Related papers: Setting Boundaries for Statistical Mechanics
Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…
The geodesic approximation is a powerful method for studying the dynamics of BPS solitons. However, there are systems, such as BPS monopoles in three-dimensional hyperbolic space, where this approach is not applicable because the moduli…
For a system to qualify as a quantum fluid, quantum-statistical effects should operate in addition to quantum-mechanical ones. Here, we address the hitherto unexplored dynamical condition for the quantum-statistical effects to be…
The formation of bound states involving multiple particles underlies many interesting quantum physical phenomena, such as Efimov physics or superconductivity. In this work we show the existence of an infinite number of such states for some…
In this thesis we shall demonstrate that a measurement of position alone in non-commutative space cannot yield complete information about the quantum state of a particle. Indeed, the formalism used entails a description that is non-local in…
The two-body potential of systems with long-range interactions decays at large distances as $V(r)\sim 1/r^\alpha$, with $\alpha\leq d$, where $d$ is the space dimension. Examples are: gravitational systems, two-dimensional hydrodynamics,…
Physics is a model of nature able to both describe and predict the results of measurements made with respect to reference systems. These reference systems, in turn, are themselves physical and thus subject to the laws of physics. The…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. The statistical mechanics of such a system is derived…
Statistical thermodynamics has a universal appeal that extends beyond molecular systems, and yet, as its tools are being transplanted to fields outside physics, the fundamental question, \textit{what is thermodynamics?}, has remained…
We consider nonequilibrium systems with complex dynamics in stationary states with large fluctuations of intensive quantities (e.g. the temperature, chemical potential, or energy dissipation) on long time scales. Depending on the…
(abridged) Both fundamental constants that describe the laws of physics and cosmological parameters that determine the cosmic properties must fall within a range of values in order for the universe to develop astrophysical structures and…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
The operations of linear algebra, calculus, and statistics are routinely applied to measurement scales but certain mathematical conditions must be satisfied in order for these operations to be applicable. We call attention to the conditions…
This paper addresses the well posedness of a dynamical model of perfect plasticity with mixed boundary conditions for general closed and convex elasticity sets. The proof relies on an asymptotic analysis of the solution of a perfect…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
The continuous limit of large systems of particles of finite size on the line is described. The particles are assumed to move freely and stick under collision, to form compound particles whose mass and size is the sum of the masses and…
In this article, we study a weighted particle representation for a class of stochastic partial differential equations with Dirichlet boundary conditions. The locations and weights of the particles satisfy an infinite system of stochastic…
The capabilities of a new approach towards the foundations of Statistical Mechanics are explored. The approach is genuine quantum in the sense that statistical behavior is a consequence of objective quantum uncertainties due to entanglement…
Statistical mechanics can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann-Gibbs statistics is based on the hypothesis of exponential sensitivity to…