Related papers: Typicality, entropy and the generalization of stat…
We consider the problem of defining free energy and other thermodynamic functions when the entropy is given as a general function of the probablity distribution, including that for non extensive forms. We find that the free energy, which is…
Investigation on foundational aspects of quantum statistical mechanics recently entered a renaissance period due to novel intuitions from quantum information theory and to increasing attention on the dynamical aspects of single quantum…
Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e. the wavefunction, of an isolated system which is determined to calculate molecular properties and to…
The universal validity of the second law of thermodynamics is widely attributed to a finely tuned initial condition of the universe. This creates a problem: why is the universe atypical? We suggest that the problem is an artefact created by…
Entropies are fundamental measures of uncertainty with central importance in information theory and statistics and applications across all the quantitative sciences. Under a natural set of operational axioms, the most general form of…
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…
We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to…
We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is…
A few decades after Hill's work on nano-thermodynamics, the development of a thermodynamic framework, to account consistently for the fluctuations of small systems due to their interactions with the surrounding environment, is still…
In the present paper the conditions for the validity of the Tsallis' Statistics are analyzed. The same has been done following the analogy with the traditional case: starting from the microcanonical description of the systems and taking…
The basic quantity for the description of the statistical properties of physical systems is the density of states or equivalently the microcanonical entropy. Macroscopic quantities of a system in equilibrium can be computed directly from…
We provide a summary of both seminal and recent results on typical entanglement. By typical values of entanglement, we refer here to values of entanglement quantifiers that (given a reasonable measure on the manifold of states) appear with…
The project concerns the interplay among quantum mechanics, statistical mechanics and thermodynamics, in isolated quantum systems. The underlying goal is to improve our understanding of the concept of thermal equilibrium in quantum systems.…
A system is glassy when the observation time is much smaller than the equilibration time. A unifying thermodynamic picture of the glassy state is presented. Slow configurational modes are in quasi-equilibrium at an effective temperature. It…
Statistical thermodynamics of small systems shows dramatic differences from normal systems. Parallel to the recently presented steady-state thermodynamic formalism for master equation and Fokker-Planck equation, we show that a…
We develop a generalized theory of (meta)equilibrium statistical mechanics in the thermodynamic limit valid for both smooth and fractal phase spaces. In the former case, our approach leads naturally to Boltzmann-Gibbs standard…
A pure quantum state can fully describe thermal equilibrium as long as one focuses on local observables. Thermodynamic entropy can also be recovered as the entanglement entropy of small subsystems. When the size of the subsystem increases,…
Complexity of two-level systems, e.g. spins, qubits, magnetic moments etc, are analysed based on the so-called correlational entropy in the case of pure quantum systems and the thermal entropy in case of thermal equilibrium that are…
The concept of entropy connects the number of possible configurations with the number of variables in large stochastic systems. Independent or weakly interacting variables render the number of configurations scale exponentially with the…
The entropy shows an unavoidable tendency of disorder in thermostatistics according to the second thermodynamics law. This provides a minimization entropy principle for quantum thermostatistics with the von Neumann entropy and nonextensive…