Heat capacity catches quantum entanglement in time ✛

Original: "Complex Heat Capacity as a Witness of Spatio-Temporal Entanglement"

arXiv:2508.15728 · 2025-08-21 · CC BY 4.0 · 1 min

A simple measurement of thermal response revealed a quantum link between past and future.

A pot of soup remembers being stirred. When heated, the temperature rises with a lag — the soup seems to glance back at the past. This thermal inertia opens a window into quantum connections between events at different times. At its root lies entropy, but the quantum world adds a layer of memory where particles influence each other across time.

The delay in thermal response is measured as imaginary heat capacity. It's a real parameter captured by calorimeters, showing how much the system "ponders" the past.

Physicists found a way to decode this memory by adapting the criterion from the Clauser–Aspect–Zeilinger inequality for time. When thermal lag becomes large and uneven, it proves temporal quantum entanglement. Surprisingly, detecting it doesn't require microscopic particles — even ordinary water will do. This method takes quantum physics beyond the standard models of the microworld.

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Usually heat capacity is just a number, but with uneven heating an imaginary component appears — a sign that the material is "oscillating" between past and present. A familiar kitchen experience: a cast-iron skillet responds slowly to the flame, and hidden in that lag is a quantum subtext.

The thermal memory of soup isn't a metaphor, but a physical bridge between "before" and "after," like in the best science fiction novels.

C''(\omega) = \frac{1}{2\hbar} \int_{-\infty}^{\infty} dt \, \langle [H(t), H(0)] \rangle e^{i\omega t}

Expresses the imaginary heat capacity through the Fourier transform of the commutator of Hamiltonians at different times; a nonzero value indicates possible temporal nonclassicality.

S_{\max}(t) = \frac{2}{N(t)} \sqrt{c^2 - s^2 + f^2}

Maximum value of the Bell parameter, where c and s are coherent oscillating terms and f is the thermal contribution; violation S_max > 2 indicates temporal nonclassicality.

Scientists

Ludwig Boltzmann Rudolf Clausius Erwin Schrödinger Hugh Everett III Jacob Bekenstein Stephen Hawking

Concepts

heat capacity thermal property measurement temporal entanglement enthalpy heat map effective temperature quantum thermometer thermal conductivity quantum entanglement manifestations joule per kelvin critical temperature Unruh effect heating time uncertainty capacity carnot limit information thermodynamics equipartition theorem nonlocality chemical model

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Heat capacity catches quantum entanglement in time ✛