Related papers: Quantum Hypothesis Testing and Non-Equilibrium Sta…
We suggest that the framework of quantum information theory, which has been developing rapidly in recent years due to intense activity in quantum computation and quantum communication, is a reasonable starting point to study non-equilibrium…
The intersection of thermodynamics, quantum theory and gravity has revealed many profound insights, all the while posing new puzzles. In this article, we discuss an extension of equilibrium statistical mechanics and thermodynamics…
Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles: positions constitute a configuration…
Statistical physics aims to describe properties of macroscale systems in terms of distributions of their microscale agents. Its central tool is the maximization of entropy, a variational principle. We review the history of this principle,…
Firstly the fluctuation theorems (FT) for expended work in a driven nonequilibrium system, isolated or thermostatted, together with the ensuing Jarzynski work-energy (W-E) relationships, will be discussed and reobtained. Secondly, the…
Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy inequalities between position and momentum.…
We describe quantum entropic functionals and outline a research program dealing with entropic fluctuations in non-equilibrium quantum statistical mechanics.
Most attempts to argue for the second law of thermodynamics fail because (1) they use the unviable frequency theory of probability and (2) they do not explain why the arrow of time seen in experiments is aligned with the thermodynamic arrow…
We examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…
Within the general formalism of quantum theory irreversibility and the arrow of time in the evolution of various physical systems are studied. Irreversible behavior often manifests itself in the guise of entropy production. This motivates…
We briefly review central concepts concerning nonextensive statistical mechanics, based on the nonadditive entropy $S_q=k\frac{1-\sum_{i}p_i^q}{q-1} (q \in {\cal R}; S_1=-k\sum_{i}p_i \ln p_i)$. Among others, we focus on possible…
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as…
The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymptotic error exponents in connection with…
Quantum mechanics is derived as an application of the method of maximum entropy. No appeal is made to any underlying classical action principle whether deterministic or stochastic. Instead, the basic assumption is that in addition to the…
The determination of a quantum observable from the first and second moments of its measurement outcome statistics is investigated. Operational conditions for the moments of a probability measure are given which suffice to determine the…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
We analyze the production of entropy along non-equilibrium processes in quantum systems coupled to generic environments. First, we show that the entropy production due to final measurements and the loss of correlations obeys a fluctuation…
The exact statistics of an arbitrary quantum observable is analytically obtained. Due to the probabilistic nature of a sequence of intermediate measurements and stochastic fluctuations induced by the interaction with the environment, the…
Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions…
Long sequences of successive direct (projective) measurements or observations of a few "uninteresting" physical quantities of a quantum system may reveal indirect, but precise and unambiguous information on the values of some very…