Microscopic Stirling Engine Reaches Effective Temperatures Hotter Than the Sun to Probe Tiny Thermodynamics

Microscopic engine simulates temperatures rivaling the Sun to study fluctuating thermodynamics

Physicists have built a particle-sized Stirling heat engine that experiences effective temperatures comparable to the Sun’s core to probe how heat, work and motion behave at the smallest scales. Rather than producing practical power, the experiment explores the noisy, fluctuating physics of microscopic systems and offers insight into processes that also matter in biology.

How the experiment works

The team, led by physicist Molly Message at King's College London, levitated a single silica sphere just 4.82 micrometers in diameter (a fraction of the width of a human hair) inside an electric trap in vacuum. They then drove the particle with engineered electrical noise that made it jitter as if it were in environments with effective temperatures up to about 13 million kelvin—far hotter than the Sun’s photosphere (~5,800 K) and approaching estimates for the Sun’s core (~15 million K).

These are effective temperatures: the particle does not physically heat to millions of kelvin. Instead, the added noise increases its random motion so it behaves as if immersed in a thermal bath at that effective temperature. Meanwhile, the surrounding environment was kept at an effective temperature roughly 100 times lower, producing an extreme temperature contrast unattainable in macroscopic Stirling engines.

Operating the microscopic Stirling cycle

A Stirling engine converts heat into mechanical motion by cyclically heating and cooling a working medium so it expands and contracts. The researchers implemented the same four-step cycle on a micrometer scale by alternating the applied electrical noise (to "heat") and modifying the trap strength (to allow expansion or enforce contraction). Each experimental run consisted of roughly 700–1,400 cycles to collect robust statistics on heat transfer and work output.

Key findings

The experiments revealed very large stochastic fluctuations in heat exchange and work. On short timescales the particle occasionally appeared to produce more work than the heat input—transient, apparent efficiencies above 100%—but these are expected statistical fluctuations at microscopic scales and do not violate energy conservation. When averaged over many cycles, the system obeys the second law of thermodynamics.

Crucially, the particle's motion displayed position-dependent diffusion: its diffusion constant varied with position inside the trap. This happens when local properties such as effective temperature or medium characteristics change spatially, altering how particles move. Such effects are important in biological settings where particles interact with membranes, complex fluids and tissues.

Broader relevance and next steps

Because position-dependent diffusion plays a role in phenomena such as protein folding and drug transport through biological media, the platform could be used as a controllable testbed to study these processes under well-characterized thermodynamic conditions. The team plans to push the engine further from equilibrium to explore even richer, fluctuating physics at the tiniest scales.

Published in Physical Review Letters.

Bottom line: A levitated 4.82-µm silica sphere driven by engineered electrical noise acts as a microscopic Stirling engine at effective temperatures up to ~13 million K, revealing giant stochastic fluctuations, transient apparent efficiencies >100%, and position-dependent diffusion—an effect with potential implications for biology and nanoscale thermodynamics research.