|Ph.D Student||Shpielberg Ohad|
|Subject||Non Equilibrium Statistical Mechanics: Electric Networks,|
Energy Forms and the Additivity Principle
|Department||Department of Physics||Supervisor||Professor Eric Akkermans|
|Full Thesis text|
Systems with many degrees of freedom are notoriously hard to grasp intuitively
as well as capture mathematically. Thermodynamics and statistical mechanics
ideas allowed for a leap in the understanding of such complex systems at equilibrium
over a century ago. Despite this success, little is known when our system
is taken out of equilibrium. Moreover, most of the knowledge concentrates on
system driven slightly out of equilibrium.
In the last 15 years, the macroscopic fluctuation theory was shown to be a
successful description of out of equilibrium diffusive systems. It was shown to
successfully capture the behavior of the few solvable models in the field. In this
Thesis, I will focus on the study of two properties of diffusive boundary driven
systems within the scope of the macroscopic fluctuation theory.
The first, current fluctuations, allows intuitive understanding of the physics
governing the system through the noise statistics of the steady state. Generally,
calculating the current fluctuations is hard. However, a clever guess, known
as the additivity principle, allows to obtain analytically an expression for the
current fluctuations. This Thesis presents a sufficient and necessary condition
for the validity of the additivity principle guess. Moreover, assuming the validity
of the additivity principle, the universality of current fluctuations is shown for
systems of arbitrary geometry.
The second property discussed is the density correlations. While in equilibrium
- away from a phase transition, correlation functions are known to decay
exponentially, for systems driven out of equilibrium, correlation functions are
generically long ranged. Using known results for diffusive classical systems, it is
shown that transport in disordered quantum systems can also be studied using
the macroscopic fluctuation theory. Moreover, an exact correspondence between
classical processes and some quantum processes is found.