Fundamentals of quantum thermodynamics

Recently, quantum thermodynamics has been formulated as a resource theory, in which free operations are so-called thermal operations, i.e. energy-conserving reversible operations and local thermalisation at a fixed temperature. A basic question is then whether a given (nonequilibrium) state can be transformed into another state under thermal operations. While partial answers to this question led to important advances such as the notion of deterministic work, quantum generalisations of the second law of thermodynamics, and the more general development of fluctuation relations, the question is still open for states with quantum coherence in the Hamiltonian basis, beyond the case of a single qubit. This project will investigate this open question and related topics dealing with thermodynamic processes and state manipulations in the fully quantum regime. This will require developing a framework to link the resource theories of informational nonequilibrium in thermodynamics and of quantum coherence. More generally, this project may explore to what extent (i.e. under which resource-theoretic constraints) quantum thermodynamics can be bridged with conventional macroscopic thermodynamics, in which the description of resources is very different, as systems are characterised by macroscopic observables like pressure and volume. A suitable question would be to find a consistent definition of temperature for quantum processes, and to validate the microscopic descriptions of relevant open quantum system dynamics.