Nonlocal observables and lightcone-averaging in relativistic thermodynamics

The unification of relativity and thermodynamics has been a subject of considerable debate over the last 100 years. The reasons for this are twofold: (i) Thermodynamic variables are nonlocal quantities and, thus, single out a preferred class of hyperplanes in spacetime. (ii) There exist different, seemingly equally plausible ways of defining heat and work in relativistic systems. These ambiguities led, for example, to various proposals for the Lorentz transformation law of temperature. Traditional ‘isochronous’ formulations of relativistic thermodynamics are neither theoretically satisfactory nor experimentally feasible. Here, we demonstrate how these deficiencies can be resolved by defining thermodynamic quantities with respect to the backward-lightcone of an observation event. This approach yields novel, testable predictions and allows for a straightforward-extension of thermodynamics to General Relativity. Our theoretical considerations are illustrated through three-dimensional relativistic many-body simulations.

💡 Research Summary

The paper tackles the long‑standing problem of formulating a consistent relativistic thermodynamics by addressing two intertwined difficulties: the non‑local nature of thermodynamic variables and the ambiguity in defining heat and work for moving observers. Traditional approaches rely on choosing a particular family of spacelike hypersurfaces—usually the “isochronous” hyperplane of simultaneity for a given observer—to integrate quantities such as energy, momentum, and entropy. This choice implicitly selects a preferred frame and leads to multiple, mutually incompatible Lorentz‑transformation laws for temperature (e.g., invariant, multiplied by γ, or divided by γ). Moreover, the definitions of heat and work become frame‑dependent, making experimental verification practically impossible.

The authors propose a radical shift: define all macroscopic thermodynamic quantities with respect to the backward light‑cone of the observation event. An observer at spacetime point (x_{0}) receives information only from events that lie inside its past light‑cone, which is the natural causal domain. By integrating the energy‑momentum tensor (T^{\mu\nu}(x)) and the entropy current (s^{\mu}(x)) over this null hypersurface, one obtains observer‑dependent but physically measurable total energy (E) and entropy (S): \