Related papers: A new entropy based on a group-theoretical structu…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
On a fine grained scale the Gibbs entropy of an isolated system remains constant throughout its dynamical evolution. This is a consequence of Liouville's theorem for Hamiltonian systems and appears to contradict the second law of…
A dynamical estimate is given for the Boltzmann entropy of the Universe, under the simplifying assumptions provided by Newtonian cosmology. We first model the cosmological fluid as the probability fluid of a quantum-mechanical system. Next,…
We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups $G$ such that every element of $G$ is contained in a compact open normal subgroup of $G$. For…
In this work, we study generalized entropies and information geometry in a group-theoretical framework. We explore the conditions that ensure the existence of some natural properties and at the same time of a group-theoretical structure for…
Reconstructing a density of states or similar distribution from moments or continued fractions is an important problem in calculating the electronic and vibrational structure of defective or non-crystalline solids. For single bands a…
Some general considerations on the notion of entropy in physics are presented. An attempt is made to clarify the question of the differentiation between physical entropy (the Clausius-Boltzmann one) and quantities called entropies…
If the N bosons that compose an ideal Bose-Einstein gas with energy E and volume V are each assumed to have the average energy of the system E/N, the entropy is easily expressed in terms of the number of bosons N and the number of…
In this paper, we extend the notion of microstate free entropy to the bi-free setting. In particular, using the bi-free analogue of random matrices, microstate bi-free entropy is defined. Properties essential to an entropy theory are…
Non-extensive systems do not allow to go to the thermodynamic limit. Therefore we have to reformulate statistical mechanics without invoking the thermodynamical limit. I.e. we have to go back to Pre-Gibbsian times. We show that Boltzmann's…
Starting from a many-body classical system governed by a trace-form entropy we derive, in the stochastic quantization picture, a family of non linear and non-Hermitian Schroedinger equations describing, in the mean filed approximation, a…
Based on the form invariance of the structures given by Khinchin's axiomatic foundations of information theory and the pseudoadditivity of the Tsallis entropy indexed by q, the concept of conditional entropy is generalized to the case of…
Polydisperse systems are commonly encountered when dealing with soft matter in general or any non simple fluid. Yet their treatment within the framework of statistical thermodynamics is a delicate task as the latter has been essentially…
The notion of conditional entropy is extended to noncomposite systems. The q-deformed entropic inequalities, which usually are associated with correlations of the subsystem degrees of freedom in bipartite systems, are found for the…
In the past several years, observational entropy has been developed as both a (time-dependent) quantum generalization of Boltzmann entropy, and as a rather general framework to encompass classical and quantum equilibrium and non-equilibrium…
Entropies associated with spatial subsystems in conventional local quantum field theories are typically divergent when the spatial regions have boundaries. However, in certain linear combinations of the entropies for various subsystems,…
All of the basic microsopic physical laws are time reversible. In contrast, the second law of thermodynamics, which is a macroscopic physical representation of the world, is able to describe irreversible processes in an isolated system…
The statistical proprieties of complex systems can differ deeply for those of classical systems governed by Boltzmann-Gibbs entropy. In particular, the probability distribution function observed in several complex systems shows a power law…
Hierarchical structures, which include multiple levels, are prevalent in statistical and machine-learning models as well as physical systems. Extending the foundational result that the maximum entropy distribution under mean constraints is…
In statistical mechanics, measuring the number of available states and their probabilities, and thus the system's entropy, enables the prediction of the macroscopic properties of a physical system at equilibrium. This predictive capacity…