Related papers: Generalizing the Extensive Postulates
The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function…
We propose a formal extension of thermodynamics and kinetic theories to a larger class of entropy functionals. Kinetic equations associated to Boltzmann, Fermi, Bose and Tsallis entropies are recovered as a special case. This formalism…
To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. The statistical distributions which can be obtained out of the mesoscopic description characterizing the behaviour of a…
We employ the machinery of smooth scaling and coarse-graining of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) to make a rigorous renormalisation group…
The explanation of the apparent universality of thermodynamics points toward the extension of the usual conceptual background of the second law. Arguments are collected that a basic guiding idea of stability of thermodynamic equilibrium…
We present a thermodynamic theory for a generic population of $M$ individuals distributed into $N$ groups (clusters). We construct the ensemble of all distributions with fixed $M$ and $N$, introduce a selection functional that embodies the…
In a first part the scope of classical thermodynamics and statistical mechanics is discussed in the broader context of formal dynamical systems, including computer programmes. In this context classical thermodynamics appears as a particular…
We show that there is a correspondence between cosmology from non-extensive thermodynamics and cosmology with fluids of redefined and generalized equation of state. We first establish the correspondence in the case of basic non-extensive…
The underlying connection between the degrees of freedom of a system and its nonextensive thermodynamic behavior is addressed. The problem is handled by starting from a thermodynamical system with fractal structure and its analytical…
Tsallis has proposed a generalisation of the standard entropy, which has since been applied to a variety of physical systems. In the canonical ensemble approach that is mostly used, average energy is given by an unnromalised, or normalised,…
In the present paper are analysed the conditions for the validity of the Tsallis Statistics. The same have been done following the analogy with the traditional case: starting from the microcanonical description of the systems and analysing…
All presently available results lead to the conclusion that nonextensivity, in the sense of nonextensive statistical mechanics (i.e., $q \ne 1$), does {\it not} modify anything to the second principle of thermodynamics, which therefore…
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…
Starting from the quantum mechanics for $N$ particles, we show that we can directly derive the microcanonical ensemble average of the physical quantity $A$ by using only the long time average and the equal probability assumption for the…
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
Dynamical equations describing physical systems at statistical equilibrium are commonly extended by mathematical tools called "thermostats". These tools are designed for sampling ensembles of statistical mechanics. We propose a dynamic…
Statistical thermodynamics is valuable as a conceptual structure that shapes our thinking about equilibrium thermodynamic states. A cloud of unresolved questions surrounding the foundations of the theory could lead an impartial observer to…
We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…
We develop a method using a coarse graining of the energy fluctuations of an equilibrium quantum system which produces simple parameterizations for the behaviour of the system. As an application, we use these methods to gain more…
Entropy in thermodynamics is an extensive quantity, whereas standard methods in statistical mechanics give rise to a non-extensive expression for the entropy. This discrepancy is often seen as a sign that basic formulas of statistical…