Related papers: Setting Boundaries for Statistical Mechanics
If the block universe view is correct, the future and the past have similar status and one would expect physical theories to involve final as well as initial boundary conditions. A plausible consistency condition between the initial and…
Stochastic boundary conditions for interactions with a particle reservoir are discussed in many-particle systems. We introduce the boundary conditions with the injection rate and the momentum distribution of particles coming from a particle…
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…
We report the complete statistical treatment of a system of particles interacting via Newtonian forces in continuous boundary-driven flow, far from equilibrium. By numerically time-stepping the force-balance equations of a model fluid we…
The use of fully or partially absorbing boundary conditions for diffusion-based problems has become paradigmatic in physical chemistry and biochemistry to describe reactions occurring in solutions or in living media. However, as chemical…
Although not as wide, and popular, as that of quantum mechanics, the investigation of fundamental aspects of statistical mechanics constitutes an important research field in the building of modern physics. Besides the interest for itself,…
We demonstrate the equilibration of isolated macroscopic quantum systems, prepared in non-equilibrium mixed states with significant population of many energy levels, and observed by instruments with a reasonably bound working range compared…
The quantum statistical mechanics of an ideal gas with a general free-particle energy obeying fractional exclusion statistics are systematically investigated in arbitrary dimensions. The pressure relations, the relation between pressure and…
The statistical mechanics of particles that populate indistinguishable energy sub-states is explored. In particular, the mathematical treatment of the microstates differs from conventional statistical mechanics where for a given degeneracy,…
Stochastic hydrodynamics is a central tool in the study of first order phase transitions at a fundamental level. Combined with sophisticated free energy models, e.g. as developed in classical Density Functional Theory, complex processes…
Statistical mechanics is one of the most powerful and elegant tools in the quantitative sciences. One key virtue of statistical mechanics is that it is designed to examine large systems with many interacting degrees of freedom, providing a…
The assumption that a complete description of an early state of the universe does not privilege any position or direction in space leads to a unified account of probability in cosmology, macroscopic physics, and quantum mechanics. Such a…
This paper shows that some of the limit-like quantities currently used in statistical mechanics are ill-defined in the mathematical sense. Along the line, it is shown that significant progresses in non-equilibrium gas dynamics can be made…
Finite physical systems have only a finite amount of distinct state. This finiteness is fundamental in statistical mechanics, where the maximum number of distinct states compatible with macroscopic constraints defines entropy. Here we show…
Statistical mechanics of the discrete nonlinear Schr\"odinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for…
Statistical mechanics is a powerful framework for analyzing optimization yielding analytical results for matching, optimal transport, and other combinatorial problems. However, these methods typically target the zero-temperature limit,…
Gauge theories on manifolds with spatial boundaries are studied. It is shown that observables localized at the boundaries (edge observables) can occur in such models irrespective of the dimensionality of spacetime. The intimate connection…
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous…
The theory of limiting modular symbols provides a noncommutative geometric model of the boundary of modular curves that includes irrational points in addition to cusps. A noncommutative space associated to this boundary is constructed, as…
Ordered chains (such as chains of amino acids) are ubiquitous in biological cells, and these chains perform specific functions contingent on the sequence of their components. Using the existence and general properties of such sequences as a…