Related papers: Second Law-Like Inequalities with Quantum Relative…
In this paper we present an extensive study of the thermodynamic properties of the two-dimensional quantum Heisenberg antiferromagnet on the square lattice; the problem is tackled by the pure-quantum self-consistent harmonic approximation,…
Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The…
General hyperbolic systems of balance laws with inhomogeneity in space and time in all constitutive functions are studied in the context of relative entropy. A framework is developed in this setting that contributes to a measure-valued weak…
The Kelvin-Planck statement of the Second Law of Thermodynamics is a stricture on the nature of heat receipt by any body suffering a cyclic process. It makes no mention of temperature or of entropy. Beginning with a Kelvin-Planck statement…
Quantum Thermodynamics is a continuous dialogue between two independent theories: Thermodynamics and Quantum Mechanics. Whenever the two theories addressed the same phenomena new insight has emerged. We follow the dialogue from equilibrium…
A microscopic definition of the thermodynamic entropy in an isolated quantum system must satisfy (i) additivity, (ii) extensivity and (iii) the second law of thermodynamics. We show that the diagonal entropy, which is the Shannon entropy in…
Uncertainty principle, a fundamental principle in quantum physics, has been studied intensively via various uncertainty inequalities. Here we derive an uncertainty equality in terms of linear entropy, and show that the sum of uncertainty in…
We proved when random-variable fluctuations obey the central limit theorem the equality of the uncertainty relation corresponds to the thermodynamic equilibrium state. The inequality corresponds to the thermodynamic non-equilibrium state.…
In our recent letter [1] we discussed that thermodynamics is violated in quantum Brownian motion beyond the weak coupling limit. In his comment, Tasaki [2] derives an inequality for the relative entropy and claims, without making any…
I give a self-contained introduction to the resource theory approach to quantum thermodynamics. I will introduce in an elementary manner the technical machinery necessary to unpack and prove the core statements of the theory. The topics…
Several models of quantum open systems are known at present to violate, according to principles of the standard quantum theory of open systems, the second law of thermodynamics. Here, a new and rather trivial model of another type is…
There are several inequalities in physics which limit how well we can process physical systems to achieve some intended goal, including the second law of thermodynamics, entropy bounds in quantum information theory, and the uncertainty…
The positivity conditions of the relative entropy between two thermal equilibrium states $\hat{\rho}_1$ and $\hat{\rho}_2$ are used to obtain upper and lower bounds for the subtraction of their entropies, the Helmholtz potential and the…
Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately it has emerged that they are in fact intimately related. In this…
Recent papers discussing thermodynamic processes in strongly coupled quantum systems claim a violation of Landauer's principle and imply a violation of the second law of thermodynamics. If true, this would have powerful consequences.…
Structure in quantum entanglement entropy is often leveraged to focus on a small corner of the exponentially large Hilbert space and efficiently parameterize the problem of finding ground states. A typical example is the use of matrix…
Quantum Landauer's principle provides a fundamental lower bound for energy dissipation occurred with information erasure in the quantum regime. While most studies have related the entropy reduction incorporated with the erasure to the lower…
In generalized resource theories, one aims to reformulate the problem of deciding whether a suitable transition (typically a transition that preserves the Gibbs state of the theory) between two given states $\rho$ and $\sigma$ exists or…
In black hole physics, the second law of thermodynamics is generally valid whether the black hole is a static or a non-static one. Considering the universe as a thermodynamical system the second law of black hole dynamics extends to the…
Statistical formulations of thermodynamic entropy, such as those by Boltzmann and Gibbs, were originally developed for classical systems and are well understood in that context. However, the foundational aspects of quantum statistical…