

Published May 1, 1970• 4 citations

Abstract

For a Hamiltonian with a ground-state energy E0 = 0, we show that for any normalized state |ψ〉, 〈ψ| e−βH |ψ〉≤e−β〈ψ|H|ψ〉a, where a=exp [−β 〈ψ| H 2 |ψ〉/〈ψ| H |ψ〉]. From this inequality, a general formula for a lower bound on the free energy is derived.

DOI: 10.1063/1.1665290

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