The resource theory of informational nonequilibrium in thermodynamics

We review recent work on the foundations of thermodynamics in the light of quantum information theory. We adopt a resource-theoretic perspective, wherein thermodynamics is formulated as a theory of what agents can achieve under a particular restriction, namely, that the only state preparations and transformations that they can implement for free are those that are thermal at some fixed temperature. States that are out of thermal equilibrium are the resources. We consider the special case of this theory wherein all systems have trivial Hamiltonians (that is, all of their energy levels are degenerate). In this case, the only free operations are those that add noise to the system (or implement a reversible evolution) and the only nonequilibrium states are states of informational nonequilibrium, that is, states that deviate from the maximally mixed state. The degree of this deviation we call the state's nonuniformity; it is the resource of interest here, the fuel that is consumed, for instance, in an erasure operation. We consider the different types of state conversion: exact and approximate, single-shot and asymptotic, catalytic and noncatalytic. In each case, we present the necessary and sufficient conditions for the conversion to be possible for any pair of states, emphasizing a geometrical representation of the conditions in terms of Lorenz curves. We also review the problem of quantifying the nonuniformity of a state, in particular through the use of generalized entropies. Quantum state conversion problems in this resource theory can be shown to be always reducible to their classical counterparts, so that there are no inherently quantum-mechanical features arising in such problems. This body of work also demonstrates that the standard formulation of the second law of thermodynamics is inadequate as a criterion for deciding whether or not a given state transition is possible.Comment: 51 pages, 9 figures, Revised Versio

How Has the Literature on Gini's Index Evolved in the Past 80 Years?

The Gini coefficient or index is perhaps one of the most used indicators of social and economic conditions. From its first proposal in English in 1921 to the present, a large number of papers on the Gini index has been written and published. Going through these papers represents a demanding task. The aim of this survey paper is to help the reader to navigate through the major developments of the literature and to incorporate recent theoretical research results with a particular focus on different formulations and interpretations of the Gini index, its social welfare implication, and source and subgroup decomposition.Gini coefficent or index; social welfare; decomposition; computation

Measurement of inequality with a finite number of pay states : the majorization set and its applications

I am grateful to Vassily Gorbanov, Tarik Yalcin and Fabrizio Germano for extended discussions and suggestions, and to an associate editor and a reviewer for constructive comments. I also wish to thank Francesco Andreoli, Geoffrey Burton, Joe Swierzbinski, Alain Trannoy, Claudio Zoli and seminar participants at the Aix-Marseille School of Economics for discussions. I am responsible for any errors.Peer reviewedPostprin

Measuring distributional effects of fiscal reforms

The purpose of this paper is to provide an overview of how to analyse the distributional effects of fiscal reforms. Thereby, distributional e¤ects shall be differentiated by four subconcepts, i.e. 1.) the traditional concept of inequality, 2.) the rather novel concept of polarisation, 3.) the concept of progression in taxation, and 4.) the concepts of income poverty and richness. The concept of inequality and the concept of income poverty are the by far most widely applied concepts in empirical analyses, probably since they appear to be the most transparent ones in their structure as well as the most controversial ones in political affairs. However, the concepts of richness, polarisation and progression in taxation shall additionally be subject of this analysis, since they appear to be useful devices on the course of analysing cause and effect of the other two concepts. --Inequality,polarisation,progression,poverty,richness

A Note on the Interpretation and Application of the Gini Coefficient

We show that the Gini coefficient is a simple linear transformation of the center of gravity of income distribution. The new derivation and inequality decomposition methods are applied to income data for Korea in order to analyze the distributional impact of the recent economic crisis. We also discuss the potential benefits of using additional higher moments of the relative income rankings.Income Inequality, the Gini coeffcient, and the Lorenz curve