143 research outputs found
Second Law-Like Inequalities with Quantum Relative Entropy: An Introduction
We review the fundamental 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.Comment: As a chapter of: M. Nakahara and S. Tanaka (eds.), "Lectures on
Quantum Computing, Thermodynamics and Statistical Physics", Kinki University
Series on Quantum Computing (World Scientific, 2012
Geometrical Expression of Excess Entropy Production
We derive a geometrical expression of the excess entropy production for
quasi-static transitions between nonequilibrium steady states of Markovian jump
processes, which can be exactly applied to nonlinear and nonequilibrium
situations. The obtained expression is geometrical; the excess entropy
production depends only on a trajectory in the parameter space, analogous to
the Berry phase in quantum mechanics. Our results imply that vector potentials
are needed to construct thermodynamics of nonequilibrium steady states
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