Editors: BinderF. 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. 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 Landauer's 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. This book has been written by over internationally recognized experts in this novel research field.

They were invited by the editors based on their expertise. The editors are as follows:. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Physics Quantum Physics. Fundamental Theories of Physics Free Preview. Presents the most up-to-date and comprehensive review of this fast-growing field Suitable for use by researchers but also accessible to interested students at the graduate level as well as quantum engineers in the private sector Covers the most interesting open problems so as to inspire newcomers Explores the most promising experimental platforms for applications to quantum technologies see more benefits.

Buy eBook. Buy Hardcover. FAQ Policy. About this book 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. Show all.

### Quantum thermodynamics

The editors are as follows: Dr. Felix Binder is an expert on quantum information theoretic approaches to thermodynamics and also studies quantum models for stochastic processes as well asquantum correlations. Luis A.

Correa is an expert on open quantum systems interested in the performanceoptimisation of quantum thermodynamic cycles e. He is also interested in quantum thermometry, or the precise measurementof ultra-cold temperatures with nano-scale spatial resolution.

Christian Gogolin is an expert on equilibration and thermalization in closed quantumsystems and has worked on a broad range of topics in quantum many-body andcondensed matter theory, quantum information theory, statistical mechanics, foundations ofquantum mechanics, and several others.

Janet Anders is an expert in the characterisation of work in the quantum regime andthermodynamic experiments at the microscale. She has worked on topics in quantuminformation theory and quantum thermodynamics, including quantum computation,entanglement in quantum many-body systems, thermodynamics in the strong couplinglimit, and non-equilibrium dynamics of levitated nanospheres.

Gerardo Adesso is an expert on quantum information theory and the characterisationof nonclassical correlations in open quantum systems, including their mathematicaldescription and their practical applications to quantum technologies such as cooling,thermometry, optical communication, sensing and metrology.

Quantum Batteries Pages Campaioli, Francesco et al. Quantum Thermometry Pages Pasquale, Antonella et al.

Biscuit market share in malaysiaInformation Erasure Pages Croucher, Toshio et al. Show next xx. Read this book on SpringerLink. Recommended for you. PAGE 1.Stochastic thermodynamics is an emergent field of research in statistical mechanics that uses stochastic variables to better understand the non-equilibrium dynamics present in many microscopic systems such as colloidal particlesbiopolymers e.

When a microscopic machine e. That is, heat energy from the surroundings will be converted into useful work. For larger engines, this would be described as a violation of the second law of thermodynamicsas entropy is consumed rather than generated.

Inhumans s01e01Loschmidt's paradox [5] states that in a time reversible system, for every trajectory there exists a time-reversed anti-trajectory. As the entropy production of a trajectory and its equal anti-trajectory are of identical magnitude but opposite sign, then, so the argument goes, one cannot prove that entropy production is positive.

For a long time, exact results in thermodynamics were only possible in linear systems capable of reaching equilibrium, leaving other questions like the Loschmidt paradox unsolved. During the last few decades fresh approaches have revealed general laws applicable to non-equilibrium system which are described by nonlinear equations, pushing the range of exact thermodynamic statements beyond the realm of traditional linear solutions.

These exact results are particularly relevant for small systems where appreciable typically non-Gaussian fluctuations occur. Thanks to stochastic thermodynamics it is now possible to accurately predict distribution functions of thermodynamic quantities relating to exchanged heat, applied work or entropy production for these systems.

The mathematical resolution to Loschmidt's paradox is called the steady state fluctuation theorem FTwhich is a generalisation of the second law of thermodynamics. The FT shows that as a system gets larger or the trajectory duration becomes longer, entropy-consuming trajectories become more unlikely, and the expected second law behaviour is recovered.

The FT was first put forward by Evans et al. The first observation and experimental proof of Evan's fluctuation theorem FT was performed by Wang et al.

## Thermodynamics in the Quantum Regime

Both, this relation and another refinement of the JR, the Hummer-Szabo relation became particularly useful for determining free energy differences and landscapes of biomolecules. These relations are the most prominent ones within a class of exact results some of which found even earlier and then rediscovered valid for non-equilibrium systems driven by time-dependent forces. A close analogy to the JR, which relates different equilibrium states, is the Hatano-Sasa relation that applies to transitions between two different non-equilibrium steady states".

Classical thermodynamics, at its heart, deals with general laws governing the transformations of a system, in particular, those involving the exchange of heat, work and matter with an environment. As a central result, total entropy production is identified that in any such process can never decrease, leading, inter alia, to fundamental limits on the efficiency of heat engines and refrigerators.

The thermodynamic characterisation of systems in equilibrium got its microscopic justification from equilibrium statistical mechanics which states that for a system in contact with a heat bath the probability to find it in any specific microstate is given by the Boltzmann factor. For small deviations from equilibrium, linear response theory allows to express transport properties caused by small external fields through equilibrium correlation functions. On a more phenomenological level, linear irreversible thermodynamics provides a relation between such transport coefficients and entropy production in terms of forces and fluxes.

Beyond this linear response regime, for a long time, no universal exact results were available. During the last 20 years fresh approaches have revealed general laws applicable to non-equilibrium system thus pushing the range of validity of exact thermodynamic statements beyond the realm of linear response deep into the genuine non-equilibrium region. These exact results, which become particularly relevant for small systems with appreciable typically non-Gaussian fluctuations, generically refer to distribution functions of thermodynamic quantities like exchanged heat, applied work or entropy production.

Stochastic thermodynamics combines the stochastic energetics introduced by Sekimoto [11] with the idea that entropy can consistently be assigned to a single fluctuating trajectory. Stochastic thermodynamics can be applied to driven i.

The dynamics of an open quantum system is then equivalent to a classical stochastic one. However, this is sometimes at the cost of requiring unrealistic measurements at the beginning and end of a process. Understanding non-equilibrium quantum thermodynamics more broadly is an important and active area of research.

The efficiency of some computing and information theory tasks can be greatly enhanced when using quantum correlated states; quantum correlations can be used not as a valuable resource in quantum computation, but also in the realm of quantum thermodynamics. For example, it has been theoretically shown that non-equilibrium quantum ratchet systems function far more efficiently then that predicted by classical thermodynamics.Quantum thermodynamics [1] [2] is the study of the relations between two independent physical theories: thermodynamics and quantum mechanics.

The two independent theories address the physical phenomena of light and matter. This paper is the dawn of quantum theory. In a few decades quantum theory became established with an independent set of rules. It differs from quantum statistical mechanics in the emphasis on dynamical processes out of equilibrium. In addition there is a quest for the theory to be relevant for a single individual quantum system. There is an intimate connection of quantum thermodynamics with the theory of open quantum systems.

The main assumption is that the entire world is a large closed system, and therefore, time evolution is governed by a unitary transformation generated by a global Hamiltonian. For the combined system bath scenario, the global Hamiltonian can be decomposed into:.

Reduced dynamics is an equivalent description of the system dynamics utilizing only system operators. Assuming Markov property for the dynamics the basic equation of motion for an open quantum system is the Lindblad equation GKLS : [6] [7].

The Heisenberg picture supplies a direct link to quantum thermodynamic observables. This assumption is used to derive the Kubo-Martin-Schwinger stability criterion for thermal equilibrium i. KMS state. This approach represents a thermodynamic idealization: it allows energy transfer, while keeping a tensor product separation between the system and bath, i.

Markovian behavior involves a rather complicated cooperation between system and bath dynamics. This observation is particularly important in the context of quantum thermodynamics, where it is tempting to study Markovian dynamics with an arbitrary control Hamiltonian. Erroneous derivations of the quantum master equation can easily lead to a violation of the laws of thermodynamics.

An external perturbation modifying the Hamiltonian of the system will also modify the heat flow. As a result, the L-GKS generator has to be renormalized.

An important class of problems in quantum thermodynamics is periodically driven systems. Periodic quantum heat engines and power-driven refrigerators fall into this class. A reexamination of the time-dependent heat current expression using quantum transport techniques has been proposed. A derivation of consistent dynamics beyond the weak coupling limit has been suggested. The second law of thermodynamics is a statement on the irreversibility of dynamics or, the breakup of time reversal symmetry T-symmetry.

This should be consistent with the empirical direct definition: heat will flow spontaneously from a hot source to a cold sink. From a static viewpoint, for a closed quantum system, the II-law of thermodynamics is a consequence of the unitary evolution. A dynamical viewpoint is based on local accounting for the entropy changes in the subsystems and the entropy generated in the baths.

In thermodynamics, entropy is related to a concrete process. In quantum mechanics, this translates to the ability to measure and manipulate the system based on the information gathered by measurement.With the rise of quantum technologies and the ability to control single atoms, ions and molecules, thermodynamics faces new challenges.

What new thermodynamic effects can be observed in the quantum microscopic realm?

Can quantum heat machines drastically outperform classical heat machines? Are there additional scale-dependent thermodynamic laws that become important only in small systems? What are the possibilities entailed in microscopic thermal control protocols?

How will the next generation of microscopic heat machines look like? These fascinating questions are at the core of my research. In the very near future, experimental capabilities will exceed our numerical capabilities when it comes to full quantum evolution followed by precise measurement of very fine-detail features of the system.

This multidisciplinary field uses tools from open quantum systems, quantum information, atomic physics, and mathematics. The quest for quantum technologies e. Some of these technologies may never be good enough for building a practical scalable quantum computer, but they are already sufficient for doing fundamental microscopic thermodynamics experiments both quantum and stochastic.

Thus, with the growing theoretical interest in quantum thermodynamics more and more labs with quantum technologies turn some of their resources to quantum thermodynamics. Skip to main content. Utility Menu Search. What is quantum thermodynamics? Global Passivity in Microscopic Thermodynamics Additional energy-information relations in thermodynamics of small systems Speed limits in Liouville space for open quantum systems.Researchers in Singapore have built a refrigerator that's just three atoms big.

This quantum fridge won't keep your drinks cold, but it's cool proof of physics operating at the smallest scales. The work is described in a paper published 14 January in Nature Communications. Researchers have built tiny 'heat engines' before, but quantum fridges existed only as proposals until the team at the Centre for Quantum Technologies at the National University of Singapore chilled with their atoms.

The device is an "absorption refrigerator. The first absorption refrigerators, introduced in the s, cycled the evaporation and absorption of a liquid, with cooling happening during the evaporation stage. They were widely used to make ice and chill food into the 20th Century.

Albert Einstein even held a patent on an improved design. Today's fridges and air conditioners more often use a compressor, but absorption refrigerators still have their uses -- science experiments included.

To create an absorption fridge with just three atoms took exquisite control. First, the researchers caught and held three atoms of the element Ytterbium in a metal chamber from which they'd removed all the air.

They also pulled one electron off each atom to leave them with a positive charge. The charged atoms -- called ions -- can then be held in place with electric fields.

Meanwhile, the researchers nudge and zap the ions with lasers to bring them into their lowest energy state of motion.

The result is that the ions are suspended almost perfectly still, strung out in a line. Another laser zap then injects some heat, making the ions wiggle about. The ions interact with each other because of their like charges. The result is three patterns of wiggle -- squishing and stretching along the line, like a slinky, rocking like a seesaw pivoting about the central atom, and zig-zagging out from the line like a waving skipping rope.

The energy in each wiggling mode is quantized, with the energy carried by a number of 'phonons'. By tuning the wiggling frequencies, the researchers set up conditions for refrigeration: making it such that a phonon moving from the see-saw to the slinky mode will drag a phonon from the zig-zag mode with it. The zig-zag mode thus loses energy, and its temperature drops.

At its coldest, it is within 40 microKelvin of absolute zero Cthe coldest temperature possible. Each round of preparing the ions and counting phonons took up to 70 milliseconds, with cooling happening for around 1ms. This process was repeated thousands of times.

Studying such small devices is important to see how thermodynamics -- our best understanding of heat flows -- may need tweaking to reflect more fundamental laws. The principles of thermodynamics are based on the average behaviours of big systems. They don't take quantum effects into account, which matters for scientists building nanomachines and quantum devices. To test quantum thermodynamics, the researchers made careful measurements of how phonons spread through the modes over time.

In particular, the researchers tested whether a quantum effect known as 'squeezing' would boost the quantum fridge's performance. Squeezing means the team fixed more precisely the position of the ions.

Liquid swipe githubBecause of the quantum uncertainty principle, that increases the fluctuation in momentum. In turn, this boosts the average number of phonons in the see-saw mode that drives the cooling. To the team's surprise, squeezing didn't help the fridge. However, they find the maximum amount of cooling, achieved with a method dubbed 'single shot', exceeds what classical equilibrium thermodynamics predicts.

In this approach, the team stop the refrigeration effect by de-tuning the wiggling modes before it reaches its natural endpoint. The cooling overshoots the equilibrium. Physicist Valerio Scarani, another member of the team, is looking forward to taking things further. So far, we have the engine of the fridge, but not the box for the beer," he says.

Note: Content may be edited for style and length.Recent years are witnessing a renewed interest in thermodynamic applications at the nanoscale. Technological advances are leading to unprecedented levels of miniaturisation in the fabrication of microscopic engines capable of producing work.

Recent experiments have produced engines built with only a few degrees of freedom, as for example a single electron transistor and the recently developed single ion engine. At the nanoscale, thermal fluctuations are quite strong and cannot be ignored any longer.

Moreover, it is also expected that at these scales and for low temperatures quantum effects play a role in the fluctuations of fundamental thermodynamic quantities, such as energy, entropy, work and heat. Quantum thermodynamics aims at understanding thermodynamic phenomena at the quantum scale.

Novel relevant questions arise, such as: how do the laws of thermodynamics emerge in the this regime? What is the role of quantum coherences and correlations, for example entanglement, in the efficiency of a thermodynamic transformation?

What is the maximum amount of work extractable from a reservoir? Quantum thermodynamics is also relevant for quantum information processing, as thermodynamic considerations play a fundamental role in the design of quantum information technologies, and to many-body physics, as concepts and tools from this field are needed for the design of many-particle quantum engines. If you wish to be placed on the wait list please send an email directly to kitpconf [at] kitp. Skip to main content.

Quantum Thermodynamics.Both thermodynamics and quantum mechanics are very important theories, but they are applicable to very different kinds of systems.

Python click button on websiteOn the other hand, quantum mechanics describes the behavior of microscopic particles. The regimes where these two theories can be applied are very different, but this does not mean that there are no connections between them. Some of these connections have arisen during the last years. Mainly, there are two different ways of connecting quantum mechanics with thermodynamics. First, macroscopic systems are composed by many microscopic ones.

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Then it is clear that, if quantum mechanics is the correct theory to describe the behavior of atoms and molecules, thermodynamics should be an emerging theory from the underlying quantum reality.

It should be possible to derive thermodynamics from quantum mechanics. In the next post of this series we will discuss some recent attempts to derive thermodynamics laws from first quantum principles 1. The second way of relating these two theories can be summarized in the next question: What happens if a quantum system interacts with a thermodynamic one? An example is a single atom interacting with a thermal bath, as the radiation that surrounds it. This question was ignored for a long time, as simple atoms were never controlled and measured.

When quantum mechanics was developed it was considered just a theory of ensembles, and single quantum systems were only imaginary tools. In thought experiments we sometimes assume that we do; this invariably entails ridiculous consequences.

Luckily, modern techniques allow researchers to experiment with single atoms and particles. Haroche and D. The development of these techniques leaded to new kind of problems, where single atoms and molecules can be analyzed when they are in contact with thermal baths. This connects the microscopic and macroscopic worlds. Furthermore, new theoretical approaches where developed in order to describe these experiments, as quantum jumps and master equations 4.

Of course, different approaches present different features, but they are all equivalent as they are derived from the same principles. Most of the results we will discuss in these series of posts have been studied by the use of the master equation approach. The master equation approach is based on modeling certain aspects of the dynamics of the system as stochastic processes. It has been used successfully in quantum optics and atomic physics for a long time 5.

Only recently, the validity of some of the approaches used and their application to systems locally coupled to baths have been analyzed 6with very interesting results.

Master equations can be used in order to describe quantum systems, under certain assumptions as weak coupling to the baths, even if only part of the quantum system interacts with the bath see figure 1. The method allows recent researchers to study interesting problems as energy transfer in quantum systems coupled to different baths, photosynthetic complexes or microscopic refrigerators.

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