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Quantum thermodynamics is an area of study which brings together two fundamental areas of science – quantum mechanics and thermodynamics. Both theories are involved with addressing the physical phenomena of light and matter; but thermodynamics is often concerned with bulk materials, whereas quantum mechanics is used with many nanoscale materials.
In this article, we look at how both areas have come together to create new thermodynamic laws which can be applied to quantum systems.
The area of thermodynamics has been around for a very long time, and for many years has been guided by the laws of classical physics.
Thermodynamics is used to describe the bulk properties of a system, and because it averages out throughout the whole system, it doesn’t consider microscopic details. However, thermodynamics is a powerful approach for determining the temperature, the heat dissipation and the work done by a system.
Whilst thermodynamics has helped to advance many technologies and areas of science, the realisation of nanomaterials has opened a completely new area where conventional laws do not play a significant part.
Once you get down to the nanoscale, a lot of the interactions and properties of a material are determined by quantum effects, i.e. effects derived from the laws of quantum mechanics. However, the laws of thermodynamics can be adapted to quantum systems, and this is where quantum thermodynamics comes in.
The field of quantum thermodynamics has grown in recent years because of highly controlled quantum experiments, the availability of powerful numerical methods and the development of novel theoretical tools.
Where traditional thermodynamics looks at the fluctuations of heat in a sample, these new tools enable researchers to also look at the fluctuations in the quantum regime. As such, these methods have been termed as stochastic thermodynamic methods.
Because of the different types of properties exhibited by quantum materials, the focus of understanding and predicting these properties is what drives quantum thermodynamics. Conventional thermodynamics doesn’t work for these systems, because the different fluctuations in thermal motion do have an effect when the material in question is small.
The dependence on the differences within the system averaging out is no longer relevant and can lead to huge decreases in accuracy if you try to apply traditional thermodynamic laws to these materials. The properties which can be determined using traditional thermodynamics, such as work, heat and entropy, are still relevant in quantum thermodynamics, but these tools can measure so much more due to the consideration of both quantum and thermal fluctuations.
The Laws of Quantum Thermodynamics
The zeroth law of thermodynamics shows that if two systems are in a thermal equilibrium with a third system, they are at a thermal equilibrium with each other. This statement still stands true for the quantum regime, but only if the system in question is closed and governed by a Hamiltonian that enables the family of states to be parametrized by thermal states (i.e. the temperature).
The first law of traditional thermodynamics surrounds the conservation of energy, and that the change in the internal energy of a system is the same as the heat supplied minus the work done by the system. In quantum thermodynamics, this rule is applied to define the thermodynamic operations in closed quantum systems as energy-conserving unitary operations.
The second law of thermodynamics states that in interacting systems, the sum of entropies increases. There are many different interpretation aspects to the second law of thermodynamics, but the most relevant is that free-energy can only decrease. This part of the second law has been adapted into a new set of quantum thermodynamic laws that govern which thermodynamic processes can take place in a quantum system, and which ones are restricted.
The third, and final, law of thermodynamics can be interpreted in many ways, but the fundamental law states that the entropy of a system will approach a constant value as the temperature of the system approaches absolute zero (zero Kelvin). There is much debate on whether this law can be violated in quantum systems, and there is no adaptation (to date) that is different to the traditional law.
Overall, traditional thermodynamic laws are still very useful principles if the system in question is a large and complex system where its properties are governed by the bulk. However, it does incorporate a huge oversimplification of the microscopic behaviour of a system, which is not applicable for systems that exist in the quantum regime. For these systems, the adaptation of classical methods into quantum thermodynamics has become a useful tool for identifying the properties of a quantum system.
Sources
- APS Physics: https://absuploads.aps.org/presentation.cfm?pid=13371
- “Focus on quantum thermodynamics”- Anders J. and Esposito M., New Journal of Physics, 2017, DOI: 10.1088/1367-2630/19/1/010201
- “Perspective on quantum thermodynamics”- Millen J. and Xuereb A., New Journal of Physics, 2016, DOI: 10.1088/1367-2630/18/1/011002
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