Related papers: Notes on microstate free entropy of projections
Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…
We derive an analytic expression for the distribution of velocities of multiple interacting active particles which we test by numerical simulations. In clear contrast with equilibrium we find that the velocities are coupled to positions.…
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…
Previously, it has been shown that the direct correlation function for a Lennard-Jones fluid could be modeled by a sum of that for hard-spheres, a mean-field tail and a simple linear correction in the core region constructed so as to…
We consider simple models of tunneling of an object with intrinsic degrees of freedom. This important problem was not extensively studied until now, in spite of numerous applications in various areas of physics and astrophysics. We show…
We experimentally determine the force exerted by a bath of active particles onto a passive probe as a function of its distance to a wall and compare it to the measured averaged density distribution of active particles around the probe.…
This work contributes to the problem of determining effective interaction between asymmetrically (likely or oppositely) charged objects whose total charge is neutralized by mobile pointlike counter-ions of the same charge, the whole system…
This paper investigates a function of macroscopic variables known as the singular potential, building on previous work by Ball and Majumdar. The singular potential is a function of the admissible statistical averages of probability…
We study the relationship between bipartite entanglement, subsystem particle number and topology in a half-filled free fermion system. It is proposed that the spin-projected particle numbers can distinguish the quantum spin Hall state from…
Due to remarkable advances in colloid synthesis techniques, systems of squares and cubes, once an academic abstraction for theorists and simulators, are nowadays an experimental reality. By means of a free minimization of the free-energy…
Physics and economics are two disciplines that share the common challenge of linking microscopic and macroscopic behaviors. However, while physics is based on collective dynamics, economics is based on individual choices. This conceptual…
We present an alternative approach to the theory of free Gibbs states with convex potentials. Instead of solving SDE's, we combine PDE techniques with a notion of asymptotic approximability by trace polynomials for a sequence of functions…
The possibility that a short-range interacting system exhibits nonadditivity is investigated. After the discussion on the precise definition of additivity and its consequence, we show that it is possible when the system is in a…
Notions of topological free entropy and of free capacity are introduced in the $C^*$-algebra context. Basic properties, basic problems and connections to potential theory and random matrix theory are discussed.
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
This paper discusses the free energy of complex dislocation microstructures, which is a fundamental property of continuum plasticity. In the past, multiple models of the self energy of dislocations have been proposed in the literature that…
With a novel 3D discrete-element method specially developed with adhesive contact mechanics, random loose packings of uniform spherical micron-sized particles are fully investigated. The results show that large velocity, large size or weak…
Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…
In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability . Here we show that the classical Shannon's entropy power inequality…
To mimic the complex transport-like collective phenomena in a man-made or natural system, we study an open network junction model of totally asymmetric simple exclusion process with bulk particle attachment and detachment. The stationary…