For the first time, scientists have figured out how to measure a system, no matter how extreme the energy difference.
Two UA physicists may have fundamentally altered thinking about thermodynamics, a branch of physics focusing on heat and how it relates to energy.
The commonly held belief within physics is that it is impossible to measure a system’s temperature if that system is not in equilibrium. “The notion of equilibrium is very central to the theory of thermodynamics and…has been codified under the zeroth law of thermodynamics. Two systems in thermal contact are in equilibrium if the systems do not exchange heat between them,” Abhay Shastry, a physics graduate student and lead author on the project, said. The system can be divided in half and those two halves share the same temperature.
Shastry was inspired to rethink this long-held belief after conversations with Charles Stafford, a UA physics professor, and other individuals involved in Stafford’s case study of thermodynamics. Stafford had published a paper last year about the zeroth and first laws of thermodynamics.
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The two researchers wanted to figure out how to mathematically prove their definition of measurement and how it applied to systems that were not in equilibrium. This type of proof is necessary for a mathematics-based theory.
“We used the notion of a weakly coupled probe,” Shastry said. This means that the tool used for measuring shouldn’t disturb the system to the point where an accurate reading is difficult.
“If one is trying to measure the temperature of a cup of coffee, the thermometer must not draw all the heat from the coffee,” Shastry said. The amount of mercury used in the thermometer needs to vary, based on the size of the system being measured.
Another factor to consider is that temperature and voltage need to be measured at the same time. If this isn’t done properly, “a measurement could be off by thousands of degrees,” Stafford said. This means that a single floating probe must be employed to ensure that both elements are measured simultaneously.
Through mathematical modeling, Shastry and Stafford were able to prove that it is possible to incorporate all of these factors when taking the temperature of a system.
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Shastry believes this discovery could be ground-breaking and will have real-world applications.
It is important to understand how to measure a system that is not in equilibrium, because it is not a common occurrence in the natural world. “This mathematical abstraction, important though it is, does not actually occur in nature,” Shastry said. “The reason is that systems are inevitably interacting with their environments and are trying to reach equilibrium with their environments.”
In the end, Shastry and Stafford have shown that the second law of thermodynamics does apply to systems that don’t fall into equilibrium. “Our main finding is that no matter how crazy the state of a system might be, it is always possible to measure its temperature and voltage,” Stafford said.
The impacts of this research could be felt throughout a number of fields.
It will help with the advancement of technology, especially as electronics become smaller and smaller, requiring more elaborate systems to keep them functional. Shastry and Stafford’s discovery suggests that it may be possible to cool micro-electric circuits in specific spots. “Heat production is a major roadblock toward further miniaturization of electronics,” Stafford said. Designs may change based on this new information and become more efficient; the data suggests that electronic systems can become capable of cooling down certain places as opposed to the whole chip. It saves time and energy.
Notably, this project also fills a hole in a Nobel-prize winning paper written by Lars Onsagerin 1968.
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