Periodic Reporting for period 1 - SAT-Q (Scattering approach to thermodynamics of quantum systems)
Reporting period: 2023-04-01 to 2025-03-31
Thermodynamics studies energy conversion processes across nature and technology, from large to small scales. Since matter and energy are described by quantum physics at extremely small scales, there came the necessity to understand how thermodynamics, a classical theory of physics applicable at large scales, fits together with quantum physics. Thus, the field called "quantum thermodynamics" aims to understand the principles of energy conversion in the quantum regime. In particular, the field is concerned with investigating (i) how thermodynamic quantities, like heat and work, can be defined for quantum systems; (ii) the role of quantum effects, finite-size effects and fluctuations in thermodynamic quantities; (iii) how to build efficient quantum thermal machines and devices. The field of quantum thermodynamics has developed rapidly in the last two decades, becoming highly relevant both for the foundations of physics and for the development of efficient and sustainable quantum technologies.
Quantum systems are especially sensitive to their surroundings, where the latter exchange energy and information with the quantum system of interest. One of the main achievements of quantum thermodynamics has been the formulation of laws of thermodynamics for quantum systems interacting with classical surroundings. In these cases, the surroundings can be treated either as an ideal source of heat or work for the quantum system. However, the question of how to formulate the laws of thermodynamics for quantum surroundings remains elusive. Rapid advancements in quantum technologies, which enable the study of quantum systems interacting with quantum surroundings, demands an urgent answer. The project "Scattering approach to thermodynamics of quantum systems" (SAT-Q) has the goal of meeting this need. In SAT-Q, the surroundings are treated quantum-mechanically, consisting of particles which travel in space and collide with a quantum system of interest. By relying on scattering, a process ubiquitous in nature and experiment, SAT-Q aims at providing a fully-quantum framework for thermodynamics which can be connected with modern quantum experiments and technologies.
The first objective of SAT-Q to understand if the nature of the quantum particles, i.e. bosons or fermions, play a role in a thermodynamics of the collision event. In particular, the objective is to identify the conditions for fermions and bosons to act as heat or work sources for the quantum system. The second objective is establish a clear connection between the scattering approach and another state-of-the-art approach to quantum thermodynamics called "quantum resource theories". Resource theories, although mathematically powerful, are very abstract; establishing a connection between them and scattering theory would validate both of them and bring the former closer to experimental realization. Finally, the third objective (which is transversal to the previous objectives) is to show that the scattering approach can correctly describe energy fluctuations. Since very small and quantum systems are sensitive to external perturbations, their energy fluctuates due to interactions with surroundings; it is extremely important to verify that fluctuations in thermodynamic quantities can be captured by the scattering approach.
By completing these objectives, SAT-Q is expected to significantly advance the field of quantum thermodynamics, providing a fully-quantum framework to investigate thermodynamics which can be tested and implemented with current technology.
Quantum systems are especially sensitive to their surroundings, where the latter exchange energy and information with the quantum system of interest. One of the main achievements of quantum thermodynamics has been the formulation of laws of thermodynamics for quantum systems interacting with classical surroundings. In these cases, the surroundings can be treated either as an ideal source of heat or work for the quantum system. However, the question of how to formulate the laws of thermodynamics for quantum surroundings remains elusive. Rapid advancements in quantum technologies, which enable the study of quantum systems interacting with quantum surroundings, demands an urgent answer. The project "Scattering approach to thermodynamics of quantum systems" (SAT-Q) has the goal of meeting this need. In SAT-Q, the surroundings are treated quantum-mechanically, consisting of particles which travel in space and collide with a quantum system of interest. By relying on scattering, a process ubiquitous in nature and experiment, SAT-Q aims at providing a fully-quantum framework for thermodynamics which can be connected with modern quantum experiments and technologies.
The first objective of SAT-Q to understand if the nature of the quantum particles, i.e. bosons or fermions, play a role in a thermodynamics of the collision event. In particular, the objective is to identify the conditions for fermions and bosons to act as heat or work sources for the quantum system. The second objective is establish a clear connection between the scattering approach and another state-of-the-art approach to quantum thermodynamics called "quantum resource theories". Resource theories, although mathematically powerful, are very abstract; establishing a connection between them and scattering theory would validate both of them and bring the former closer to experimental realization. Finally, the third objective (which is transversal to the previous objectives) is to show that the scattering approach can correctly describe energy fluctuations. Since very small and quantum systems are sensitive to external perturbations, their energy fluctuates due to interactions with surroundings; it is extremely important to verify that fluctuations in thermodynamic quantities can be captured by the scattering approach.
By completing these objectives, SAT-Q is expected to significantly advance the field of quantum thermodynamics, providing a fully-quantum framework to investigate thermodynamics which can be tested and implemented with current technology.
Early results in scattering theory have shown that colliding particles can act as a heat or work source for the quantum systems, and that this depends on their degree of localization in space: while delocalized particles tend to act as heat sources, localized particles tend to act as work sources. However, it was unclear whether the fermionic or bosonic nature of the particles had any relevance. In order to assess this, the first objective of SAT-Q was to identify the conditions for fermions and bosons to act as heat or work sources for the quantum system. We first performed analytical and numerical work of the surroundings, which were treated as a non-interacting quantum gas consisting of fermions or bosons. We then modelled a scattering process of a particle in this gas with a quantum system and evaluated the impact of the particle nature and localization; for this last step, we used standard quantum scattering theory and theory of open quantum systems already applied to thermodynamics in previous studies. We did not find find any meaningful impact of the bosonic and fermionic nature on the ensuing thermodynamics of the colliding particles.
We now describe our work in fluctuations, which is by far the most significant research of this project. We have shown that a colliding particle, which is extremely delocalized in space and with very high kinetic energies, effectively measures the energy fluctuations of a quantum system. This result was obtained with straightforward analytics and confirmed and exemplified numerically, using the insight of previous studies of the scattering approach to thermodynamics. This is a strong result which shows that the scattering approach can capture thermodynamic fluctuations of the system, while going beyond state-of-the-art approaches relying on idealised measurement schemes which are difficult to implement in practice. Interestingly, this result also allowed us to prove a direct connection to quantum resource theories, showing that quantum resource theories approaches to thermodynamic fluctuations are equivalent to our approach. Finally, our strongest achievement was proving that energy fluctuations obey the important "fluctuation relations". Fluctuation relations are a hallmark of thermodynamics at very small scales and are usually derived from state-of-the-art approaches relying on idealised measurement schemes. We have proved the existence of more general fluctuation relation in scattering theory, holding independently of the kinetic energy of the particle and without relying on external measurements. In our framework, it is the particle itself that induces and measures the energy fluctuations of the system.
We now describe our work in fluctuations, which is by far the most significant research of this project. We have shown that a colliding particle, which is extremely delocalized in space and with very high kinetic energies, effectively measures the energy fluctuations of a quantum system. This result was obtained with straightforward analytics and confirmed and exemplified numerically, using the insight of previous studies of the scattering approach to thermodynamics. This is a strong result which shows that the scattering approach can capture thermodynamic fluctuations of the system, while going beyond state-of-the-art approaches relying on idealised measurement schemes which are difficult to implement in practice. Interestingly, this result also allowed us to prove a direct connection to quantum resource theories, showing that quantum resource theories approaches to thermodynamic fluctuations are equivalent to our approach. Finally, our strongest achievement was proving that energy fluctuations obey the important "fluctuation relations". Fluctuation relations are a hallmark of thermodynamics at very small scales and are usually derived from state-of-the-art approaches relying on idealised measurement schemes. We have proved the existence of more general fluctuation relation in scattering theory, holding independently of the kinetic energy of the particle and without relying on external measurements. In our framework, it is the particle itself that induces and measures the energy fluctuations of the system.
Our results represent a significant step beyond state-of-the-art in thermodynamics of quantum systems. We have shown that a colliding particle can induce and measure thermodynamic fluctuations, acting as a source of heat or work depending on its quantum localization. Furthermore, we have shown a precise connection between scattering theory and quantum resource theories, which validates our approach and brings the latter approach closer to physical implementation. Altogether, our results show the universality of the scattering framework as a fully-quantum framework for thermodynamics which can be verified in modern experimental settings. They also contribute to elucidate thermodynamic principles in the quantum regime, potentially leading to the design of efficient and sustainable technologies.