Sciweavers

Share
CORR
2010
Springer

Balanced distribution-energy inequalities and related entropy bounds

9 years 12 months ago
Balanced distribution-energy inequalities and related entropy bounds
Let A be a self-adjoint operator acting over a space X endowed with a partition. We give lower bounds on the energy of a mixed state from its distribution in the partition and the spectral density of A. These bounds improve with the renement of the partition, and generalize inequalities by Li-Yau and Lieb-Thirring for the Laplacian in Rn . They imply an uncertainty principle, giving a lower bound on the sum of the spatial entropy of , as measured from X, and some spectral entropy, with respect to its energy distribution. On Rn , this yields lower bounds on the sum of the entropy of the densities of and its Fourier transform. A general log-Sobolev inequality is also shown. It holds on mixed states, without Markovian or positivity assumption on A.
Michel Rumin
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CORR
Authors Michel Rumin
Comments (0)
books