Related papers: Challenges about entropy
We have presented first an axiomatic derivation of Boltzmann entropy on the basis of two axioms consistent with two basic properties of thermodynamic entropy. We have then studied the relationship between Boltzmann entropy and information…
Macroscopic nonextensive thermodynamics is studied without recourse to microscopic statistical mechanics. It is shown that if entropy is nonextensive, the concept of physical temperature introduced through the generalized zeroth law of…
The microcanonical entropy $S=\ln[W(E)]$ is the {\em geometrical measure} of the microscopic redundancy or ignorance about the N-body system. {\em Even for astronomical large systems} is the microcanonical entropy everywhere {\em single…
We review here the microcanonical and canonical ensembles constructed on an underlying generalized quantum dynamics and the algebraic properties of the conserved quantities. We discuss the structure imposed on the microcanonical entropy by…
The development of reliable methods for estimating microcanonical averages constitutes an important issue in statistical mechanics. One possibility consists of calculating a given microcanonical quantity by means of typical relations in the…
In statistical physics, the challenging combinatorial enumeration of the configurations of a system subject to hard constraints (microcanonical ensemble) is mapped to a mathematically easier calculation where the constraints are softened…
It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the…
We give meaning to the first and second laws of thermodynamics in case of mesoscopic out-of-equilibrium systems which are driven by diffusion processes. The notion of the entropy production is analyzed. The role of the Helmholtz extremum…
Employing different statistical ensembles may lead to qualitatively different results concerning averages of physical observables on the mesoscopic scale. Here we discuss differences between the canonical and the grandcanonical ensembles…
We develop a geometric foundation of microcanonical thermodynamics in which entropy and its derivatives are determined from the geometry of phase space, rather than being introduced through an a priori ensemble postulate. Once the minimal…
For several independent reasons, the idea that notorious sources of entropy could exist in the Universe has been recently revived. Taking advantage of a new framework accounting for non-equilibrium processes in cosmology, we explicitly…
There are three levels of description in classical statistical mechanics, the microscopic/dynamic, the macroscopic/statistical and the thermodynamic. At one end there is a well-used concept of equilibrium in thermodynamics and at the other…
A definition of the thermodynamic entropy based on the time-dependent probability distribution of the macroscopic variables is developed. When a constraint in a composite system is released, the probability distribution for the new…
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…
The essence of the second law of classical thermodynamics is the `entropy principle' which asserts the existence of an additive and extensive entropy function, S, that is defined for all equilibrium states of thermodynamic systems and whose…
In our derivation of the second law of thermodynamics from the relation of adiabatic accessibility of equilibrium states we stressed the importance of being able to scale a system's size without changing its intrinsic properties. This…
The quest for a microscopic foundation of Thermodynamics is addressed within the Nonunitary Newtonian Gravity model through the study of a specific closed system, namely a three-dimensional harmonic nanocrystal. A numerical calculation of…
In systems with detailed balance, the stationary distribution and the equilibrium distribution are identical, creating a clear connection between energetic and entropic quantities. Many driven systems violate detailed balance and still pose…
Traditionally, phase transitions are defined in the thermodynamic limit only. We propose a new formulation of equilibrium thermo-dynamics that is based entirely on mechanics and reflects just the {\em geometry and topology} of the N-body…
In this paper, we draw attention to the problem of phase transitions in systems with locally affine microcanonical entropy, in which partial equivalence of (microcanonical and canonical) ensembles is observed. We focus on a very simple spin…