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In bulk systems the calculation of the main thermodynamic quantities leads to the same expectation values in the thermodynamic limit, regardless of the choice of the statistical ensemble. Single linear molecules can be still regarded as…
A Hamiltonian model living in a bounded phase space and with long-range interactions is studied. It is shown, by analytical computations, that there exists an energy interval in which the microcanonical entropy is a decreasing convex…
We first show that the currently accepted statistical mechanics for granular matter is flawed. The reason is that it is based on the volume function, which depends only on a minute fraction of all the structural degrees of freedom and is…
Jamming is a geometric phase transition occurring in dense particle systems in the absence of temperature. We use computer simulations to analyse the effect of thermal fluctuations on several signatures of the transition. We show that…
A pedagogical approach for deriving the statistical mechanical partition function, in a manner that emphasizes the key role of entropy in connecting the microscopic states to thermodynamics, is introduced. The connections between the…
We investigate the distribution of the volume and coordination number associated to each particle in a jammed packing of monodisperse hard sphere using the mesoscopic ensemble developed in Nature 453, 606 (2008). Theory predicts an…
We study the energy and entropies for $N$ independent harmonic oscillators in the microcanonical and the canonical ensembles in the Tsallis classical and the Tsallis quantum statistics of entropic parameter $q$, where $N$ is the number of…
In quantum theory, equilibrium statistical mechanics is usually formulated through the canonical ensemble, whose privileged status is tied to the Euclidean continuation of time evolution. The microcanonical ensemble, by contrast, is…
We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space…
We review a recently proposed theory of random packings. We describe the volume fluctuations in jammed matter through a volume function, amenable to analytical and numerical calculations. We combine an extended statistical mechanics…
We study the configurational probability distribution of a mono-atomic gas with a finite number of particles N in the micro-canonical ensemble. We give two arguments why the thermodynamic entropy of the configurational subsystem involves…
We investigate the nature of randomness in disordered packings of frictional spheres. We calculate the entropy of 3D packings through the force and volume ensemble of jammed matter, a mesoscopic ensemble and numerical simulations using…
Configurational entropy is an important factor in the free energy change of many macromolecular recognition and binding processes, and has been intensively studied. Despite great progresses that have been made, the global sampling remains…
Granular material is showing very often in geotechnical engineering, petroleum engineering, material science and physics. The packings of the granular material play a very important role in their mechanical behaviors, such as stress-strain…
Granular segregation is ubiquitous in industrial, geological or daily-life context, but there is still no unifying theoretical approach. In this review, we examine two examples of granular segregation -- shallow rapid flows and rotating…
Motivated by recent experiments on the approach to jamming of a weakly forced granular medium using an immersed torsion oscillator [Nature 413 (2001) 407], we propose a simple model which relates the microscopic dynamics to macroscopic…
The thermodynamics for a system with given temperature, density, and volume is described by the Canonical ensemble. The thermodynamics for a corresponding system with the same temperature, volume, and average density is described by the…
Using X-ray tomography, we experimentally investigate granular segregation phenomena in a mixture of particles with different densities under quasi-static cyclic shear. We quantitatively characterize their height distributions at steady…
We investigate equal spheres packings generated from several experiments and from a large number of different numerical simulations. The structural organization of these disordered packings is studied in terms of the network of common…
One goal of this paper is to discuss the classical definition of granular temperature as an extension of its thermodynamic equivalent and a useful concept which provides an important characterization of fluidized granular matter. Following…