Related papers: Statistical Mechanics, Gravity, and Euclidean Theo…
Classical and quantum statistical mechanics are cast here in the language of projective geometry to provide a unified geometrical framework for statistical physics. After reviewing the Hilbert space formulation of classical statistical…
Gibbs statistical mechanics is derived for the Hamiltonian system coupling self-consistently a wave to N particles. This identifies Landau damping with a regime where a second order phase transition occurs. For nonequilibrium initial data…
The formal structure of geometrical thermodynamics is reviewed with particular emphasis on the geometry of equilibria submanifolds. On these submanifolds thermodynamic metrics are defined as the Hessian of thermodynamic potentials. Links…
We consider degrees of freedom for a quantum de Sitter spacetime. The problem is studied from both a Lorentzian and a Euclidean perspective. From a Lorentzian perspective, we compute dynamical properties of the static patch de Sitter…
A celebrated result by Jacobson is the derivation of Einstein's equations from Unruh's temperature, the Bekenstein-Hawking entropy and the Clausius relation. This has been repeatedly taken as evidence for an interpretation of Einstein's…
Using the system-bath model Hamiltonian this thesis covers the equilibrium and out of equilibrium properties of quantum open systems. Topics included are the calculation of thermodynamical quantities of open systems, derivation of quantum…
The critical behavior of a 3D Ising-like system is studied at the microscopic level of consideration. The free energy of ordering is calculated analytically as an explicit function of temperature, an external field and the initial…
We develop a method using a coarse graining of the energy fluctuations of an equilibrium quantum system which produces simple parameterizations for the behaviour of the system. As an application, we use these methods to gain more…
The concept of work is studied in quantum thermostatistics of a system surrounded by an environment and driven by an external force. It is found that there emerges the gauge theoretical structure in a nonequilibrium process, the field of…
An approach to the description of subdynamics inside non-relativistic quantum field theory is presented, in which the notions of relevant observable, time scale and complete positivity of the time evolution are stressed. A scattering theory…
Classical gravitational evolution admits an elegant and compact re-expression in terms of gauge covariant generalizations of Lie derivatives with respect to a spatial phase space dependent $su(2)$ valued vector field called the Electric…
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation…
The black hole area theorem suggests that classical general relativity is the thermodynamic limit of a quantum statistics. The degrees of freedom of the statistical theory cannot be the spacetime metric. We argue that the statistical theory…
Discrete formulations of (quantum) gravity in four spacetime dimensions build space out of tetrahedra. We investigate a statistical mechanical system of tetrahedra from a many-body point of view based on non-local, combinatorial gluing…
This thesis uses Path Integrals and Green's Functions to study Gravity, Quantum Field Theory and Statistical Mechanics, particularly with respect to: finite temperature quantum systems of different spin in gravitational fields; finite…
Systems with many interacting stochastic constituents are fully characterized by their free energy. Computing this quantity is therefore the objective of various approaches, notably perturbative expansions, which are applied in problems…
Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles.…
The Hubbard model describes a lattice system of quantum particles with local (on-site) interactions. Its free energy is analytic when \beta t is small, or \beta t^2/U is small; here, \beta is the inverse temperature, U the on-site repulsion…
We describe a novel algorithm that learns a Hamiltonian from local expectations of its Gibbs state using the free energy variational principle. The algorithm avoids the need to compute the free energy directly, instead using efficient…
Among various approaches in proving gauge independence, models containing an explicit gauge dependence are convenient. The well-known example is the gauge parameter in the covariant gauge fixing which is of course most suitable for the…