This dissertation details the development and implementation of novel experimental techniques for cooling neutral atoms. Based on a method first proposed by Maxwell in a nineteenth century thought experiment, these techniques reduce the entropy of an ensemble by allowing unidirectional transmission through a barrier and thus compressing the ensemble without doing work or increasing its temperature. Because of their general nature, these techniques are much more broadly applicable than traditional laser and evaporative cooling methods, with the potential to cool the vast majority of the periodic table and even molecules. An implementation that cools in one dimension is demonstrated for an ensemble of magnetically trapped rubidium atoms which are irreversibly transferred to a gravito-optical trap. Analysis of the experimental results confirms that phase-space is completely compressed in one dimension. The results also indicate that the overall cooling performance is limited only by the dynamics of atoms in the magnetic trap and may be improved with a more ergodic system. Three-dimensional cooling may be accomplished with a modified technique which substitutes a radio-frequency-dressed magnetic trap for the gravito-optical trap. Application of this technique to atomic hydrogen and progress toward building an experimental apparatus are discussed. / text

A time-reversible Maxwell's demon is demonstrated which creates a density difference between two chambers initialized to have equal density. The density difference is estimated theoretically and confirmed by computer simulations. It is found that the reversible Maxwell's demon compresses phase space volume even though its dynamics are time reversible. The significance of phase space volume compression in operating a microscopic heat engine is also discussed.

"Dynamics" is very roughly the study of how objects change in time; for instance whether an electrical circuit goes to equilibrium, due to thermal dissipation. By "information", we mean how helpful it is to observe an object in order to know it better, for instance how many binary digits we can acquire on the value of a voltage by an appropriate measure. A "computation" is a physical process, e.g. the flow of current into a complex set of transistors, that after some time eventually gives us the solution of a mathematical problem (such as "Is 13 prime?"). We are interested to various relations between these concepts. In a first chapter, we unify some arguments in the literature to show that a whole class of quantities of dynamical systems are uncomputable. For instance the topological entropy of tilings and Turing machines. Then we propose a precise meaning to the statement "This dynamical system is a computer", at least for symbolic systems, such as cellular automata. We also show, for instance, that a "computer" must be dynamically unstable, and can even be chaotic. In a third chapter, we compare how complicated it is to control a system according whether we can acquire information on it ("feedback") or not ("open loop"). We are specifically interested in finite-state systems. In last chapter we show how to control a scalar linear system when only a finite amount of information can be acquired at every step of time.