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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.22247 |
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| _version_ | 1866908956467658752 |
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| author | Vaknin, David |
| author_facet | Vaknin, David |
| contents | Classical thermodynamics treats temperature as a state variable characterizing systems in equilibrium with idealized infinite reservoirs. We argue that this framing, while computationally exact, obscures an essential physical reality: any system at finite characteristic energy $E_c = k_B T$ continuously emits thermal radiation and cools unless energy input compensates these losses. What thermodynamics calls ``thermal equilibrium'' is, at the microscopic level, a dynamically sustained steady state maintained by continuous photon exchange.
We derive that the average photon energy required to sustain a Planck distribution is $\langle hν\rangle = π^4 E_c/[30\,ζ(3)] \approx 2.701\,E_c$, quantifying the energetic throughput that any real system must sustain to maintain a given temperature. We resolve the apparent contradiction with the purely mechanical Maxwell velocity distribution: billiard-ball kinetics correctly describe the \emph{shape} of the distribution at a given $E_c$, but cannot account for how $E_c$ is established or maintained against radiative losses in any real system of charged particles. We further show that every finite thermal reservoir is itself maintained by photon exchange at a larger scale, organizing physical systems into a natural hierarchy from individual samples through cryostats, laboratories, and planetary surfaces to stellar interiors, with the classical infinite reservoir emerging as the large-capacity limit within that hierarchy rather than a fundamental physical entity. We also comment on the relation between thermodynamic entropy $S = k_B \ln W$ and the dimensionless entropy $\mathcal{S} = \ln W$, emphasizing that $k_B$ primarily fixes units (J/K) rather than introducing new statistical content. These results do not modify thermodynamics but provide its mechanistic interpretation in terms of quantum electrodynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22247 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Temperature as a Dynamically Maintained Steady State: Photonic Mechanisms, Maintenance Cost, and the Limits of the Infinite-Reservoir Idealization Vaknin, David Quantum Physics Statistical Mechanics Classical thermodynamics treats temperature as a state variable characterizing systems in equilibrium with idealized infinite reservoirs. We argue that this framing, while computationally exact, obscures an essential physical reality: any system at finite characteristic energy $E_c = k_B T$ continuously emits thermal radiation and cools unless energy input compensates these losses. What thermodynamics calls ``thermal equilibrium'' is, at the microscopic level, a dynamically sustained steady state maintained by continuous photon exchange. We derive that the average photon energy required to sustain a Planck distribution is $\langle hν\rangle = π^4 E_c/[30\,ζ(3)] \approx 2.701\,E_c$, quantifying the energetic throughput that any real system must sustain to maintain a given temperature. We resolve the apparent contradiction with the purely mechanical Maxwell velocity distribution: billiard-ball kinetics correctly describe the \emph{shape} of the distribution at a given $E_c$, but cannot account for how $E_c$ is established or maintained against radiative losses in any real system of charged particles. We further show that every finite thermal reservoir is itself maintained by photon exchange at a larger scale, organizing physical systems into a natural hierarchy from individual samples through cryostats, laboratories, and planetary surfaces to stellar interiors, with the classical infinite reservoir emerging as the large-capacity limit within that hierarchy rather than a fundamental physical entity. We also comment on the relation between thermodynamic entropy $S = k_B \ln W$ and the dimensionless entropy $\mathcal{S} = \ln W$, emphasizing that $k_B$ primarily fixes units (J/K) rather than introducing new statistical content. These results do not modify thermodynamics but provide its mechanistic interpretation in terms of quantum electrodynamics. |
| title | Temperature as a Dynamically Maintained Steady State: Photonic Mechanisms, Maintenance Cost, and the Limits of the Infinite-Reservoir Idealization |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2601.22247 |