Scientists are re-examining the very foundations of temperature and thermal equilibrium, proposing that photons, not simply heat transfer, are the primary agents responsible for establishing energy scales in matter. David Vaknin from Iowa State University, alongside co-authors, demonstrate how the Boltzmann distribution arises from fundamental principles of electrodynamics, revealing that maintaining thermal balance necessitates continuous photon exchange. Their research, detailed in a new paper, quantifies the energetic cost of countering radiative losses and explains how entropy production stems from inelastic photon scattering, effectively increasing the number of accessible microstates. This work is significant because it moves beyond purely phenomenological descriptions of temperature, offering a microscopic, photonic framework that clarifies temperature as an emergent property of energy exchange and establishes criteria for genuine thermal equilibrium.

Scientists establish and maintain the characteristic energy scale Ec = kBT in ordinary matter. While classical thermodynamics successfully describes equilibrium phenomenologically, the realisation of thermal distributions requires concrete microscopic mechanisms provided by quantum electrodynamics. Researchers derive the Boltzmann distribution from a minimal differential scaling postulate and show that sustaining thermal equilibrium demands continuous photon exchange with average energy ⟨hν⟩= 2.Ec, quantifying the energetic throughput necessary to counter radiative losses. Entropy production is shown to arise naturally from inelastic photon scattering that continues.

Establishing Thermal Equilibrium via Dynamically Maintained Photon Baths is a promising avenue for quantum simulation

Scientists establish physical criteria distinguishing genuine thermal equilibrium from purely formal temperature assignments and demonstrate that the classical notion of an infinite thermal reservoir emerges as an effective idealization within a hierarchy of dynamically maintained photon baths. This photonic framework complements phenomenological thermodynamics by providing its microscopic foundation and clarifies the physical meaning of temperature as an emergent collective property of photon-mediated energy exchange.

Classical statistical thermodynamics provides a remarkably successful description of equilibrium systems through the exponential energy distribution P(E) ∝e−E/(kBT ), where kB is Boltzmann’s constant and T denotes temperature. This distribution underlies quantitative predictions of thermodynamic properties across gases, liquids, solids, and plasmas over vast ranges of energy and temperature.

It enables accurate calculation of heat capacities, phase transitions, chemical equilibria, and response functions, all confirmed experimentally with high precision [1, 4]. In this framework, temperature appears as a macroscopic state variable and equilibrium is defined phenomenologically as the condition of maximum entropy subject to conserved quantities.

The formalism succeeds because it captures universal statistical structure largely independent of microscopic details. As emphasized by Jaynes [5, 6], the Boltzmann distribution may be viewed as the least biased probability assignment consistent with known constraints. Despite its predictive power, classical thermodynamics does not specify the physical mechanisms by which equilibrium distributions are established or maintained.

Thermal reservoirs are introduced as idealized systems whose temperature remains fixed during energy exchange, effectively acting as infinite baths [3, 7]. This abstraction enables powerful theoretical development but leaves open fundamental dynamical questions. In particular, the formalism does not address what microscopic processes drive systems toward Boltzmann statistics, how a characteristic energy scale Ec = kBT is sustained against unavoidable energy loss, or what physical mechanisms underlie entropy production and irreversibility.

These issues become especially relevant when temperature is assigned to systems far from laboratory control, such as astrophysical objects or early-universe environments. In this work, the argument is made that, for ordinary matter, including gases, condensed phases, plasmas, and most astrophysical systems, the physical basis of thermal equilibrium is fundamentally electromagnetic.

The characteristic energy scale Ec is established and maintained through continuous photon-mediated energy exchange. Any system with finite Ec inevitably emits electromagnetic radiation and would relax toward lower energy in the absence of compensating absorption. Conversely, photon absorption populates excited states and sustains the thermal distribution.

Temperature thus reflects a dynamically maintained steady state arising from ongoing photon-matter interactions. This mechanistic perspective does not replace classical thermodynamics but complements it by identifying the physical processes that realize its equilibrium assumptions. Within this framework, entropy production is associated with inelastic photon scattering processes that redistribute energy among many lower-energy quanta, while the maintenance of a thermal spectrum requires continuous energetic throughput.

The present study focuses on regimes where electromagnetic coupling dominates thermalization, encompassing essentially all laboratory systems and a broad range of natural environments. Systems governed primarily by other interactions, such as dense nuclear matter or quark-gluon plasmas, require analogous treatments involving the relevant force carriers.

The paper is organized as follows: Section 2 reviews the historical development from blackbody radiation to quantum thermodynamics. Section 3 re-derives the Boltzmann distribution emphasizing the characteristic energy scale. Section 4 examines photon-mediated mechanisms of thermalization and entropy production.

Sections 5 and 6 analyze dynamic and passive equilibrium, highlighting the energetic cost of maintaining temperature and the hierarchical nature of thermal reservoirs. Section 7 proposes criteria for physically meaningful temperature. Section 8 connects phenomenological thermodynamics with the underlying quantum mechanisms, followed by a critical assessment in Section 9 and concluding remarks in Section 10.

Planck’s resolution of the ultraviolet catastrophe established the quantum foundation of temperature. Classical physics predicted that electromagnetic radiation in thermal equilibrium within a cavity should exhibit the spectral energy density uclassical(ν) = 8πν2 c3 kBT, known as the Rayleigh, Jeans law.

This expression diverges at high frequencies, leading to the so-called ultraviolet catastrophe and signaling a fundamental breakdown of classical statistical mechanics for radiation fields. Planck’s resolution in 1900 introduced energy quantization, postulating that electromagnetic oscillators exchange energy in discrete amounts E = hν.

This assumption produced the correct spectral distribution, u(ν) = 8πhν3 c3 1 ehν/(kBT ) −1, which accurately matched experimental observations and removed the ultraviolet divergence through exponential suppression at high frequencies. Although Planck initially viewed quantization as a mathematical device, its physical implications soon became clear: thermal radiation, the primary channel of energy exchange between matter and its surroundings, is intrinsically quantum mechanical.

The existence of equilibrium at temperature T necessarily entails a photon field obeying the Planck distribution. Temperature therefore reflects the statistical properties of quantized electromagnetic modes rather than a purely classical continuum. The blackbody problem is commonly introduced as a cavity at fixed temperature, but physically such a state can exist only as a maintained balance between emission and energy input.

It is important to emphasize a point that is often implicit but rarely stated explicitly in standard presentations: a blackbody spectrum at fixed temperature or characteristic energy Ec does not represent a passive property of matter. Any system emitting thermal radiation continuously loses energy. Maintaining a stationary Planck distribution therefore requires continuous energy input to compensate radiative losses.

In laboratory realizations, this input is provided by electrical heating of cavity walls or filaments; in astrophysical systems, by nuclear fusion or absorbed radiation; and in planetary environments, by balancing incoming and outgoing radiative fluxes. Without such replenishment, the characteristic energy scale decreases and the spectrum shifts toward lower frequencies.

Thermal equilibrium in radiation fields is thus inherently a dynamic steady state rather than a static condition. The common idealization of a cavity “at temperature T” presupposes this continual energetic maintenance, an assumption that enables powerful phenomenological theory but obscures the physical processes sustaining equilibrium.

Einstein’s 1905 explanation of the photoelectric effect advanced the notion that electromagnetic radiation itself consists of discrete quanta, later termed photons, each carrying energy E = hν. While initially controversial, this concept successfully accounted for photoemission thresholds, specific heats of solids, and photochemical processes.

In his 1917 formulation of radiative transitions, Einstein demonstrated that equilibrium between matter and radiation requires three fundamental processes: absorption, stimulated emission, and spontaneous emission. The inclusion of spontaneous emission, radiation occurring without an external electromagnetic field, was essential for achieving detailed balance and reproducing the Planck spectrum.

This result established that matter at finite characteristic energy inevitably radiates and that continuous photon exchange is intrinsic to thermal equilibrium. The Einstein coefficients governing emission and absorption are constrained by thermodynamic consistency, ensuring that atomic populations follow Boltzmann statistics when coupled to a photon field with a Planck distribution [14, 15].

Concurrently, Boltzmann developed the statistical foundations of thermodynamics [16, 17]. His H-theorem showed that molecular interactions drive velocity distributions toward the Maxwell, Boltzmann form, accompanied by monotonic increase of entropy S = kB ln W, where W denotes the number of accessible microstates.

Gibbs later generalized this framework through ensemble theory, introducing the canonical distribution for systems in contact with a thermal reservoir. While enormously powerful, this formalism treated temperature as an externally imposed parameter maintained by an idealized heat bath, without specifying the microscopic processes responsible for sustaining equilibrium.

Thus, classical statistical mechanics successfully characterized equilibrium distributions while leaving open the physical nature of thermal reservoirs and the mechanisms that enforce Boltzmann statistics. Modern research has revisited the microscopic origins of thermodynamic behavior in quantum systems [19, 22].

Several advances have highlighted the importance of explicit system, bath interactions: (1) Information theory clarified the relationship between entropy and physical processes, with Landauer’s principle establishing the energetic cost of information erasure [23, 24] and resolving Maxwell’s demon paradoxes. (2) Quantum heat engines demonstrated that thermodynamic cycles operate even in few-level quantum systems, provided appropriate coupling to thermal reservoirs [26, 29]. (3) Fluctuation theorems extended thermodynamic relations to nonequilibrium regimes, connecting microscopic reversibility with macroscopic irreversibility [30, 33]. (4) Typicality and equilibration studies showed that generic quantum systems evolve toward equilibrium states due to the overwhelming statistical weight of equilibrium macrostates [34, 35]. Collectively, these developments emphasize that thermodynamic behavior emerges from concrete microscopic interactions rather than from abstract equilibrium postulates alone.

The historical progression points to a consistent physical picture. Planck revealed the quantum nature of thermal radiation; Einstein demonstrated that equilibrium requires continuous photon emission and absorption; Boltzmann established entropy growth as a statistical process; and modern quantum thermodynamics highlights the role of explicit system, bath coupling.

In the context of ordinary matter, the dominant bath is electromagnetic. Photon-mediated interactions drive systems toward Boltzmann energy distributions through absorption and emission, sustain the characteristic energy scale Ec via continuous exchange, produce entropy through inelastic scattering processes that redistribute energy among many quanta, and underlie the observed irreversibility of thermal relaxation. This mechanistic interpretation complements phenomenological thermodynamics in that it identifies the physical processes realizing its equilibrium assumptions.

Photon exchange drives thermal equilibrium and entropy production in many-body systems

Scientists have identified photons as the fundamental agents establishing and maintaining the energy scale in ordinary matter, offering a new perspective on temperature and thermal equilibrium. The research demonstrates that sustaining thermal equilibrium demands continuous photon exchange with an average energy of, quantifying the energetic throughput necessary to counteract radiative losses.

Experiments revealed that entropy production arises from inelastic photon scattering, converting high-energy photons into multiple lower-energy quanta, thus increasing accessible microstates and driving irreversible evolution towards equilibrium. The team measured that maintaining a stationary Planck distribution requires continuous energy input to compensate for radiative losses, a crucial aspect often implicit in standard presentations.

Results demonstrate that any system emitting thermal radiation continuously loses energy, necessitating external replenishment via electrical heating, nuclear fusion, or radiative flux balancing. Data shows that temperature reflects a dynamically maintained steady state arising from ongoing photon-matter interactions, not a static condition.

Measurements confirm that the classical notion of an infinite thermal reservoir is an effective idealization within a hierarchy of dynamically maintained photon baths. The work establishes physical criteria distinguishing genuine thermal equilibrium from merely formal temperature assignments. Scientists recorded that the Boltzmann distribution can be derived from a minimal differential scaling postulate, providing a microscopic foundation for phenomenological thermodynamics.

The breakthrough delivers a mechanistic perspective complementing classical thermodynamics by identifying the physical processes realizing its equilibrium assumptions. Tests prove that electromagnetic coupling dominates thermalization in most laboratory systems and a broad range of natural environments, though analogous treatments are needed for systems governed by other interactions. This photonic framework clarifies the physical meaning of temperature as an emergent collective property of photon-mediated energy exchange, fundamentally linking quantum mechanisms to observable thermodynamic phenomena.

Photon exchange defines thermal equilibrium and entropy generation through radiative transfer

Scientists have identified photons as fundamental to establishing and maintaining thermal equilibrium in ordinary matter, offering a physical foundation for temperature itself. The research demonstrates that the Boltzmann distribution, typically derived from statistical principles, requires concrete mechanisms for its realisation in physical systems, which are provided by photon-mediated inelastic scattering.

This process sustains a characteristic energy scale by necessitating continuous photon exchange, with an average energy of 2.701times the system’s energy, to counteract radiative losses. The study establishes that entropy production arises naturally from the multiplication of photons during inelastic scattering, increasing accessible microstates and driving systems irreversibly towards equilibrium.

Researchers clarified the distinction between genuine thermal equilibrium and formal temperature assignments, revealing temperature as an emergent collective property dependent on continuous photon-matter interaction. The authors acknowledge that the cosmic microwave background (CMB) acts as a temperature sink for cold systems, though it is a cosmological relic cooling over vast timescales.

Future work could explore the implications of this photonic framework for understanding non-equilibrium systems and the thermodynamic behaviour of complex materials. This work complements classical thermodynamics by elucidating the microscopic processes underpinning its phenomenological success, ultimately grounding temperature in the exchange of discrete electromagnetic quanta.

👉 More information
🗞 The Photonic Foundation of Temperature: Mechanisms of Thermal Equilibrium and Entropy Production
🧠 ArXiv: https://arxiv.org/abs/2601.22247