Related papers: Question on Conditional Entropy
One of the defining traits of quantum mechanics is the uncertainty principle which was originally expressed in terms of the standard deviation of two observables. Alternatively, it can be formulated using entropic measures, and can also be…
Recommendations based on behavioral data may be faced with ambiguous statistical evidence. We consider the case of association rules, relevant e.g.~for query and product recommendations. For example: Suppose that a customer belongs to…
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…
The major problem in information theoretic analysis of neural responses and other biological data is the reliable estimation of entropy--like quantities from small samples. We apply a recently introduced Bayesian entropy estimator to…
Configurational entropy is an important factor in the free energy change of many macromolecular recognition and binding processes, and has been intensively studied. Despite great progresses that have been made, the global sampling remains…
We seek an entropy estimator for discrete distributions with fully empirical accuracy bounds. As stated, this goal is infeasible without some prior assumptions on the distribution. We discover that a certain information moment assumption…
The present paper studies continuity of generalized entropy functions and relative entropies defined using the notion of a deformed logarithmic function. In particular, two distinct definitions of relative entropy are discussed. As an…
We study the contextuality of a three-level quantum system using classical conditional entropy of measurement outcomes. First, we analytically construct the minimal configuration of measurements required to reveal contextuality. Next, an…
Projective measurement can increase the entropy of a state $\rho$, the increased entropy is not only up to the basis of projective measurement, but also has something to do with the properties of the state itself. In this paper we define…
The postulates of thermodynamics were originally formulated for macroscopic systems. They lead to the definition of the entropy, which, for a homogeneous system, is a homogeneous function of order one in the extensive variables and is…
The concept of composability states that entropy of the total system composed of independent subsystems is a function of entropies of the subsystems. Here, the most general pseudoadditivity rule for composable entropy is derived based only…
The example provided in the comment [arXiv:0803.2241] concerns a situation where the system is initially at negative temperature. It is known that in such cases the Law of Entropy Decrease holds. Nevertheless, this does not challenge the…
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…
The concept of entropy in nonequilibrium macroscopic systems is investigated in the light of an extended equation of motion for the density matrix obtained in a previous study. It is found that a time-dependent information entropy can be…
Entropy is one of the key thermodynamic variables reflecting changes in the state of matter. Unlike other thermodynamic variables, it is well-defined also for nonequilibrium steady states through its relation to information. Applying this…
We prove the quantum conditional Entropy Power Inequality for quantum additive noise channels. This inequality lower bounds the quantum conditional entropy of the output of an additive noise channel in terms of the quantum conditional…
PAE cannot be made a basis for either a generalized statistical mechanics or a generalized information theory. Either statistical independence must be waived, or the expression of the averaged conditional probability as the difference…
In sharp contrast to the corresponding classical systems cases it is not yet understood how to define a mechanical quantity with the interpretation of entropy creation rate for nonequilibrum stationary states of finite quantum systems with…
A lower bound of the reduced relative entropy is given by the use of a variational expression. The reduced Tsallis relative entropy is defined and some results are given. In particular, the convexity of the reduced Tsallis relative entropy…
Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input…