Related papers: Beyond Point Particles -- Extended Structural Dyna…
Structure formation in 1+1 dimensions is considered, with emphasis on the effects of shell-crossing. The breakdown of the perturbative expansion beyond shell-crossing is discussed, and it is shown, in a simple example, that the perturbative…
It is established that black holes have entropy and behave as thermodynamical systems. Associating entropy to gravitational fields has not remained limited to black holes, necessitating the notion of the second law of thermodynamics in…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
Growth processes in many living organisms create thin, soft materials with an intrinsically hyperbolic geometry. These objects support novel types of mesoscopic defects - discontinuity lines for the second derivative and branch points -…
The approach to the analysis of the dynamic of non-equilibrium open systems within the framework of the laws of classical mechanics on the example a hard-disks is offered. This approach was based on Hamilton and Liouville generalized…
We derive the multiparticle-correlation expansion of the excess entropy of classical particles in the canonical ensemble using a new approach that elucidates the rationale behind each term in the expansion. This formula provides the…
We extend stochastic thermodynamics by relaxing the two assumptions that the Markovian dynamics must be linear and that the equilibrium distribution must be a Boltzmann distribution. We show that if we require the second law to hold when…
In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian…
Newtonian physics is describes macro-objects sufficiently well, however it does not describe microobjects. A model of Extended Mechanics for Quantum Theory is based on an axiomatic generalization of Newtonian classical laws to arbitrary…
We construct an explicit representation of the algebra of local diffeomorphisms of a manifold with realistic dimensions. This is achieved in the setting of a general approach to the (quantum) dynamics of a physical system which is…
This paper presents an {\it ab initio} derivation of the expression given by irreversible thermodynamics for the rate of entropy production for different classes of diffusive processes. The first class are Lorentz gases, where…
This thesis reports progress in two domains, causal structures and microscopic thermodynamics, both of which are pertinent in the development of quantum technologies. The first part is dedicated to the analysis of causal structure, which…
We propose a housekeeping/excess decomposition of entropy production for general nonlinear dynamics in a discrete space, including chemical reaction networks and discrete stochastic systems. We exploit the geometric structure of…
This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of…
The Lie product and the order relation are viewed as defining structures for Hamiltonian dynamical systems. Their admissible combinations are singled out by the requirement that the group of the Lie automorphisms be contained in the group…
Physical laws for elementary particles can be described by the quantum dynamics equation given a Hamiltonian. The solution are probability amplitudes in Hilbert space that evolve over time. A probability density function over position and…
Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for the…
Quantum mechanics is derived as an application of the method of maximum entropy. No appeal is made to any underlying classical action principle whether deterministic or stochastic. Instead, the basic assumption is that in addition to the…
By decoupling forward and backward stochastic trajectories, we construct a family of martingales and work theorems for both overdamped and underdamped Langevin dynamics. Our results are made possible by an alternative derivation of work…
The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic…