The starting point of the analysis is a decades-old idea with a distinguished pedigree. In 1995, Ted Jacobson demonstrated that Einstein’s field equations could be derived from the Clausius relation of thermodynamics, TdS = dQ, applied to local horizons, suggesting that gravity itself might be an emergent, thermodynamic phenomenon rather than a fundamental force. Later work by Sai Akbar and Rong-Gen Cai extended this program to cosmology, showing that the Friedmann equations, which describe how the universe expands, can be recovered by applying what is known as the unified first law of thermodynamics to the apparent horizon of a flat Friedmann–Lemaître–Robertson–Walker universe. This law, formulated by Sean Hayward, reads TdS = −dE + WdV, where E is the total energy inside the horizon, W is the work density, and V is the enclosed volume. In this picture, the Friedmann equations are not imposed dynamical laws but thermodynamic equations of state.

The new study revisits this derivation with a sharp eye on a detail that is easy to miss. The apparent horizon, whose radius in a flat universe is simply the inverse of the Hubble parameter, is a dynamical boundary that grows and shrinks with cosmic evolution. Crucially, it is not comoving: it does not expand along with the fluid of galaxies the way an ordinary box of gas does. Standard cosmological conservation laws are written for comoving volumes that scale with the cube of the scale factor, but the horizon-thermodynamic framework naturally selects the volume enclosed by the apparent horizon, because that is the region causally accessible to an observer. The authors show that the identification of the total energy as the energy density times this horizon volume is not a convenient assumption but a consequence of the Misner-Sharp mass definition, which fixes the energy inside the horizon to be exactly half its radius.

This non-comoving volume has a striking consequence. Even if no particles are being created anywhere in the cosmos, the total number of particles inside the apparent horizon changes with time, simply because the boundary sweeps through the cosmic fluid. When the universe decelerates, the horizon expands faster than the fluid and swallows additional particles; when it accelerates, the opposite happens and particles effectively stream out across the boundary. The researchers call this effect the horizon flux, and their central claim is that it is not a minor geometric artifact but a physically essential ingredient that any consistent thermodynamic treatment of cosmology must include. Neglecting it, they argue, has led previous analyses to incorrect conclusions about which forms of matter can power cosmic acceleration.

To incorporate gravitationally induced particle creation, the team builds on the framework of irreversible thermodynamics developed by Ilya Prigogine and collaborators in the late 1980s. In this picture, the expanding gravitational field transfers energy into the matter sector, producing new particles and generating an effective negative pressure, the so-called creation pressure, that mimics the behavior of dark energy. The particle number density then obeys a modified balance equation featuring a production rate Γ, and the total pressure of the fluid is decomposed into an equilibrium part plus the creation pressure. When this generalized description is inserted into the unified first law applied at the apparent horizon, the modified acceleration equation emerges naturally, with the creation pressure appearing alongside the ordinary matter terms, confirming that modified Friedmann dynamics follows from the horizon-based thermodynamic description.

The heart of the paper is a clean decomposition of how the particle count and the matter entropy inside the horizon actually evolve. The total rate of change splits into two distinct contributions: a genuine bulk creation term, proportional to the production rate Γ times the number of particles, and a geometric horizon flux term, proportional to three times the Hubble parameter times the deceleration parameter q. During the decelerating epoch, when q is positive, both terms push the matter entropy upward. But once the universe transitions to acceleration, the horizon flux turns negative, draining particles from the horizon volume. For the matter entropy to remain non-decreasing, as the second law demands, the bulk creation rate must then satisfy a strict inequality: Γ must be at least as large as minus three times the horizon flux term, meaning production must roughly keep pace with the expansion itself.

Combining this thermodynamic constraint with the background dynamics for a pressureless fluid yields a remarkable result. The deceleration parameter is bounded below by −1, and for any viable accelerating phase the production rate is confined to the range between the Hubble parameter and three times the Hubble parameter. In other words, Γ > H emerges as a robust lower bound demanded simultaneously by the dynamics and by thermodynamic consistency. The authors then show that whenever this condition holds, the acceleration of the scale factor is positive, meaning that cold, pressureless dark matter with a genuine creation rate exceeding the expansion rate can consistently account for late-time cosmic acceleration without invoking any exotic fluid or cosmological constant. This directly challenges recent observational analyses suggesting that particle creation models only work when the produced component has an equation of state more negative than −1/3, a conclusion the authors attribute to those analyses neglecting the horizon contribution altogether.

The team also derives the Generalized Second Law for this open-system setting, writing the total entropy budget as the sum of the horizon entropy and the matter entropy, with contributions from the horizon sector, bulk creation, boundary fluxes, and possible non-adiabaticity per particle. Under the physically natural assumption of adiabatic creation, in which newly produced particles are born in thermal equilibrium with the cosmic fluid and the entropy per particle stays constant, the total entropy production rate reduces to a simple expression governed by a single kinematic factor, one minus q squared, multiplied by a positive coupling. To test this against reality, the authors employed Gaussian Processes, a non-parametric statistical technique, applied to the Cosmic Chronometers dataset, which provides model-independent measurements of the expansion rate across cosmic history. The reconstruction shows that entropy production peaked precisely at the transition from deceleration to acceleration, around redshift 0.6, and then declined smoothly toward zero as the universe approaches a de Sitter state, exactly as the adiabatic framework predicts, without ever crossing into an unphysical regime of negative entropy production.

There are important caveats. The authors note that in the strictly adiabatic limit, where total entropy production vanishes, their framework becomes observationally indistinguishable from the standard Lambda-CDM model at the level of the background expansion, so any detectable departure from the concordance model requires strictly positive entropy production and additional parametrization of the coupling between horizon flux and matter. The production rate in their formulation depends on both the Hubble parameter and its time derivative, extending the usual matter-creation framework in which the rate depends on H alone, and a full statistical confrontation with supernova, baryon acoustic oscillation, and Hubble tension data is left for future work. Still, the conceptual payoff is considerable: a rigorous accounting of the moving horizon boundary transforms matter creation from a phenomenological curiosity into a thermodynamically consistent mechanism, and suggests that the dark energy driving cosmic acceleration may be nothing more than the irreversible work done by spacetime itself as it creates the matter filling the universe.

Subject of Research: Thermodynamic derivation of modified Friedmann equations with horizon flux and gravitationally induced particle creation in cosmology

Article Title: Beyond comoving volume: horizon flux and matter creation in modified cosmology from the unified first law of thermodynamics

Article References: Cárdenas, V. H., Cruz, M., & Lepe, S. (2026). Beyond comoving volume: horizon flux and matter creation in modified cosmology from the unified first law of thermodynamics. The European Physical Journal C, 86(9), Article 1110. https://doi.org/10.1140/epjc/s10052-026-16334-3

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16334-3

Keywords: cosmology, apparent horizon, thermodynamics, particle creation, dark energy, Friedmann equations, generalized second law, cold dark matter, unified first law, FLRW universe, entropy production, Hubble tension

Unimodular gravity has long intrigued theorists precisely because of how it handles the cosmological constant problem, arguably the most notorious discrepancy between theory and observation in physics. Quantum field theory predicts a vacuum energy vastly larger than what astronomers measure, yet in unimodular gravity the situation changes fundamentally. By restricting the symmetry of Einstein’s theory so that transformations must preserve the four-dimensional volume element, the theory yields only the trace-free part of Einstein’s field equations. The cosmological constant then ceases to be a parameter fixed by the microscopic physics and instead appears as a constant of integration, much like the energy of a pendulum, whose value is determined by initial conditions rather than by quantum loops.

The price of this elegant restructuring is a modified conservation law. In standard general relativity, the energy-momentum tensor of matter is covariantly conserved, which forces the cosmological constant to be truly constant. In unimodular gravity, that constraint is relaxed, and the divergence of the energy-momentum tensor is balanced by the gradient of the Lagrange multiplier that enforces the volume restriction. Solving the resulting equation reveals that the cosmological term splits into two pieces: a fixed integration constant and an arbitrary function of time, which the authors call the energy diffusion function. This function quantifies exactly how much local energy conservation fails, and it acts as a continuous source or sink of energy for the cosmic fluids filling the universe.

Physically motivated guesses for this diffusion function have been proposed before. One striking example draws on the continuous spontaneous localization model of quantum collapse, in which energy is genuinely created during wavefunction collapse, suggesting a diffusion term proportional to the energy density of the fluid itself. Earlier work showed that when only dark matter diffuses, the resulting cosmology closely reproduces the standard Lambda-CDM model, and related diffusion scenarios have even been explored as a way to ease the Hubble tension, the persistent disagreement between different measurements of the universe’s expansion rate. The trouble, as the Chilean team emphasizes, is that no widely accepted diffusion function follows from an established physical process, so most proposals rest on phenomenological convenience or mathematical simplicity rather than principle.

The new study attacks this problem from the opposite direction. Rather than postulating a diffusion law and studying its consequences, the authors recast the cosmological equations as an autonomous dynamical system and ask what diffusion functions the phase-space structure itself demands. The key move is to introduce a dimensionless variable called the diffusion slope, defined as minus the logarithmic derivative of the diffusion function with respect to the e-fold number, a natural clock for cosmic expansion. For the system to close, this slope must be invertible along the trajectories — a condition satisfied whenever it evolves monotonically. Remarkably, when the slope is held constant, the formalism automatically spits out the power-law diffusion functions that had previously been introduced by hand, suggesting that the dynamical systems perspective can rediscover and organize known models rather than merely accommodate them.

With the autonomous system in hand, the team mapped out the fixed points of cosmic evolution and their stability. The familiar matter-dominated era appears as a saddle point, not an attractor, meaning the universe inevitably passes through it rather than lingering. The de Sitter solution, where expansion accelerates at a constant rate under the influence of the integration constant, emerges as a genuine late-time attractor for positive diffusion slopes. More intriguingly, the analysis uncovered a novel matter-diffusion scaling solution in which the diffusion term tracks the dark matter density, maintaining a constant fractional share of the cosmic energy budget. Within a specific range of parameters, this scaling regime itself drives accelerated expansion — entirely without a cosmological constant — although it represents a transient stage rather than a final destiny.

Perhaps the most provocative result concerns the purely diffusion-dominated configuration. When the diffusion function becomes constant, it behaves exactly like a cosmological constant, producing exponential expansion with an effective equation-of-state parameter of minus one. In that regime, the diffusion sector alone can power late-time acceleration, with no fundamental vacuum energy required at all. The stability analysis revealed subtlety here: linear theory alone cannot settle the fate of this point because one eigenvalue vanishes, so the researchers supplemented their analytic work with numerical integration of the phase-space flow, showing that trajectories are attracted along one direction but repelled along another. The diffusion-dominated solution is therefore a saddle, a waystation the cosmos may visit but not a permanent home — the true endpoint remains the de Sitter state governed by the integration constant.

Beyond the asymptotic regimes, the authors built a full reconstruction machinery analogous to potential reconstruction in scalar-field cosmology. By specifying a curvature function that controls how the diffusion slope bends in logarithmic space, one can integrate the slope evolution and then reconstruct the diffusion function itself through a simple exponential integral. The constant-curvature family already displays rich behavior: curvature equal to one recovers power-law diffusion, curvature greater than one drives the diffusion term smoothly to zero as the universe expands, and curvature below one produces a finite-time singularity in the slope, signaling a breakdown of the description. More elaborate curvature functions that cross unity allow the slope to station at multiple values, enabling trajectories that interpolate between a rapidly decaying diffusion contribution in the early universe and an asymptotically constant component at late times — precisely the kind of transition a viable dark energy candidate might need.

The framework also clarifies what thermodynamics demands. Using the Gibbs relation, the team showed that the second law of thermodynamics requires the diffusion function to be non-increasing as the universe expands, guaranteeing positive entropy production. Notably, this condition constrains only the trend, not the sign, of the diffusion term, which can push the effective cosmological constant either up or down. The reconstruction formalism respects this automatically: because the diffusion function is built from a strictly positive exponential factor, it cannot change sign dynamically, keeping every reconstructed model consistent with the thermodynamic constraint from the outset.

The implications reach well beyond formal elegance. Because the diffusion sector exchanges energy with dark matter, it should alter the growth of cosmic structure, leaving fingerprints in the matter power spectrum and in the growth rate of galaxies that could distinguish diffusion cosmologies from Lambda-CDM. The authors identify this perturbative analysis, together with a direct confrontation of the reconstructed models with observational data, as the natural next step of their program. If the coming generation of surveys continues to hint that dark energy is not perfectly constant — as recent measurements have suggested — then a framework that generates and classifies diffusion models from first principles, rather than by trial and error, may prove exactly what cosmologists need to make sense of a universe that refuses to sit still.

Subject of Research: Cosmological diffusion models and energy non-conservation in unimodular gravity, analyzed through dynamical systems reconstruction

Article Title: Unimodular gravity with arbitrary diffusion function: a dynamical system reconstruction approach

Article References: Unimodular gravity with arbitrary diffusion function: a dynamical system reconstruction approach. (n.d.). https://doi.org/10.1140/epjc/s10052-026-16363-y

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16363-y

Keywords: unimodular gravity, cosmological constant problem, dark energy, energy diffusion function, dynamical systems, phase-space fixed points, de Sitter expansion, scaling solutions, entropy production, Lambda-CDM, Hubble tension, theoretical cosmology

The central quantity in the study is the chord-based Reynolds number, a dimensionless measure of the ratio of inertial to viscous forces in the flow over a compressor blade. As the researchers simulated and tested conditions from 0 to 20 kilometers of altitude, this parameter fell from 6.13 × 10⁵ at sea level to a mere 0.55 × 10⁵ at the top of the range, more than a tenfold reduction. At such low Reynolds numbers, the thin layer of air that clings to each blade surface, the boundary layer, behaves very differently. It remains laminar and smooth for longer, and the transition to turbulent flow that normally helps the boundary layer resist separation is significantly delayed. That delay, the study shows, is the root cause of a cascade of problems that ultimately determine how much the compressor can be loaded before it stalls.

To capture these effects, the team used the SST k-ω turbulence model coupled with the γ-Reθ transition model, a computational pairing widely regarded as one of the most reliable approaches for predicting where boundary layers transition from laminar to turbulent in engineering flows. The simulations were validated against ground-based high-altitude simulation experiments conducted at near-stall operating conditions, the regime where the compressor is pushed close to the stability limit and where the consequences of degraded flow physics are most severe. By examining aerodynamic performance alongside detailed flow structures, the researchers were able to trace exactly where and how losses arise inside the blade passages as altitude increases.

The headline finding is that performance degradation is emphatically nonlinear. Efficiency does not fall in a gentle, proportional slide as the air thins. Instead, the compressor holds up reasonably well down to the critical transition near Re_c ≈ 1.22 × 10⁵, and beyond that threshold the decline in adiabatic efficiency and stall margin accelerates sharply. This kind of critical behavior matters enormously for aircraft designers, because it means that extrapolating performance from modest altitude tests to extreme-altitude cruise could badly overestimate how much thrust margin and stability margin an engine actually possesses near the edge of its operating envelope.

Why does the collapse happen so abruptly? The flow mechanism analysis offers a compelling answer. As the boundary layer transition is delayed, corner separations, the stubborn pockets of reversed flow that form where the blade suction surface meets the hub and casing end walls, appear prematurely and spread radially outward across a much larger fraction of the blade span. At sea-level Reynolds numbers these corner separations are localized nuisances; at high altitude they become expansive, performance-sapping regions of blocked flow. The separation does not merely grow, it changes character, and that change in character is what drives the nonlinear degradation.

Perhaps the most striking structural change involves the passage vortex, a rotating secondary flow structure that normally occupies a modest corner of the blade passage. Under low Reynolds number conditions, the radial passage vortex evolves into large-scale bow-shaped structures that come to dominate the blockage of the entire flow passage. With these bow-shaped structures choking the passage, the authors found a fundamental reshuffling of stall physics: corner stall replaces the tip leakage vortex, the familiar culprit in many compressor stability studies, as the primary initiator of stall. This is a significant conceptual result for the turbomachinery community, because it suggests that stability enhancement strategies designed with tip leakage in mind may be aiming at the wrong mechanism when aircraft operate at extreme altitude.

To quantify where the losses actually originate, the team employed a regional loss decomposition based on the dissipation function and entropy production analysis, two thermodynamically grounded techniques that attribute irreversibility to specific zones of the flow field. The results reveal a clear redistribution of loss sources with altitude. The contributions of leading-edge and trailing-edge losses, which reflect the viscous and mixing penalties at the blade’s front and rear, actually decrease as altitude rises. In contrast, losses in the hub region, the tip region, and the mid-span passage regions increase dramatically once the critical altitude is crossed, becoming the dominant sources of wasted energy. In other words, the machine does not simply get uniformly worse; the geography of loss migrates inward and outward from the blade surfaces into the passage core.

The most extreme statistic in the study concerns the total dissipation function, an integrated measure of how much flow kinetic energy is irreversibly converted into heat. At the lowest Reynolds numbers tested, this quantity exhibits exponential growth exceeding two orders of magnitude compared with baseline conditions. A hundredfold increase in dissipation means that the compressor is churning the thin air into turbulence and heat at an extraordinary rate relative to the useful work it extracts, which is the thermodynamic signature of the efficiency collapse documented in the performance maps. It also underscores how radically the internal flow departs from its sea-level character once the critical threshold is passed.

The practical implications extend across several domains of aeronautical engineering. For high-altitude aircraft, including long-endurance unmanned platforms and hypersonic vehicles whose turbines must function in very low density air, the identification of a critical Reynolds number gives designers a concrete boundary condition for performance prediction models. The finding that corner separation and bow-shaped passage vortices govern low-Reynolds-number stall suggests that flow control strategies, such as boundary layer suction, vortex generator vanes, or plasma actuators, should be targeted at the hub and casing corner regions rather than exclusively at the blade tips. The study’s authors note that their results provide guidance for high-altitude compressor design, performance prediction, and flow control strategies, and the entropy-based loss decomposition offers a template for diagnosing exactly where future design interventions would pay the greatest dividends.

Beyond its engineering value, the work contributes to fundamental low-Reynolds-number flow physics, an area that has drawn growing attention as the field moves toward compact cores, high-altitude operations, and electric aviation concepts with smaller compressors that naturally operate at lower chord Reynolds numbers. By coupling rigorous experiments with transition-sensitive simulation, and by grounding loss accounting in dissipation and entropy production rather than crude pressure measurements alone, the study sets a methodological benchmark for future investigations. It also complements a broader research program by the same group, which has examined stall precursors, surge frequency prediction, and the coupling between compressor chambers and surge dynamics. Together, these efforts sketch a more complete picture of what happens when a compressor is pushed to its limits in air too thin to behave the way ground-level design rules assume, a picture that will be essential as aviation pushes higher into the atmosphere.

Subject of Research: Low Reynolds number flow physics and performance degradation of axial compressors at high altitude

Article Title: Performance Degradation and Flow Loss Evolution of an Axial Compressor at Near-Stall Conditions Under High Altitude Low Reynolds Number Regime

Article References: Qiao, Y., Chu, W., Liu, K., Li, Q., Liu, K., & Zhang, H. (2026). Performance Degradation and Flow Loss Evolution of an Axial Compressor at Near-Stall Conditions Under High Altitude Low Reynolds Number Regime. International Journal of Aeronautical and Space Sciences. https://doi.org/10.1007/s42405-026-01283-8

Image Credits: AI Generated

DOI: 10.1007/s42405-026-01283-8

Keywords: axial compressor, Reynolds number, high altitude, stall margin, boundary layer transition, corner separation, passage vortex, entropy production, adiabatic efficiency, turbomachinery, flow loss, computational fluid dynamics