Related papers: Entropy and reversible catalysis
We generalize several results of the classical theory of Thermodynamic Formalism by considering a compact metric space $M$ as the state space. We analyze the shift acting on $M^\mathbb{N}$ and consider a general a-priori probability for…
This paper is devoted to systematic study of properties of the quantum entropy and of the Holevo capacity considered as a function of a set of quantum states. The properties of restriction of the quantum entropy to arbitrary set of states…
An initial unknown quantum state can be determined with a single measurement apparatus by letting it interact with an auxiliary, "Ancilla", system as proposed by Allahverdyan, Balian and Nieuwenhuizen [Phys. Rev. Lett. 92, 120402 (2004)].…
Motivated by the notion that the mathematics of gravity can be reproduced from a statistical requirement of maximal entropy, we study the consequence of introducing an entropic source term in the Einstein-Hilbert action. For a spatially…
*First-principles derivation of the entropy production in erectric static conduction. *The second-order (symmetric) density matrix contributes to the entropy production. *New schemes of steady states formulated using a relaxation-type von…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
Entropy is a fundamental property of both classical and quantum systems, spanning myriad theoretical and practical applications in physics and computer science. We study the problem of obtaining estimates to within a multiplicative factor…
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…
Within an inherently classical perspective, there is always an unavoidable energy cost associated with the information deletion and this common lore is at the heart of the Landauer's conjecture that does not impose, per se, any relevant…
Phase-space versions of quantum mechanics -- from Wigner's original distribution to modern discrete-qudit constructions -- represent some states with negative quasi-probabilities. Conventional Shannon and R\'enyi entropies become…
We develop two general approaches to characterising the manipulation of quantum states by means of probabilistic protocols constrained by the limitations of some quantum resource theory. First, we give a general necessary condition for the…
We consider critical models in one dimension. We study the ground state in thermodynamic limit [infinite lattice]. Following Bennett, Bernstein, Popescu, and Schumacher, we use the entropy of a sub-system as a measure of entanglement. We…
We introduce a novel notion of invariance feedback entropy to quantify the state information that is required by any controller that enforces a given subset of the state space to be invariant. We establish a number of elementary properties,…
The deterministic and time-reversal symmetric dynamics of isolated quantum systems is at odds with irreversible equilibration observed in generic thermodynamic systems. Standard approaches at a reconciliation employ subjective restrictions…
For the general class of quasifree fermionic right mover/left mover systems over the infinitely extended two-sided discrete line introduced in [8] within the algebraic framework of quantum statistical mechanics, we study the von Neumann…
When reformulated as a resource theory, thermodynamics can analyze system behaviors in the single-shot regime. In this, the work required to implement state transitions is bounded by {\alpha}-Renyi divergences and so differs in identifying…
We discuss entropy production in nonequilibrium steady states by focusing on paths obtained by sampling at regular (small) intervals, instead of sampling on each change of the system's state. This allows us to study directly entropy…
A method of representing probabilistic aspects of quantum systems is introduced by means of a density function on the space of pure quantum states. In particular, a maximum entropy argument allows us to obtain a natural density function…
In this paper we discuss about the validity of the Shannon entropy functional in connection with the correct Gibbs-Hertz probability distribution function. We show that there is no contradiction in using the Shannon-Gibbs functional and…
We analyze general enough models of repeated indirect measurements in which a quantum system interacts repeatedly with randomly chosen probes on which Von Neumann direct measurements are performed. We prove, under suitable hypotheses, that…