Statistical thermodynamics of long-range interacting systems and near-field thermal radiation

Abstract

Two main topics are examined in this thesis: classical systems with long-range interactions and thermal radiation in the near-field regime. In the first part, we present a thermodynamic approach describing systems with long-range interactions which takes into account the intrinsic nonadditivity in these systems. The basic concept behind this approach is to consider a large ensemble of replicas of the system where the standard formulation of thermodynamics can be naturally applied and the properties of a single system can be consequently inferred. The formulation of the thermodynamic for these systems is in close connection with Hill's thermodynamics of systems with small number of particles. It is shown that systems with long-range interactions can attain equilibrium configurations in the unconstrained ensemble. In this statistical ensemble, the control parameters are the temperature, pressure, and chemical potential, while the energy, volume, and number of particles fluctuate. We consider a solvable model as a concrete example of a system that achieves stable equilibria in this ensemble. We also give a complete description of the phase-diagram of the Thirring model in both the microcanonical and the canonical ensemble, highlighting the main features of ensemble inequivalence. I the second part, we study energy and entropy fluxes of near-field thermal radiation in many-body systems, with application to energy-conversion processes. It is shown that the maximum work that can be obtained from the thermal radiation emitted by two planar sources in the near-field regime is much larger than that corresponding to the blackbody limit. This quantity as well as an upper bound for the efficiency of the process are computed from the formulation of thermodynamics in the near-field regime. The case when the difference of temperatures of the hot source and the environment is small, relevant for energy harvesting, is studied in detail. We also show that thermal radiation energy conversion can be more efficient in the near-field regime. Moreover, by analyzing the thermodynamic performance of three-body near-field heat engines, we demonstrate that the power they supply can be substantially larger than that of two-body systems, showing their strong potential for energy harvesting. Theoretical limits for energy and entropy fluxes in three-body systems are discussed and compared with their corresponding two-body counterparts. Such considerations confirm that the thermodynamic availability in energy-conversion processes driven by three-body photon tunneling can exceed the thermodynamic availability in two-body systems.

En esta tesis se estudia la termodinámica y mecánica estadística de sistemas clásicos con interacciones de largo alcance y de la radiación térmica de campo cercano. En la primera parte, introducimos un formalismo termodinámico apropiado para sistemas con interacciones de largo alcance, en el cual se tiene en cuenta la no aditividad intrínseca en estos sistemas. Para estos sistemas, mostramos que la temperatura, presión y potencial químico pueden ser variables independientes. A su vez, dependiendo del sistema, lo anterior da lugar a poder tomar estas variables como parámetros de control para definir las configuraciones de equilibrio. Para estudiar este hecho, hemos introducido un modelo que cumple estas condiciones. En la segunda parte de la tesis, hemos desarrollado un esquema termodinámico para describir procesos de conversión de energía en trabajo útil en sistemas con interacción térmica radiativa en el campo cercano. Se ha mostrado explícitamente que de la radiación térmica de campo cercano puede extraerse un trabajo útil mayor que el obtenido de la radiación térmica de cuerpo negro. Hemos mostrado, además, que la potencia obtenida en sistemas con tres cuerpos en interacción puede ser considerablemente superior que en el caso de dos cuerpos.