Thermodynamics in the quantum regime : fundamental aspects and new directions Quantum Thermodynamics is a novel research field which explores the emergence of thermodynamics from quantum theory and addresses thermodynamic phenomena which appear in finite size non equilibrium and finite time contexts. Blending together elements from open quantum systems statistical mechanics quantum many body physics and quantum information theory it pinpoints thermodynamic advantages and barriers emerging from genuinely quantum properties such as quantum coherence and correlations. Owing to recent experimental efforts the field is moving quickly towards practical applications such as nano scale heat devices or thermodynamically optimised protocols for emergent quantum technologies. Starting from the basics the present volume reviews some of the most recent developments as well as some of the most important open problems in quantum thermodynamics. The self contained chapters provide concise and topical introductions to researchers who are new to the field. Experts will find them useful as a reference for the current state of the art. In six sections the book covers topics such as quantum heat engines and refrigerators fluctuation theorems the emergence of thermodynamic equilibrium thermodynamics of strongly coupled systems as well as various information theoretic approaches including Landauers principle and thermal operations. It concludes with a section dedicated to recent quantum thermodynamics experiments and experimental prospects on a variety of platforms ranging from cold atoms to photonic systems and NV centres Introduction to Quantum Thermodynamics: History and prospects (Robert Alicki and Ronnie Kosloff) Part I: Continuous and discrete quantum heat device Thermodynamic principles and implementations of quantum machines (Arnab Ghosh Wolfgang Niedenzu Victor Mukherjee and Gershon Kurizki) Performance of quantum thermodynamic cycles (Tova Feldmann and José P. Palao) Quantum features and signatures of quantum thermal machines (Amikam Levy and David Gelbwaser Klimovsky) Friction free quantum machines (Adolfo del Campo Aurélia Chenu Shujin Deng and Haibin Wu) Physical implementations of quantum absorption refrigerators (Mark Mitchison and Patrick Hofer) Quantum thermodynamics of nanoscale thermoelectrics and electronic devices (Robert S. Whitney Rafael Sánchez and Janine Splettstoesser) Quantum batteries (Francesco Campaioli Felix A. Pollock and Sai Vinjanampathy) Quantum rotor engines (Stella Seah Stefan Nimmrichter Alexandre Roulet and Valerio Scarani) Part II: Fluctuating work and irreversiblity in the quantum regime Quantum fluctuation theorems (Ken Funo Masahito Ueda and Takahiro Sagawa) Fluctuating work in coherent quantum systems: proposals and limitations (Elisa Bäumer Matteo Lostaglio Martí Perarnau Llobet and Rui Sampaio) The coherent crooks equality (Zoe Holmes) The role of quantum work statistics in many body physics (John Goold Francesco Plastina Andrea Gambassi and Alessandro Silva) Ancilla assisted measurement of quantum work (Gabriele De Chiara Paolo Solinas Federico Cerisola and Augusto J. Roncaglia) Work heat and entropy production along quantum trajectories (Cyril Elouard and Hamed M.Mohammady) Characterizing irreversibility in open quantum systems (Tiago B. Batalhão Stefano Gherardini Jader P. Santos Gabriel T. Landi and Mauro Paternostro) Part III: Equilibration and thermalization Dynamical typicality for initial states with a preset measurement statistics of several commuting observables (Ben N. Balz Jonas Richter Jochen Gemmer Robin Steinigeweg and Peter Reimann) Equilibration times in closed quantum many body systems (H. Wilming T. R. de Oliveira A. J. Short and J. Eisert) Nonequilibrium many body quantum dynamics: from full random matrices to real systems (Lea F. Santos and E. J. Torres Herrera) Properties of thermal quantum states: locality of temperature decay of correlations and more (Martin Kliesch and Arnau Riera) Quantum thermometry (Antonella De Pasquale and Thomas M. Stace) Part IV: Thermodynamics of strongly coupled open systems Hamiltonian of mean force for strongly coupled systems (Harry J. D. Miller) The reaction coordinate mapping in quantum thermodynamics (Ahsan Nazir and Gernot Schaller) Hierarchical Equations of Motion Approach to Quantum Thermodynamics (Akihito Kato and Yoshitaka Tanimura) Cooling to absolute zero: the unattainability principle (Nahuel Freitas Rodrigo Gallego Lluís Masanes and Juan Pablo Paz) Part V: Information theoretic approaches to quantum thermodynamics Resource theory of quantum thermodynamics: Thermal operations and Second Laws (Nelly Huei Ying Ng and Mischa Prebin Woods) One shot information theoretical approaches to fluctuation theorems (Andrew J. P. Garner) The second law and beyond in microscopic quantum setups (Raam Uzdin) Information erasure (Toshio Croucher Jackson Wright André R. R. Carvalho Stephen M. Barnett Joan A. Vaccaro) Trade off between work and correlations in quantum thermodynamics (Giuseppe Vitagliano Claude Klöckl Marcus Huber and Nicolai Friis) Quantum thermodynamics with multiple conserved quantities (Erick Hinds Mingo Yelena Guryanova Philippe Faist and David Jennings) Smooth entropy in axiomatic thermodynamics (Mirjam Weilenmann Lea Krämer Gabriel and Renato Renner) Thermodynamics from information (Manabendra Nath Bera Andreas Winter and Maciej Lewenstein) Part VI: Experimental platforms for quantum thermodynamics One dimensional atomic superfluids as a model system for quantum thermodynamics (Jörg Schmiedmayer) Single particle thermodynamics with levitated nanoparticles (James Millen and Jan Giesler) Single atom heat engine in a tapered ion trap (Samuel T. Dawkins Obinna Abah Kilian Singer and Sebastian Deffner) Quantum thermodynamics in a single electron box (Jonne V. Koski and Jukka P. Pekola) Probing quantum fluctuations of work with a trapped ion (Yao Lu Shuoming An Jing Ning Zhang and Kihwan Kim) Maxwell’s demon in photonic systems (Luca Mancino Mario A. Ciampini Mihai D. Vidrighin Marco Sbroscia Ilaria Gianani and Marco Barbieri) Maxwell’s demon in superconducting systems (Nathanaël Cottet and Benjamin Huard) NV color centers in diamond as a platform for quantum thermodynamics (Nir Bar Gill)