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This Special Issue contains novel results in the area of out-of-equilibrium classical and quantum thermodynamics. Contributions are from different areas of physics, including statistical mechanics, quantum information and many-body systems.

quantum Otto engine --- Curzon–Ahlborn efficiency --- endoreversible quantum thermodynamics --- large deviations --- phase transitions --- condensation of fluctuations --- fluctuation relations --- magnetic cycle --- quantum otto cycle --- quantum thermodynamics --- quantum heat engines --- nonequilibrium systems --- ergotropy --- quantum correlations --- information thermodynamics --- collision model --- thermalization --- many-body quantum systems --- fluctuation relation --- Crooks equality --- coherence --- athermality --- photon added thermal state --- photon subtracted thermal state --- binomial states --- generalised coherent states --- laser cooling --- cavitation --- sonoluminescence --- fluctuation theorems --- collisional models

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Data science, information theory, probability theory, statistical learning and other related disciplines greatly benefit from non-negative measures of dissimilarity between pairs of probability measures. These are known as divergence measures, and exploring their mathematical foundations and diverse applications is of significant interest. The present Special Issue, entitled “Divergence Measures: Mathematical Foundations and Applications in Information-Theoretic and Statistical Problems”, includes eight original contributions, and it is focused on the study of the mathematical properties and applications of classical and generalized divergence measures from an information-theoretic perspective. It mainly deals with two key generalizations of the relative entropy: namely, the R_ényi divergence and the important class of f -divergences. It is our hope that the readers will find interest in this Special Issue, which will stimulate further research in the study of the mathematical foundations and applications of divergence measures.

Bregman divergence --- f-divergence --- Jensen–Bregman divergence --- Jensen diversity --- Jensen–Shannon divergence --- capacitory discrimination --- Jensen–Shannon centroid --- mixture family --- information geometry --- difference of convex (DC) programming --- conditional Rényi divergence --- horse betting --- Kelly gambling --- Rényi divergence --- Rényi mutual information --- relative entropy --- chi-squared divergence --- f-divergences --- method of types --- large deviations --- strong data–processing inequalities --- information contraction --- maximal correlation --- Markov chains --- information inequalities --- mutual information --- Rényi entropy --- Carlson–Levin inequality --- information measures --- hypothesis testing --- total variation --- skew-divergence --- convexity --- Pinsker’s inequality --- Bayes risk --- statistical divergences --- minimum divergence estimator --- maximum likelihood --- bootstrap --- conditional limit theorem --- Bahadur efficiency --- α-mutual information --- Augustin–Csiszár mutual information --- data transmission --- error exponents --- dimensionality reduction --- discriminant analysis --- statistical inference --- n/a --- Jensen-Bregman divergence --- Jensen-Shannon divergence --- Jensen-Shannon centroid --- conditional Rényi divergence --- Rényi divergence --- Rényi mutual information --- strong data-processing inequalities --- Rényi entropy --- Carlson-Levin inequality --- Pinsker's inequality --- Augustin-Csiszár mutual information