Antoine Rignon-Bret: The second law: from Lindblad equation to black holes

mardi 3 févr. 2026, 10:30 → 11:30 Europe/Paris

In this talk, I will present how techniques from quantum information theory and quantum thermodynamics can be used to derive the second law of thermodynamics for quantum fields. I will begin with the case of a finite quantum system undergoing a Markovian evolution driven by an infinite bath, whose dynamics are governed by the Lindblad equation and whose thermodynamic properties are well understood. Building on this framework, I will show how a natural generalization allows us to extend these methods to the thermodynamics of quantum fields defined on causal horizons. Unlike finite quantum systems, quantum field theory admits many unitarily inequivalent Hilbert spaces, each constructed from a distinct choice of vacuum state. I will argue that these different vacua can be interpreted as corresponding to different reservoirs driving the dynamics. In particular, I will demonstrate how Wall’s proof of the generalized second law fits naturally within this framework, and how analogous thermodynamic laws describing black hole thermodynamics emerge for asymptotic observers. These laws correspond to different thermodynamic potentials associated with distinct vacuum states, such as the Boulware, Hartle–Hawking, and Unruh vacua.