Quantum thermodynamics is an emerging research field aiming to extend standard thermodynamics and non-equilibrium statistical physics to ensembles of sizes well below the thermodynamic limit, in non-equilibrium situations, and with the full inclusion of quantum effects. Fueled by experimental advances and the potential of future nanoscale applications this research effort is pursued by scientists with different backgrounds, including statistical physics, many-body theory, mesoscopic physics and quantum information theory, who bring various tools and methods to the field. A multitude of theoretical questions are being addressed ranging from issues of thermalisation of quantum systems and various definitions of "work", to the efficiency and power of quantum engines. This overview provides a perspective on a selection of these current trends accessible to postgraduate students and researchers alike.

Einstein realized that the fluctuations of a Brownian particle can be used to ascertain the properties of its environment. A large number of experiments have since exploited the Brownian motion of colloidal particles for studies of dissipative processes, providing insight into soft matter physics and leading to applications from energy harvesting to medical imaging. Here, we use heated optically levitated nanospheres to investigate the non-equilibrium properties of the gas surrounding them. Analysing the sphere's Brownian motion allows us to determine the temperature of the centre-of-mass motion of the sphere, its surface temperature and the heated gas temperature in two spatial dimensions. We observe asymmetric heating of the sphere and gas, with temperatures reaching the melting point of the material. This method offers opportunities for accurate temperature measurements with spatial resolution on the nanoscale, and provides a means for testing non-equilibrium thermodynamics.

We study the intrinsic computational power of correlations exploited in measurement-based quantum computation. By defining a general framework the meaning of the computational power of correlations is made precise. This leads to a notion of resource states for measurement-based classical computation. Surprisingly, the Greenberger-Horne-Zeilinger and Clauser-Horne-Shimony-Holt problems emerge as optimal examples. Our work exposes an intriguing relationship between the violation of local realistic models and the computational power of entangled resource states.PACS numbers: 03.67. Lx, 03.65.Ud, 89.70.Eg A striking implication of measurement-based quantum computation (MBQC) is that correlations possess intrinsic computational power. MBQC is an approach to computation radically different to conventional circuit models. In a circuit model, information is manipulated by a network of logical gates. In contrast, in the standard model of MBQC (also known as "one-way" quantum computation) information is processed by a sequence of adaptive single-qubit measurements on an entangled multi-qubit resource state [1,2,3]. Impressive characterization of the necessary properties of quantum resource states that enable universal quantum computation in the measurement model has already been achieved [4,5]. However, it is not the quantum states themselves, but the correlated classical data returned by the measurements which embodies this computational power. A necessary ingredient to extract this power is a classical control computer (see Fig. 1), which processes and feeds forward measurement outcomes and directs future adaptive measurements. From this classical computer's perspective, the correlated measurement outcomes enable it to compute problems beyond its own power.In this Letter we will make the notion of the computational power of a correlated resource precise. By doing so, a natural classical analogue of measurement-based computation emerges and we find a link to quantum non-locality. Specifically, we show that the GreenbergerHorne-Zeilinger (GHZ) problem [6] and the ClauserHorne-Shimony-Holt (CHSH) construction [7] emerge as closely related to measurement-based classical computation (MBCC), as does the Popescu-Rohrlich non-local box [8].Framework for MBQC.-We wish to study the computational power of correlated resources in a more general setting than the particular models of MBQC which have been proposed [1,2,3,4,5]. To achieve this, let us first define a general framework of computational models which shares the essential features of MBQC. It consists of two components, a correlated multi-partite resource and a classical control computer. A correlated multipartite resource consists of a number of parties, which ex- change classical information with the control computer, see Fig. 1. The correlations in their outputs are solely due to their joint history and no direct communication between parties is allowed during the computation. There shall be just a single exchange of data with each party. This restriction is an import...

Thermodynamics is a highly successful macroscopic theory widely used across the natural sciences and for the construction of everyday devices, from car engines to solar cells. With thermodynamics predating quantum theory, research now aims to uncover the thermodynamic laws that govern finite size systems which may in addition host quantum effects. Recent theoretical breakthroughs include the characterisation of the efficiency of quantum thermal engines, the extension of classical non-equilibrium fluctuation theorems to the quantum regime and a new thermodynamic resource theory has led to the discovery of a set of second laws for finite size systems. These results have substantially advanced our understanding of nanoscale thermodynamics, however putting a finger on what is genuinely quantum in quantum thermodynamics has remained a challenge. Here we identify information processing tasks, the so-called projections, that can only be formulated within the framework of quantum mechanics. We show that the physical realisation of such projections can come with a non-trivial thermodynamic work only for quantum states with coherences. This contrasts with information erasure, first investigated by Landauer, for which a thermodynamic work cost applies for classical and quantum erasure alike. Repercussions on quantum work fluctuation relations and thermodynamic single-shot approaches are also discussed.