The second law of thermodynamics at the microscopic scale

In quantum statistical mechanics, equilibrium states have been shown to be the typical states for a system that is entangled with its environment, suggesting a possible identification between thermodynamic and von Neumann entropies. In this paper, we investigate how the relaxation toward equilibrium is made possible through interactions that do not lead to significant exchange of energy, and argue for the validity of the second law of thermodynamics at the microscopic scale.Comment: 3 pages, 1 figur

Statistical mechanics of covariant systems with multi-fingered time

Recently, in [Class. Quantum Grav. 33 (2016) 045005], the authors proposed a new approach extending the framework of statistical mechanics to reparametrization-invariant systems with no additional gauges. In this work, the approach is generalized to systems defined by more than one Hamiltonian constraints (multi-fingered time). We show how well known features as the Ehrenfest- Tolman effect and the J\"uttner distribution for the relativistic gas can be consistently recovered from a covariant approach in the multi-fingered framework. Eventually, the crucial role played by the interaction in the definition of a global notion of equilibrium is discussed.Comment: 5 pages, 2 figure

On the road to covariant statistical mechanics

D’après la relativité générale, l’espace-temps n’est pas l’arène absolue imaginée par Newton, dans laquelle les particules se meuvent, sont créées ou annihilées. Au contraire, il s’agit d’un objet dynamique, identifié au champ gravitationnel, qui possède ses propres degrés de liberté locaux et, en tant que tel, peut être sujet à des fluctuations thermiques. Une meilleure compréhension des propriétés statistiques de ces fluctuations locales est essentielle pour la cosmologie primordiale, la gravité quantique, ou encore l’étude des trous noirs. Malheureusement, l’application de la mécanique statistique à des systèmes relativistes fait face à une difficulté conceptuelle majeure : l’absence de variable temporelle privilégiée. Dans cette thèse, nous présentons trois approches vers une formulation covariante de la mécanique statistique. D'abord, l’hypothèse de temps thermique renverse la logique habituelle en proposant que l’existence d’un temps privilégié dérive de l’état dans lequel se trouve le système. Une autre voie consiste à étendre l’hypothèse ergodique de la mécanique statistique standard, afin d’inclure les moyennes temporelles définies au moyen d’horloges internes au système. Enfin, l’idée que la thermodynamique pourrait trouver son origine à l’échelle microscopique dans l’intrication des systèmes quantiques est étudiée, l’état statistique étant alors déterminé par la structure de l’espace de Hilbert. Dans tous les cas, la notion de sous-système apparaît comme étant l’élément essentiel pour parvenir à une formulation covariante de la mécanique statistique.According to general relativity, spacetime is not the absolute arena that Newton had imagined, where particles move, are created or annihilated. Instead, it is a dynamical object identified with the gravitational field, that possesses its own local degrees of freedom and, as such, can be subject to thermal fluctuations. A better understanding of the statistical properties of these local fluctuations would be highly relevant for early cosmology, quantum gravity, or the study of black holes. Unfortunately, the application of statistical mechanics ideas to relativistic systems faces a major conceptual difficulty: the absence of a preferred time. In this thesis, we present three approaches to covariant statistical mechanics. First, the thermal time hypothesis reverses the common logic and proposes the existence of a preferred time to be subsequent to the actual state of the system. An alternative path consists in extending the ergodic hypothesis of standard statistical mechanics to include time averages performed using internal clocks. Lastly, the idea that thermodynamics could find its origin at the microscopic scale in the entanglement of quantum systems is studied, the statistical state being then determined by the structure of the Hilbert space. In all cases, the notion of subsystem appears as the essential element to achieve a covariant formulation of statistical mechanics

Statistical mechanics of covariant systems with multi-fingered time

5 pages, 2 figuresInternational audienceRecently, in [Class. Quantum Grav. 33 (2016) 045005], the authors proposed a new approach extending the framework of statistical mechanics to reparametrization-invariant systems with no additional gauges. In this work, the approach is generalized to systems defined by more than one Hamiltonian constraints (multi-fingered time). We show how well known features as the Ehrenfest- Tolman effect and the J\"uttner distribution for the relativistic gas can be consistently recovered from a covariant approach in the multi-fingered framework. Eventually, the crucial role played by the interaction in the definition of a global notion of equilibrium is discussed

Statistical mechanics of reparametrization-invariant systems. It takes three to tango.

9 pages, 2 figuresInternational audienceIt is notoriously difficult to apply statistical mechanics to generally covariant systems, because the notions of time, energy and equilibrium are seriously modified in this context. We discuss the conditions under which weaker versions of these notions can be defined, sufficient for statistical mechanics. We focus on reparametrization invariant systems without additional gauges. The key idea is to reconstruct statistical mechanics from the ergodic theorem. We find that a suitable split of the system into two non-interacting components is sufficient for generalizing statistical mechanics. While equilibrium acquires sense only when the system admits a suitable split into three weakly interacting components ---roughly: a clock and two systems among which a generalization of energy is equi-partitioned. The key property that allows the application of statistical mechanics and thermodynamics is an additivity condition of such generalized energy