Related papers: Undecidability, entropy and information loss in co…
The deterministic notions of capacity and entropy are studied in the context of communication and storage of information using square-integrable, bandlimited signals subject to perturbation. The $(\epsilon,\delta)$-capacity, that extends…
Here, we investigate the uncertainty of dynamical observables in classical systems manipulated by repeated measurements and feedback control; the precision should be enhanced in the presence of an external controller but limited by the…
We consider Hamiltonian quantum systems with energy bandwidth \Delta E and show that each measurement that determines the time up to an error \Delta t generates at least the entropy (\hbar/(\Delta t \Delta E))^2/2. Our result describes…
Computations implemented on a physical system are fundamentally limited by the laws of physics. A prominent example for a physical law that bounds computations is the Landauer principle. According to this principle, erasing a bit of…
This paper revisits Brownian motion from the perspective of Information Theory, aiming to explore the connections between Information Theory, Thermodynamics, and Complex Science. First, we propose a single-particle discrete Brownian motion…
The theory of noncommutative dynamical entropy and quantum symbolic dynamics for quantum dynamical systems is analised from the point of view of quantum information theory. Using a general quantum dynamical system as a communication channel…
When a physical system is put in contact with a very large thermal bath, it undergoes a dissipative (i.e., an apparently irreversible) process that leads to thermal equilibrium. This dynamical process can be described fully within quantum…
In this paper, we analyze the relationship between entropy and information in the context of the mixing process of two identical ideal gases. We will argue that entropy has a special information-based feature that is enfolded in the…
We provide a simple physical interpretation, in the context of the second law of thermodynamics, to the information inequality (a.k.a. the Gibbs' inequality, which is also equivalent to the log-sum inequality), asserting that the relative…
After Shannon, entropy becomes a fundamental quantity to describe not only uncertainity or chaos of a system but also information carried by the system. Shannon's important discovery is to give a mathematical expression of the mutual…
The notion of Shannon entropy is crucial for the theory of classical information. In quantum information theory, an analogous key role is played by the von Neumann entropy: quantum information processing is closely related to entropy…
On the standard microscopic model of friction we confirm the common belief that the irreversible entropy production originates from the increase of Shannon information. We reveal that the reversible microscopic dynamics would continuously…
We address the problem of quantifying the information content of a source for an arbitrary information theory, where the information content is defined in terms of the asymptotic achievable compression rate. The functions that solve this…
Thermodynamic uncertainty relations reveal a fundamental trade-off between the precision of a trajectory observable and entropy production, where the uncertainty of the observable is quantified by its variance. In information theory,…
Thermodynamic entropy is determined by a heat measurement through the Clausius equality. The entropy then formalizes a fundamental limitation of operations by the second law of thermodynamics. The entropy is also expressed as the Shannon…
We present a quantum information theory that allows for the consistent description of quantum entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices, rather than probability…
We give a detailed analysis of the Gibbs-type entropy notion and its dynamical behavior in case of time-dependent continuous probability distributions of varied origins: related to classical and quantum systems. The purpose-dependent usage…
This study investigates entropy's potential for analyzing scientific research patterns across disciplines. Originating from thermodynamics, entropy now measures uncertainty and diversity in information systems. We examine Shannon Entropy,…
Quantum information theory, particularly its entropic formulations, has made remarkable strides in characterizing quantum systems and tasks. However, a critical dimension remains underexplored: computational efficiency. While classical…
We calculate Shannon information entropy of trapped interacting bosons in both the position and momentum spaces, $S_r$ and $S_k$ respectively. The total entropy maintains the fuctional form $S=a + b \ln N$ for repulsive bosons. At the…