English
Related papers

Related papers: Relative and Discrete Utility Maximising Entropy

200 papers

Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…

General Physics · Physics 2017-05-10 Tommaso Toffoli

The paper deals with the generalization of both Boltzmann entropy and distribution in the light of most-probable interpretation of statistical equilibrium. The statistical analysis of the generalized entropy and distribution leads to some…

Quantum Physics · Physics 2009-11-13 C. G. Chakrabarti , Indranil Chakrabarty

The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting that the BGS entropy is a special case of relative entropy.…

Statistical Mechanics · Physics 2008-11-26 Jörn Dunkel , Peter Talkner , Peter Hänggi

We consider the maximum entropy problems associated with R\'enyi $Q$-entropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the…

Information Theory · Computer Science 2008-12-18 Jean-François Bercher

We have presented a new axiomatic derivation of Shannon Entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function.We have then modified shannon entropy to take account…

Quantum Physics · Physics 2007-05-23 C. G. Chakrabarti , Indranil Chakrabarty

We study the class of self-similar probability density functions with finite mean and variance which maximize R\'{e}nyi's entropy. The investigation is restricted in the Schwartz space $S(\mathbb{R}^d)$ and in the space of…

Mathematical Physics · Physics 2015-10-28 Agapitos N. Hatzinikitas

We consider the problem of maximizing expected utility from consumption in a constrained incomplete semimartingale market with a random endowment process, and establish a general existence and uniqueness result using techniques from convex…

Portfolio Management · Quantitative Finance 2008-12-10 Ioannis Karatzas , Gordan Zitkovic

It is possible to derive the maximum entropy principle from thermodynamic stability requirements. Using as a starting point the equilibrium probability distribution, currently used in non-extensive thermostatistics, it turns out that the…

Statistical Mechanics · Physics 2007-05-23 Jan Naudts

Pseudoentropy characterizations provide a quantitatively precise demonstration of the close relationship between computational hardness and computational randomness. We prove a unified pseudoentropy characterization that generalizes and…

Computational Complexity · Computer Science 2025-09-05 Lunjia Hu , Salil Vadhan

In this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow, that is, the equations for mass, momentum, and a system for the energy matrix. These are the second…

Mathematical Physics · Physics 2018-02-22 Hans Wilhelm Alt

This Chapter is written for the Festschrift celebrating the 70th birthday of the distinguished economist Duncan Foley from the New School for Social Research in New York. This Chapter reviews applications of statistical physics methods,…

Statistical Finance · Quantitative Finance 2012-05-01 Victor M. Yakovenko

In this work we study the continuous time exponential utility maximization problem in the framework of an investor who is informed about the price changes with a delay. This leads to a non-Markovian stochastic control problem. In the case…

Mathematical Finance · Quantitative Finance 2025-10-06 Yan Dolinsky

This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…

Information Theory · Computer Science 2018-12-11 Igal Sason

We discuss how the method of maximum entropy, MaxEnt, can be extended beyond its original scope, as a rule to assign a probability distribution, to a full-fledged method for inductive inference. The main concept is the (relative) entropy…

Data Analysis, Statistics and Probability · Physics 2009-11-10 Ariel Caticha

The problem of robust utility maximization in an incomplete market with volatility uncertainty is considered, in the sense that the volatility of the market is only assumed to lie between two given bounds. The set of all possible models…

Probability · Mathematics 2015-04-07 Anis Matoussi , Dylan Possamaï , Chao Zhou

In this paper, we introduce two measures for the resource theory of imaginarity. One is induced by $\alpha$--$z$--R\'enyi relative entropy and the other, defined for positive definite density matrices, is induced by Tsallis relative…

Quantum Physics · Physics 2025-03-25 Xiangyu Chen , Qiang Lei

Works, briefly surveyed here, are concerned with two basic methods: Maximum Probability and Bayesian Maximum Probability; as well as with their asymptotic instances: Relative Entropy Maximization and Maximum Non-parametric Likelihood.…

Statistics Theory · Mathematics 2008-04-25 M. Grendar

Two new relative entropy quantities, called the min- and max-relative entropies, are introduced and their properties are investigated. The well-known min- and max- entropies, introduced by Renner, are obtained from these. We define a new…

Quantum Physics · Physics 2016-11-18 Nilanjana Datta

We shall prove that the celebrated R\'enyi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the $Z$-entropies. Each of them, under suitable hypotheses, generalizes the celebrated…

Mathematical Physics · Physics 2017-02-07 Piergiulio Tempesta

A new upper bound on the relative entropy is derived as a function of the total variation distance for probability measures defined on a common finite alphabet. The bound improves a previously reported bound by Csisz\'ar and Talata. It is…

Information Theory · Computer Science 2015-10-20 Igal Sason , Sergio Verdu