Second Law-Like Inequalities with Quantum Relative Entropy: An Introduction

Details Second Law-Like Inequalities with Quantum Relative Entropy: An Introduction Second Law-Like Inequalities with Quantum Relative Entropy: An Introduction

2012-02-05

arxiv.org/abs/1202.0983v2

Physics

Condensed Matter

Statistical Mechanics

To appear in "Lectures on Quantum Computing, Thermodynamics and Statistical Physics," Kinki University Series on Quantum Compu

Scientific paper

We review the basic properties of the quantum relative entropy for finite-dimensional Hilbert spaces. In particular, we focus on several inequalities that are related to the second law of thermodynamics, where the positivity and the monotonicity of the quantum relative entropy play key roles; these properties are directly applicable to derivations of the second law (e.g., the Clausius inequality). Moreover, the positivity is closely related to the quantum fluctuation theorem, while the monotonicity leads to a quantum version of the Hatano-Sasa inequality for nonequilibrium steady states. Based on the monotonicity, we also discuss the data processing inequality for the quantum mutual information, which has a similar mathematical structure to that of the second law. Moreover, we derive a generalized second law with quantum feedback control. In addition, we review a proof of the monotonicity in line with Petz.

Affiliated with

Also associated with

No associations

Rating

Second Law-Like Inequalities with Quantum Relative Entropy: An Introduction does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Second Law-Like Inequalities with Quantum Relative Entropy: An Introduction, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Second Law-Like Inequalities with Quantum Relative Entropy: An Introduction will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-461812