Related papers: From Boltzmann-Gibbs ensemble to generalized ensem…
This paper generalizes the entropy maximization problem leading to the Boltzmann-Gibbs distribution through the nonadditive entropy $S_{q,s}(p)=k_{s}\sum^{W}_{i\geq1}p_{i}\ln_{q}1/p_{i}$, $q\in(0,1)$, which is a rescaled version of $S_{q}$…
The basic aspects of both Boltzmann-Gibbs (BG) and nonextensive statistical mechanics can be seen through three different stages. First, the proposal of an entropic functional ($S_{BG} =-k\sum_i p_i \ln p_i$ for the BG formalism) with the…
Based on the Tsallis entropy, the nonextensive thermodynamic properties are studied as a q-deformation of classical statistical results using only probabilistic methods and straightforward calculations. It is shown that the constant in the…
A complex interplay between the academic issue about generalization of the thermodynamics and the practical matter about setting standards for a sustainable evolution of both tailored devices and natural systems is considered. It is…
We consider the micro-canonical ensemble of a classical Hamiltonian dynamical system, the Hamiltonian being parameter dependent and in the possible presence of other first integrals. We describe a thermodynamic formalism in which a 1st law…
Few parameters dependent generalised entropy includes Tsallis entropy, R{\'e}nyi entropy, Sharma-Mittal entropy, Barrow entropy, Kaniadakis entropy, etc as particular representatives. Its relation to physical systems is not always clear. In…
The coupled entropy is proven to correct a flaw in the derivation of the Tsallis entropy and thereby solidify the theoretical foundations for analyzing the uncertainty of complex systems. The Tsallis entropy originated from considering…
A great many observables seen in intermediate energy heavy ion collisions can be explained on the basis of statistical equilibrium. Calculations based on statistical equilibrium can be implemented in microcanonical ensemble (energy and…
Macroscopic thermodynamics, via the weak coupling approximation, assumes that the equi?librium properties of a system are not affected by interactions with its environment. However, this assumption may not hold for quantum systems, where…
We develop a consistent stochastic thermodynamics for environments composed of thermodynamic reservoirs in an external conservative force field, that is environments described by the Generalized or Gibbs canonical ensemble. We demonstrate…
Bose-Einstein condensation represents a remarkable phase transition, characterized by the formation of a single quantum subsystem. As a result, the statistical properties of the condensate are highly unique. In the case of a Bose gas, while…
This study derives the relativistic transformations of thermodynamic quantities from the Lorentz transformations applied to the four-momentum components of a thermodynamic system, which is stationary in the inertial reference frame $K_0$…
The basic idea of a microscopic understanding of Thermodynamics is to derive its main features from a microscopic probability distribution. In such a vein, we investigate the thermal statistics of quasi-probabilities's semi-classical…
In ordinary statistical mechanics the Boltzmann-Shannon entropy is related to the Maxwell-Bolzmann distribution $p_i$ by means of a twofold link. The first link is differential and is offered by the Jaynes Maximum Entropy Principle. The…
Observational entropy -- a quantity that unifies Boltzmann's entropy, Gibbs' entropy, von Neumann's macroscopic entropy, and the diagonal entropy -- has recently been argued to play a key role in a modern formulation of statistical…
Conventional simulations of complex systems in the canonical ensemble suffer from the quasi-ergodicity problem. A simulation in generalized ensemble overcomes this difficulty by performing a random walk in potential energy space and other…
Thermodynamics and its quantum counterpart are traditionally described with statistical ensembles. Canonical typicality has related statistical mechanics for a system to ensembles of global energy eigen- states of system and its environment…
In economics, construction of perfect models in a way that would be comparable to the standards customary in physical sciences is generally not feasible. In particular, the observed value for an economic equilibrium may deviate…
In order to overcome the limitations of the original expression of the probability distribution appearing in literature of Incomplete Statistics, a new expression of the probability distribution is derived, where the Lagrange multiplier %B%…
We derive Tsallis entropy, Sq, from universal thermostat independence and obtain the functional form of the corresponding generalized entropy-probability relation. Our result for finite thermostats interprets thermodynamically the subsystem…