Related papers: Convergence of macrostates under reproducible proc…
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…
We apply a common measure of randomness, the entropy, in the context of iterated functions on a finite set with n elements. For a permutation, it turns out that this entropy is asymptotically (for a growing number of iterations) close to…
We argue that symmetrization of an incoming microstate with similar states in a sea of microstates contained in a macroscopic detector can produce an effective image, which does not contradict the no-cloning theorem, and such a…
It is known that when a system interacts with its environment, the entanglement contained in the system is redistributed since parts of the system entangle with the environment. On the other hand, the entanglement of a system with its…
We consider conservative quantum evolutions possibly interrupted by macroscopic measurements. When started in a nonequilibrium state, the resulting path-space measure is not time-reversal invariant and the weight of time-reversal breaking…
Moore and Schroeder proposed an effective approach to introducing entropy and the second law through computational study of models with easily countable states at fixed energy. But such systems are rare: the only familiar examples are the…
We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations are quantified by parameters that are subject to the "concentration of measure" phenomenon, meaning that on a…
Predictive equivalence in discrete stochastic processes have been applied with great success to identify randomness and structure in statistical physics and chaotic dynamical systems and to inferring hidden Markov models. We examine the…
Fluctuations of observables as functions of time, or "fluctuation patterns", are studied in a chaotic microscopically reversible system that has irreversibly reached a nonequilibrium stationary state. Supposing that during a certain, long…
Weak convergence of the empirical copula process is shown to hold under the assumption that the first-order partial derivatives of the copula exist and are continuous on certain subsets of the unit hypercube. The assumption is…
Coherence of a quantum state intrinsically depends on the choice of the reference basis. A natural question to ask is the following: if we use two or more incompatible reference bases, can~there be some trade-off relation between the…
Compact data representations are one approach for improving generalization of learned functions. We explicitly illustrate the relationship between entropy and cardinality, both measures of compactness, including how gradient descent on the…
We revisit the maximum-entropy inference of the state of a finite-level quantum system under linear constraints. The constraints are specified by the expected values of a set of fixed observables. We point out the existence of…
For distinguishing quantum states sampled from a fixed ensemble, the gap in bipartite and single-party distinguishability can be interpreted as a nonlocality of the ensemble. In this paper, we consider bipartite state discrimination in a…
If a quantum experiment includes random processes, then the results of repeated measurements can appear consistent with irreversible decoherence even if the system's evolution prior to measurement was reversible and unitary. Two thought…
In quantum systems, entropy production is typically defined as the quantum relative entropy between two states. This definition provides an upper bound for any flux (of particles, energy, entropy, etc.) of bounded observables, which proves…
The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation…
We study a recent conjecture about the behavior of the quantum relative entropy compared to the relative entropy of entanglement in open bipartite systems. The conjecture states that, under a dissipative time-evolution, the positive rate of…
The principle of local distinguishability states that an arbitrary physical state of a bipartite system can be determined by the combined statistics of local measurements performed on the subsystems. A necessary and sufficient requirement…
The chemical reactions are very complex, and include oscillation, condensation, catalyst and self-organization, etc. In these case changes of entropy may increase or decrease. The second law of thermodynamics is based on an isolated system…