The Half-Century Limitation in Hawking's Framework
In the early 1970s, Stephen Hawking and other researchers recognized that black holes appear to follow rules similar to the laws of thermodynamics — the branch of physics that explains how heat, energy, and disorder behave in ordinary systems. Hawking's laws of black hole mechanics provided a profound connection between extreme and ordinary physics, and have been the paradigm for 50 years.
But they had a serious limitation: they were formulated for black holes at equilibrium — unchanging over time. Real black holes are rarely static. They accumulate matter, collide with other black holes, and gradually lose energy through quantum processes (Hawking radiation). Yet the traditional laws could not describe these dynamic, out-of-equilibrium black holes.
As Abhay Ashtekar, Atherton University Professor and Evan Pugh Professor of Physics Emeritus at Penn State and leader of the research team, put it: "They were formulated for black holes at equilibrium — or unchanging over time — but black holes are constantly changing; they form, merge, and eventually evaporate. We wanted to find a way to overcome this limitation."
Dynamical Horizons: A New Solution
The problem lies in how entropy is measured. Hawking proposed that a black hole's entropy is proportional to the area of its event horizon — the boundary beyond which nothing can escape. But event horizons are "teleological": their location can depend on events that occur in the future, making them unsuitable as a physical measure for an evolving black hole.
The Penn State team, including graduate students Daniel E. Paraizo and Jonathan Shu, proposed replacing event horizons with "dynamical horizons." Unlike event horizons, a dynamical horizon can be defined using the black hole's physical properties at a specific moment — its energy and spin. The new definition links entropy more directly to these observable properties, avoiding the teleological problem.
Published in Physical Review Letters
The research, titled "Thermodynamics of Black Holes, Far from Equilibrium," was published in Physical Review Letters on June 24, 2026, where it was highlighted as an editor's suggestion. The expanded framework allows physicists to apply the first and second laws of thermodynamics to black holes at any stage of evolution.
This could help interpret black hole mergers detected through gravitational waves by LIGO-Virgo-KAGRA and investigate the still-mysterious process by which black holes evaporate in quantum theory.
"This allows us to extend the first and second laws of thermodynamics to black holes that are not at equilibrium, thereby overcoming the limitations of the paradigm that has been used for over half a century," Ashtekar said.
