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Quantum memory: New model describes interaction between particles and environment in heat transport
The approach combines thermodynamics and quantum mechanics to better understand energy transformations in the subatomic world
Optimizing quantum superconductors may be possible with the expansion of knowledge generated by physics – Photo: Jacopo Werther/Wikimedia Commons
Under specialized microscopes, everything moves according to quantum mechanics – in a world so small that it doesn’t follow our giant rules. This is the quantum universe, the smallest scale of everything.
Physicists’ interest in quantum dynamics stems from the limitations of classical theories. Traditional mechanics – the one that explains an apple falling from a tree – loses its validity at the subatomic level, where particles interact in ways that classical models simply cannot describe. As a result, the old theory gives way to the new rules introduced by quantum thinking.
Guilherme Zambon, a doctoral student at USP’s São Carlos Institute of Physics (IFSC), is the first author of a study that applied a mathematical model to describe the interaction between particles and the environment in heat transport: “In addition to greater precision, the aim is to reduce energy consumption.” In the future, the method could be used as a basis for applications in thermal systems that require less heat loss, such as batteries and quantum computers.
The researcher investigates the possibilities of this invisible world, particularly the energy dynamics at the nanoscale. “We adopted an approach that focuses on the constraints thermodynamics places on quantum processes to better understand what is physically possible,” he explains.
The study employed complex mathematical methods to associate thermodynamics to quantum physics. The technique, described in an article published in the journal Physical Review Letters, allows “connecting areas with greater rigor, making it applicable to general problems,” Zambon says. “We created a bridge between knowledge,” he adds.
Quantum amnesia
Since the first steam engines, thermodynamics has tried to answer one question: how to extract the maximum energy from a system? The answer is more complicated today, precisely because we understand more about the world.
For a long time, it was believed that the atom was the smallest unit of matter, until we began colliding them. These collisions caused their “fragments” to break apart, revealing even smaller particles, which are now the focus of quantum physics. This field of study aims to understand and describe the behavior and interactions of these subatomic components.
The analysis of these particles is generally conducted within a quantum system – a slice of the universe chosen to delimit the research and restrict the study variables. Zambon explains that, in practice, we don’t have complete control over what happens there: “The particles interact with the environment in a way that isn’t very well understood.”
One possibility for studying subatomic interactions is to “close” the system, isolating it from external influences and facilitating its investigation.
Another strategy is to simplify its evolution over time. It is assumed that there is no connection between different events – as if the system forgot about the succession of transformations and focused only on the present. This “quantum amnesia” facilitates the analysis and calculation of the experiment, but considers that any energy loss from the system to the external environment is definitive and cannot be recovered. This is called Markovian dynamics, named after the Russian mathematician Andrey Markov, who described it.
The study conducted by Zambon goes against this idea. In the real world, these systems are highly complex, and there is “uncertainty about what is happening,” he says. Ignoring connections between phenomena leads to “results with a greater margin of error,” with an incomplete – and possibly inefficient – understanding of energy extraction. “This connection is what is called memory, it is what gives rise to non-Markovianity,” he summarizes.
Subatomic memories
“Imagine a grain of sand in a completely still sea,” the researcher illustrates. “If you tap on it, the wave generated goes far away and never comes back.” This grain of sand in the sea represents a Markovian relationship, where there is no memory. “What it does doesn’t come back to it, because the sea is too big, and the grain is too small,” Zambon explains.
“Now imagine a grain in a glass of water,” he continues. “The wave generated will hit the edge of the glass and return to its point of origin.” In this case, it is a non-Markovian dynamic, in which the system’s memory is a determining factor and interferes in its own evolution. “The environment is not big enough. Then, after a while, the interaction reverberates and returns to the grain of sand.”
Both approaches have significant applications in physics. “In many cases, the Markovian approach is a good approximation of reality. But it’s not always true,” he says.
Zambon explains that interactions between phenomena can be useful for understanding what is happening when a more accurate description of physical systems is needed – such as optimizing the energy consumption of the new generation of quantum electronics. “Memory is not negligible. It has a significant role there.”
The temporal connection is not limited to the theoretical world: “Non-Markovianity is significant because it is present in the physical processes you find in nature and in the laboratory.” If a quantum system has memory, the ability to relate different events allows for a deeper and more faithful analysis of reality.
To investigate these energy transformations on a quantum scale, the researcher adopted the Resource Theory of Thermodynamics. This method of analysis understands the characteristics of the system as resources that can be used. It is a way of visualizing what can be obtained from the state of a system. The premise allows us to understand how much useful work (that is, usable energy) can be extracted. Here, memory isn’t just a detail – it can be the key to increasing the performance of thermal systems, such as batteries.
A new tool
Is there a general way to describe the role of memory in quantum thermodynamics? This was the question that guided Zambon’s doctorate.
The study of thermodynamics from a non-Markovian perspective was not something new. Previous results already showed the application of the concept to subatomic systems – but only in specific cases that could not be extended to other scenarios. What the researcher proposed in his article was the generalization of this technique, with the goal of showing how it would be applicable to general cases of quantum physics.
Quantum physics, in general, analyzes systems based on spot measurements – like photographs that freeze instants. To overcome this condition, Zambon proposes the use of a new tool: process tensors. This mathematical tool makes it possible to describe the evolution of the quantum system. With its help, it is possible to map the transformations that occur over time.
These “photos” represent the moments in which physicists conduct operations on the system. When operations cease, it is assumed that the environment is transforming. “When I turn off my operation, the environment turns on its. And so on,” Zambon explains.
“This is something that has been done for a long time,” Zambon points out. “But it was assumed that these operations of the environment on the system were not correlated,” he continues. The physicist explains that, previously, it was considered that the phenomena were independent of each other – which is only true for Markovian systems.
“If the dynamics are non-Markovian, the action of the environment on the system is a sequence of interleaved and connected operations,” he clarifies. And the process tensor is the mathematical object that represents this sequence of connected transformations in the evolution of the quantum system. “Its application results in the most complete analysis possible.”
From theory to practice
From this approach, a “Markovian gradient” was created. Zambon called the categories defined for each “degree of Markovianity” steps. At each step, the system analysis became more complex and comprehensive.
These limits were established to help understand the role of the environment in subatomic transformations. By introducing controlled levels of Markovianity, the benefits of temporal analysis in the system become clearer. In other words, the hierarchy proposed by the researcher outlines strategies with increasing advantages, which can be explored to extract more useful energy than would be possible in memoryless processes.
If you move up the hierarchy, and use increasingly complex systems to access non-Markovianity, more benefits are extracted. But we are still far from ideal: applications often fail to achieve the theoretical results observed.
– Guilherme Zambon
Zambon says this new technology allows for deeper investigation of the quantum world. “The approach makes it possible to study the connection between thermodynamics and non-Markovianity more assertively,” he says. The technique is still theoretical, but it could be a significant step towards increasing the efficiency of thermal systems – batteries, for example.
The article Quantum Processes as Thermodynamic Resources: The Role of Non-Markovianity can be read here.
More information: guilhermezambon@usp.br, with Guilherme Zambon
*Intern under the supervision of Tabita Said and Júlio Bernardes
**Intern under the supervision of Moisés Dorado
English version: Nexus Traduções, edited by Denis Pacheco
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A reprodução de matérias e fotografias é livre mediante a citação do Jornal da USP e do autor. No caso dos arquivos de áudio, deverão constar dos créditos a Rádio USP e, em sendo explicitados, os autores. Para uso de arquivos de vídeo, esses créditos deverão mencionar a TV USP e, caso estejam explicitados, os autores. Fotos devem ser creditadas como USP Imagens e o nome do fotógrafo.