It was proved that balance equations for systems with corpuscular structure can be derived if a kinematic description by piece-wise analytic functions is available (Vamoş et al., Physica A 227 (1996) 81). This article presents a rigorous derivation of an one-dimensional hydrodynamic model for...

Starting from the Liouville equation, we derive the exact hierarchy of equations satisfied by the reduced distribution functions of the single species point vortex gas in two dimensions. Considering an expansion of the solutions in powers of 1/N (where N is the number of vortices) in a proper...

The exact forms of the degenerate Maxwell–Boltzmann (MB), Bose–Einstein (BE) and Fermi–Dirac (FD) entropy functions, derived by Boltzmann's principle without the Stirling approximation [R.K. Niven, Physics Letters A, 342(4) (2005) 286], are further examined. Firstly, an apparent paradox in...

We study the growth of correlations in systems with weak long-range interactions. Starting from the BBGKY hierarchy, we determine the evolution of the two-body correlation function by using an expansion of the solutions of the hierarchy in powers of 1/N in a proper thermodynamic limit N→+∞,...

We derive the free energy of the chiral Potts model by the infinite lattice “inversion relation” method. This method is non-rigorous in that it always needs appropriate analyticity assumptions. Guided by previous calculations based on exact finite-lattice functional relations, we find that...

Correlations and other collective phenomena are considered in a schematic model of pairwise interacting, competing and collaborating agents facing a binary choice and situated at the nodes of the complete graph and a 2-dimensional regular lattice, respectively. The agents may be subjected to an...

A stochastic numerical scheme for an extended immersed boundary method which incorporates thermal fluctuations for the simulation of microscopic biological systems consisting of fluid and immersed elastica was introduced in reference [2]. The numerical scheme uses techniques from stochastic...

Predicting measurable thermodynamic and kinetic properties of solids from first-principles requires the use of statistical mechanics. A major challenge for materials of technological importance arises from the fact that first-principles electronic structure calculations of elementary excited...

The framework of "Modern Theory of Critical State Transitions"1,2 considers the relation between different levels of organization in complex systems in terms of critical state transitions. A state transition between levels entails changes of scale of observables and, concurrently, new formats of...