#### Thermodynamic and information theoretic relations for general quantum systems

To be applicable for nano-scale systems thermodynamics must be revised to account for, in addition to thermal fluctuations, quantum fluctuations. These effects are becoming measurable as rapid experimental progress in controlling and manipulating the dynamics of small systems is being made. Extremely small at the macroscale, and therefore neglected in the usual formulation of thermodynamics, they dominate at the micro and nanoscale.

A multitude of questions open up, and these will need to be addressed in order to make optimal use of the new technologies on the horizon: What are the correct/most useful definitions of work and heat for closed and open quantum processes? How does quantum measurement affect them? Can quantum engines be build that explore quantum fluctuations to provide technological advantages over classical ones? If entanglement allows the extraction of work could one use the abundance of entanglement in the world for that purpose? Finally, WG 2 will aim to find a general description of non-equilibrium quantum processes, for example by generalising the extremely successful classical theory of fluctuation theorems and combining it with insights from the study of quantum channels and information theoretic relations.

##### Current state of knowledge

Much recent work has focussed on the issues of extending definitions and understanding of heat and work to the microscopic scale. It is now appreciated that these thermodynamic quantities, which are process variables rather than state variables in classical mechanics, have, in general, no quantum observable associated with them, and that work corresponds to a two-point correlation function rather than an expectation value. Studies of the second law for systems with quantum correlations have further shown that it is possible to extract work essentially from these correlations. This has led to a strong interest in questions that are information-theoretic in flavour, such as the re-interpretation of Landauer’s principle and Maxwell’s demon in the quantum regime. Recent work and current controversy is also concerned with what is the smallest possible heat engine and refrigerator, and what are their efficiencies in the quantum regime. Finally, a range of remarkable stochastic generalizations of the second law of thermodynamics, valid for arbitrary classical non-equilibrium processes, have been derived in the form of detailed fluctuation theorems that quantify the occurrence of negative entropy events. While some progress has been made on the quantum generalizations, most work assumes stochastic paths governed by quantum probabilities and does not incorporate quantum coherence throughout the processes.

##### Goals of the Working Group

There are many different ideas about extending both equilibrium and non-equilibrium thermodynamic notions to account for the quantum regime soon to be encountered experimentally. In bringing workers with very different ideas and backgrounds together, participants in WG2 will aim to:

- Clarify fundamental notions of heat and work in the quantum regime and derive laws that govern equilibrium and out-of equilibrium quantum processes.
- Establish if and how quantum correlations within a system and with its environment affect standard thermodynamic laws.
- Investigate the performance of thermodynamic devices coupled to novel quantum environments.
- Develop a full-fledged framework of thermodynamics for micro and nanoscale many-body quantum systems and establish if the power of quantum mechanics, such as quantum coherence, quantum correlations and quantum measurements, can be used to design new quantum engines with improved efficiencies.
- Investigate information-theoretic implications of this framework, such as Landauer’s principle and feedback scenarios, i.e. Maxwell’s demon “breaking” of the second law.