21 research outputs found
Thermodynamics of exponential Kolmogorov-Nagumo averages
This paper investigates generalized thermodynamic relationships in physical
systems where relevant macroscopic variables are determined by the exponential
Kolmogorov-Nagumo average. We show that while the thermodynamic entropy of such
systems is naturally described by R\'{e}nyi's entropy with parameter ,
their statistics under equilibrium thermodynamics are still described by an
ordinary Boltzmann distribution, which can be interpreted as a system with
inverse temperature quenched to another heat bath with inverse
temperature . For the non-equilibrium case, we show
how the dynamics of systems described by exponential Kolmogorov-Nagumo averages
still observe a second law of thermodynamics and H-theorem. We further discuss
the applications of stochastic thermodynamics in those systems - namely, the
validity of fluctuation theorems - and the connection with thermodynamic
length.Comment: 12 pages, 1 table. arXiv admin note: text overlap with
arXiv:2203.1367
Variants of Mixtures: Information Properties and Applications
In recent years, we have studied information properties of various types of mixtures of probability distributions and introduced a new type, which includes previously known mixtures as special cases. These studies are disseminated in different fields: reliability engineering, econometrics, operations research, probability, the information theory, and data mining. This paper presents a holistic view of these studies and provides further insights and examples. We note that the insightful probabilistic formulation of the mixing parameters stipulated by Behboodian (1972) is required for a representation of the well-known information measure of the arithmetic mixture. Applications of this information measure presented in this paper include lifetime modeling, system reliability, measuring uncertainty and disagreement of forecasters, probability modeling with partial information, and information loss of kernel estimation. Probabilistic formulations of the mixing weights for various types of mixtures provide the Bayes-Fisher information and the Bayes risk of the mean residual function
Group entropies: from phase space geometry to entropy functionals via Group Theory
The entropy of Boltzmann-Gibbs, as proved by Shannon and Khinchin, is based on four axioms, where the fourth one concerns additivity. The group theoretic entropies make use of formal group theory to replace this axiom with a more general composability axiom. As has been pointed out before, generalised entropies crucially depend on the number of allowed degrees of freedom N. The functional form of group entropies is restricted (though not uniquely determined) by assuming extensivity on the equal probability ensemble, which leads to classes of functionals corresponding to sub-exponential, exponential or super-exponential dependence of the phase space volume W on N. We review the ensuing entropies, discuss the composability axiom and explain why group entropies may be particularly relevant from an information-theoretical perspective
Convergence Rates for Quantum Evolution and Entropic Continuity Bounds in Infinite Dimensions
By extending the concept of energy-constrained diamond norms, we obtain
continuity bounds on the dynamics of both closed and open quantum systems in
infinite-dimensions, which are stronger than previously known bounds. We
extensively discuss applications of our theory to quantum speed limits,
attenuator and amplifier channels, the quantum Boltzmann equation, and quantum
Brownian motion. Next, we obtain explicit log-Lipschitz continuity bounds for
entropies of infinite-dimensional quantum systems, and classical capacities of
infinite-dimensional quantum channels under energy-constraints. These bounds
are determined by the high energy spectrum of the underlying Hamiltonian and
can be evaluated using Weyl's law