Related papers: Empirical relationship as a stepping-stone to theo…
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations.…
The purpose of this note is to see to what extent ideal gas laws can be obtained from simple Newtonian mechanics, specifically elastic collisions. We present simple one-dimensional situations that seem to validate the laws. The first…
Stationary adiabatic flows of real gases issued from a source of given intensity are studied. Thermodynamic states of gases are described by Legendrian or Lagrangian manifolds. Solutions of Euler equations are given implicitly for any…
A numerical model is built, simulating the principles of kinetic gas theory, to predict pressures of molecules in a spherical pressure vessel; the model tracks a single particle and multiplies the force on the spherical walls by a mole of…
A recently suggested equation of state with the induced surface tension is generalized to the case of quantum gases with mean-field interaction. The self-consistency conditions of such a model and the necessary one to obey the Third Law of…
We use the non-equilibrium statistical field theory for classical particles recently developed by Mazenko and Das and Mazenko, together with the free generating functional for particles initially correlated in phase space derived in…
We formulate an approximate thermodynamic theory of the phase transition in driven lattice gases with attractive nearest-neighbor interactions. We construct the van der Waals equation of state for a driven system where a nonequilibrium…
We propose a classical, i.e., local-real physical model of processes underlying EPR experiments. The model leads to the prediction, that the visibility of the output signal will exhibit increasing variation as the coincidence window is…
In classical phenomenological thermodynamics the first and second laws can be regarded as independent statements. Statistical mechanics provides a microscopic substratum that explains thermodynamics in probabilistic terms via a microstate…
This thesis investigates the connection between quantum theory, thermodynamics and information theory. Theories with structure similar to that of quantum theory are considered, mathematically described by the framework of "Generalized…
Traditional derivations of the van der Waals equation typically use standard recipes involving ensemble averages of statistical mechanics. In this work, we study a box of weakly interacting gas particles in one-dimension from a purely…
The discovery of physical laws consistent with empirical observations lies at the heart of (applied) science and engineering. These laws typically take the form of nonlinear differential equations depending on parameters, dynamical systems…
In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in…
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic…
The Fokker--Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions are limited to special cases, and resorting to numerical simulation is often…
Non-parametric methods avoid the problem of having to specify a particular data generating mechanism, but can be computationally intensive, reducing their accessibility for large data problems. Empirical likelihood, a non-parametric…
The piecewise parabolic method and related schemes are widely used to model stellar flows. Several different methods for extending the validity of these methods to a general equation of state have been proposed over time, but direct…
The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal…
A generalization of the quantum van der Waals equation of state for a multi-component system in the grand canonical ensemble is proposed. The model includes quantum statistical effects and allows to specify the parameters characterizing…