Related papers: Quantum Hypothesis Testing and Non-Equilibrium Sta…
Concepts of quantum open systems and ideas of correlation dynamics in nonequilibrium statistical mechanics, as well as methods of closed-time-path effective action and influence functional in quantum field theory can be usefully applied for…
Non-equilibrium quantum thermodynamics is essential to describe new devices that operate far from the regime where the usual thermodynamical laws are obeyed. When quantum fluctuations dominate, defining and measuring work and heat, two…
Using the system-bath model Hamiltonian this thesis covers the equilibrium and out of equilibrium properties of quantum open systems. Topics included are the calculation of thermodynamical quantities of open systems, derivation of quantum…
In statistical mechanics, measuring the number of available states and their probabilities, and thus the system's entropy, enables the prediction of the macroscopic properties of a physical system at equilibrium. This predictive capacity…
Bounds on quantum probabilities and expectation values are derived for experimental setups associated with Bell-type inequalities. In analogy to the classical bounds, the quantum limits are experimentally testable and therefore serve as…
Non-equilibrium fluctuation theorems (NFTs) relate work performed on a system as its Hamiltonian varies with time, to equilibrium data of the initial and final states. In a classical context the system energy can be directly measured, while…
We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the…
The derivation of macroscopic irreversible dynamics of nonequilibrium systems from microscopic equations was recently revisited from the point of view of infinitely extended quantum systems. Here we have briefly reviewed the $C^*$ algebra…
The recent article "Entropic Updating of Probability and Density Matrices" [1] derives and demonstrates the inferential origins of both the standard and quantum relative entropies in unison. Operationally, the standard and quantum relative…
We consider statistical methods based on finite samples of locally randomized measurements in order to certify different degrees of multiparticle entanglement in intermediate-scale quantum systems. We first introduce hierarchies of…
An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is…
The familiar textbook quantum mechanics of laboratory measurements incorporates a quantum mechanical arrow of time --- the direction in time in which state vector reduction operates. This arrow is usually assumed to coincide with the…
Entropy in thermodynamics is an extensive quantity, whereas standard methods in statistical mechanics give rise to a non-extensive expression for the entropy. This discrepancy is often seen as a sign that basic formulas of statistical…
The quantum statistical mechanics of an ideal gas with a general free-particle energy obeying fractional exclusion statistics are systematically investigated in arbitrary dimensions. The pressure relations, the relation between pressure and…
As experiments continue to push the quantum-classical boundary using increasingly complex dynamical systems, the interpretation of experimental data becomes more and more challenging: when the observations are noisy, indirect, and limited,…
The problem of estimating a parameter of a quantum system through a series of measurements performed sequentially on a quantum probe is analyzed in the general setting where the underlying statistics is explicitly non-i.i.d. We present a…
It is shown how to resolve the apparent contradiction between the macroscopic approach of phase space and the validity of the uncertainty relations. The main notions of statistical mechanics are re-interpreted in a quantum-mechanical way,…
We illustrate the mathematical theory of entropy production in repeated quantum measurement processes developed in a previous work by studying examples of quantum instruments displaying various interesting phenomena and singularities. We…
In this thesis, we present and discuss the quantum statistical foundations of relativistic hydrodynamics with special emphasis on the entropy current. We show that it is possible to provide a rigorous definition for this quantity in the…
The maximum entropy principle (MEP) apparently allows us to derive, or justify, fundamental results of equilibrium statistical mechanics. Because of this, a school of thought considers the MEP as a powerful and elegant way to make…