Microscale Engine Runs at Solar-Core Temperatures
The introduction of heat engines at the end of the 18th century transformed society by enabling large-scale conversions of heat into mechanical work. More recently, scientists have built microscale engines, unveiling new and fascinating phenomena. In this microrealm where fluctuations dominate, heat and work no longer behave deterministically but stochastically. Understanding the physics underlying these tiny engines could provide insight into a wide range of microscale machines, such as molecular motors, cellular factories, and nanoscale sensors. Now Molly Message from King’s College London and her colleagues have built and studied a tiny engine in the form of a levitated glass microparticle [1]. By tailoring the trapping electric fields, the team produced effective temperatures of the order of 10 million kelvins, comparable to the conditions in the core of the Sun. In this extreme regime, the researchers encountered some counterintuitive thermodynamic phenomena, which may help explain the nonequilibrium behavior of various biological systems.
Large-scale, traditional engines come in a variety of forms. A prototypical example is the Stirling engine, which is typically envisioned as a gas confined within a moving piston and alternating between hot and cold baths. The phase diagram of this machine consists of a cycle in which the gas expands when heated and contracts when cooled. Repeating this cycle drives the piston back and forth, producing mechanical work.
Now imagine the same cycle being performed not on a gas but on a single particle. Recent advances in the control of micro- and nanosystems have made it possible to experimentally realize this thought experiment, with heat engines whose working substance has been reduced to a micrometer-sized bead [2] or even a single atom [3]. This shrinking of system size has revealed how work and other quantities behave randomly at microscales. Further exploration of this stochastic thermodynamics will require complete control of the system parameters.
Message and colleagues have taken an essential step in this direction by demonstrating the ability to drive a microscale heat engine into an unprecedented temperature regime. Their system consists of a charged, 5-µm-wide glass bead held aloft in a Paul trap, which is a device that uses oscillating electric fields to create a confining potential in all three dimensions (Video 1). To generate an effective temperature, the team introduces noise into the trap’s electric fields. This noise exerts a fluctuating force on the particle, equivalent to the random, molecular-scale collisions between an object and its surrounding thermal environment [4]. The noisy electric field, therefore, behaves like a thermal bath around the microparticle, giving or taking heat.
By adjusting the noise amplitude and the trap strength, the team could independently tune the bath’s effective temperature and the particle’s confinement, which is equivalent to the piston volume of a macroscopic engine. Raising the bath temperature or squeezing the volume causes the particle to jiggle around in the trap more energetically. Previous microscale engines have been thermally excited in similar types of traps, but Message and colleagues are able to reach higher temperatures in their system because their trap is deeper and has less damping.
The researcher’s control of the trap environment allowed them to implement the four-stroke Stirling cycle (Fig. 1). For each 90-second cycle, the noise was first ramped up while the trap volume was kept constant (isochoric heating). Next, the trap strength was loosened (isothermic expansion) before the noise was ramped down (isochoric cooling). Finally, the trap was tightened (isothermic compression), and the cycle repeated.
Unlike macroscopic engines—for which the energy dynamics are obtained from thermodynamic variables such as pressure and volume—the work and heat coming from single-particle engines are linked to changes in the particle’s potential and kinetic energies, which can be extracted from the particle’s trajectory over a single cycle [5]. Message and colleagues used a motion-sensitive camera to track the jiggling of the particle, and they used these trajectory data to compute the work output for each cycle.
The researchers found that their particle was very sensitive to the strongly fluctuating forces in the high-temperature regime. The particle exhibited stochastic motion, and its work output varied greatly from one cycle to the next. Remarkably, the high temperature used in the experiments made it easier to directly observe rare events where the intrinsic randomness led to apparent violations of the second law of thermodynamics. For example, the particle’s efficiency (work divided by heat input) sometimes went above 100%, or heat temporarily flowed into the particle from the cold bath—impossibilities at the macroscopic scale but fleeting occurrences in the microscopic world.
Another intriguing observation, enabled by the high temperature, was the emergence of position-dependent diffusion related to a spatial temperature gradient inside the trap. When the particle became hotter, it explored a larger portion of the trap and thus experienced temperatures at the outer region of the trap that were different from those in the center. These temperature inhomogeneities induced dynamics that deviated markedly from standard Brownian motion. The observed position-dependent diffusion could be accounted for by a model that Message and colleagues introduced.
Such position-dependent diffusion is standard in chemical and biological processes. For instance, protein folding proceeds at a faster or slower pace depending on how close the molecule is to its final shape. Owing to the extreme complexity of the energy landscape in these nonequilibrium systems, this experimental setup offers a particularly appealing platform for modeling position-dependent diffusion in a fully controlled setting. Further tinkering with the extreme engine could also yield crucial insights for engineering the next generation of microscopic technologies.
References
- M. Message et al., “Extreme-temperature single-particle heat engine,” Phys. Rev. Lett. 135, 217101 (2025).
- V. Blickle and C. Bechinger, “Realization of a micrometre-sized stochastic heat engine,” Nat. Phys. 8, 143 (2011).
- J. Roßnagel et al., “A single-atom heat engine,” Science 352, 325 (2016).
- I. A. Martínez et al., “Adiabatic processes realized with a trapped Brownian particle,” Phys. Rev. Lett. 114, 120601 (2015).
- E. Sekimoto, Stochastic Energetics, Lecture Notes in Physics Vol. 799 (Springer, Berlin, 2010)[Amazon][WorldCat].