title: Information-theoretic equilibrium and observable thermalization.
abstract: A crucial point in statistical mechanics is the definition of the notion of thermal equilibrium, which can be given as the state that maximises the von Neumann entropy, under the validity of some constraints. Arguing that such a notion can never be experimentally probed, in this paper we propose a new notion of thermal equilibrium, focused on observables rather than on the full state of the quantum system. We characterise such notion of thermal equilibrium for an arbitrary observable via the maximisation of its Shannon entropy and we bring to light the thermal properties that it heralds. The relation with Gibbs ensembles is studied and understood. We apply such a notion of equilibrium to a closed quantum system and show that there is always a class of observables which exhibits thermal equilibrium properties and we give a recipe to explicitly construct them. Eventually, an intimate connection with the Eigenstate Thermalisation Hypothesis is brought to light.
authors.affiliation: Atomic and Laser Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK.
authors.forename: F
authors.initials: F
authors.lastname: Anzà
authors.affiliation: Atomic and Laser Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK.|Centre for Quantum Technologies, National University of Singapore, 117543, Singapore.|Department of Physics, National University of Singapore, 2 Science Drive 3, 117551, Singapore.|Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, 100084, Beijing, China.
authors.forename: V
authors.initials: V
authors.lastname: Vedral