Physicists identify overlooked uncertainties in real-world experiments

Equations that describe physical systems often assume that measurable characteristics of the system (temperature or chemical potential, for example) can be known precisely. But the real world is much more complicated than that and uncertainty is inevitable. Temperatures fluctuate, instruments malfunction, the environment interferes, and systems evolve over time.

The rules of statistical physics deal with the uncertainty in the state of a system that arises when that system interacts with its environment. But they have long missed another type, say Professor David Wolpert and Jan Korbel, a postdoctoral researcher at the Complexity Science Hub in Vienna, Austria.

In a new article published in Physical examination researchthe two physicists argue that the uncertainty of the thermodynamic parameters themselves, integrated into the equations that govern the energetic behavior of the system, can also influence the outcome of an experiment.

“At present, almost nothing is known about the thermodynamic consequences of this type of uncertainty, despite its inevitability,” says Wolpert. In the new paper, he and Korbel study ways to modify the equations of stochastic thermodynamics to accommodate them.

When Korbel and Wolpert met at a 2019 workshop on information and thermodynamics, they began talking about this second type of uncertainty in the context of non-equilibrium systems.

“We asked ourselves: what happens if you don’t know exactly the thermodynamic parameters governing your system? » Korbel remembers. “And then we started playing.” Equations that describe thermodynamic systems often include precisely defined terms for things like temperature and chemical potentials. “But as an experimenter or observer, you don’t necessarily know these values” with great precision, Korbel explains.

Even more frustrating, they realized that it was impossible to accurately measure parameters such as temperature, pressure, or volume, both due to measurement limitations and the fact that these quantities change rapidly. They recognized that uncertainty regarding these parameters influences not only information about the initial state of the system, but also its evolution.

It’s almost paradoxical, Korbel says. “In thermodynamics, you assume uncertainty about your state, so you describe it probabilistically. And if you have quantum thermodynamics, you do it with quantum uncertainty,” he says. “But on the other hand, you assume that all parameters are known with exact precision.”

Korbel says the new work has implications for a range of natural and artificial systems. If a cell needs to sense temperature to carry out a chemical reaction, for example, then its accuracy will be limited. The uncertainty in the temperature measurement could mean the cell is doing more work and consuming more energy. “The cell has to pay this extra cost for not knowing the system,” he says.

Optical tweezers offer another example. These are high-energy laser beams configured to create a sort of trap for charged particles. Physicists use the term “rigidity” to describe the tendency of the particle to resist the movement of the trap. To determine the optimal configuration of the lasers, they measure the stiffness as precisely as possible. To do this, they usually take repeated measurements, assuming that the uncertainty comes from the measurement itself.

But Korbel and Wolpert propose another possibility: the uncertainty would arise from the fact that the rigidity itself could change as the system evolves. If this is the case, identical and repeated measurements will not capture it, and finding the optimal configuration will remain difficult to achieve. “If you keep following the same protocol, then the particle doesn’t end up at the same point, you might have to push a little bit,” which means extra work that isn’t described by conventional equations.

This uncertainty could manifest itself at all scales, Korbel says. What is often interpreted as uncertainty in measurements may be disguised uncertainty in parameters. Perhaps an experiment was performed near a window where the sun was shining, then repeated on a cloudy day. Or maybe the air conditioner came on between tries. In many situations, he says, “it’s relevant to look at this other type of uncertainty.”