Supercritical hydrogen-yielding cracking of heavy hydrocarbon feedstocks exhibits universal critical regimes that fundamentally determine hydrogen production efficiency. A variational thermodynamic model is developed to describe these transitions. The model is based on the minimization of thermodynamic irreversibilities and leads to the Euler-Lagrange equation, from which the Gusev Exergetic Invariant emerges in its canonical form:

This invariant governs the transition between Low-H₂, Plateau, and High-H₂ regimes. The hydrogen-yield parameter acts as an order parameter, while the functional of irreversibilities becomes equivalent to a Landau-Ginzburg functional. Critical exponents β = 1/2, γ = 1, δ = 3 are derived and shown to be universal. A renormalization-group (RG) structure is established, revealing a critical fixed point corresponding to the plateau regime. The theory provides  a unified framework for optimizing hydrogen production in supercritical cracking reactors.

This study examines the technological, institutional, economic, and geopolitical dimensions of nuclear-hydrogen energy development in leading countries. Nuclear-hydrogen systems are assessed as integrated platforms that combine nuclear baseload generation with high-efficiency hydrogen production through electrolysis and thermochemical cycles. The analysis covers China, the United States, Russia, South Korea, France, and Canada, highlighting differences in reactor technologies, electrolysis integration strategies, and national policy frameworks. High-temperature gas-cooled reactors (HTGRs) demonstrate the highest readiness for thermochemical hydrogen production, while Generation III+ reactors are primarily deployed for large-scale electrolysis. Institutional assessment reveals significant regulatory asymmetry, with advanced licensing pathways in the United States and France and evolving frameworks in China and the EU. Economic evaluation shows that nuclear-derived hydrogen can achieve competitive levelized costs under high capacity factors and large-scale deployment, with China demonstrating structural cost advantages. Geopolitical analysis identifies emerging regional clusters and the growing role of nuclear-hydrogen diplomacy in shaping energy security and export strategies. The findings indicate that nuclear-hydrogen systems can support deep industrial decarbonization, enhance energy resilience, and contribute to long-term hydrogen infrastructure development.

The proposed work formulates the foundations of Exergic Field Theory (EFT), a new fundamental theoreticalphysical paradigm, in which exergy is considered as a primary physical quantity that determines the dynamics, structure, and evolution of cosmic systems at all scales. Unlike traditional approaches, where exergy is treated as an engineering or thermodynamic characteristic, EFT introduces exergy as a field invariant related to the geometry of spacetime, local gradients of available energy, and the structure of physical interactions. According to this theory, the exergnetic field acts as a universal mediator between thermodynamics, gravity, and cosmological evolution, providing a unified formalism for describing processes from microscopic to cosmological scales.

The work begins with an analysis of the limitations of the standard cosmological model ΛCDM and the classical general theory of relativity, which, despite their success, require the introduction of external entities – dark matter, dark energy, inflationary field – without a strict physical origin. It is shown that many observed phenomena, including the stratification of cosmic objects, the large-scale structure of the universe, as well as the thermodynamic properties of astrophysical systems, can be naturally explained through the exergetic formalism, without resorting to additional hypothetical components. In this context, exergy is considered a fundamental structural parameter that determines the degree of energy availability for performing work in gravitational and cosmological systems.

In the central part of the article, the Lagrangian of the exergetic field is introduced, based on the variational principle, which combines geometric and thermodynamic aspects. It is shown that the exergetic field can be described by a tensor structure that includes scalar, vector, and tensor components, each of which is responsible for a specific class of physical processes. Equations of motion are derived, similar to the Einstein equations, but containing additional terms that reflect local and global exergetic gradients. These equations lead to the emergence of new integrals of motion and invariants that have no counterparts in classical gravity, but naturally explain the observed stratification of cosmic objects, scale inhomogeneity, and stability of structures.

Special attention is paid to exergetic invariants that determine the stable states of space systems. It is shown that such invariants can serve as natural criteria for the formation of planetary systems, small body belts, comet clouds, and large astrophysical structures. In particular, the connection between the exergetic field and the dynamics  of the Kuiper Belt and the Oort Cloud is analyzed, where exergetic gradients determine the distribution of masses, orbital characteristics, and long-term evolution of objects. These results demonstrate that exergetic formalism can explain  a wide range of observed phenomena without introducing additional hypothetical entities.

Next, the connection of the exergy field with the thermodynamics of the Universe is considered. It is shown that exergy can be interpreted as a measure of the structural order of cosmic systems, and its gradients as a driving force of evolution. In this context, the exergy field acts as a natural bridge between microscopic statistical physics and macroscopic cosmology. A new interpretation of cosmological evolution is proposed, in which the expansion  of the universe, the formation of structures, and the thermodynamic arrow of time are interconnected manifestations  of exergetic dynamics. This approach provides a new perspective on the problem of entropy in cosmology, suggesting  a mechanism in which exergy acts as a regulator of structural complexity.

An important part of the work is the analysis of the physical consequences of EFT. It has been shown that  the theory predicts a number of observable effects, including: (1) the natural appearance of large-scale stratification  of cosmic objects; (2) the existence of stable exergetic layers that determine the distribution of masses; (3) the possibility of explaining the anomalies in the rotation of galaxies without introducing dark matter; (4) the appearance of new types of wave solutions, such as exergetic waves, which can be detected experimentally. These waves have unique properties that distinguish them from gravitational waves, and they can be detected using video tomography methods developed  in previous works by the author.

A separate section is devoted to the discussion of experimental and observational possibilities for testing EFT. Potential methods for registering exergetic waves are considered, including multi-channel interferometric systems, optical and radio frequency detectors, as well as methods for reconstructing signals based on video tomographic algorithms. It is shown that modern technologies make it possible to begin experimental verification of a number of EFT predictions in the near future. In addition, space missions are being discussed in which exergetic effects can be most pronounced, such as missions to the Kuiper Belt, the Oort Cloud, and the interstellar medium.

The final part of the article discusses the place of Exergic Field Theory in modern physics. It is shown that EFT does not contradict existing theories, but rather extends them by offering a new fundamental level of description that unites thermodynamics, gravity, and cosmology. The theory has a high level of explanatory power, mathematical rigor, and a wide range of observable consequences. It forms the basis for further development in both fundamental physics and applied fields, from space engineering to energy technologies. This work completes the formation of the theoretical core of the exergetic paradigm and paves the way for a unified physical picture in which the structure and evolution  of the universe are determined by the universal laws of exergetic dynamics.

The relevance of this study stems from the need to find new solutions to improve the safety of large-capacity nuclear power plants with passive safety systems. In case of beyond design basis accidents with severe core damage, hydrogen resulting from the high-temperature interaction of steam with zirconium alloy fuel rod cladding, mixed with air and steam, can form an explosive atmosphere that threatens containment integrity and the release of radioactive substances into the environment. To prevent such phenomena, nuclear power plants use various control measures and technical means aimed at preventing the formation of explosive hydrogen-containing mixtures. This study presents methodological approaches to ensuring hydrogen explosion safety and provides results of justifying the effectiveness of control measures implemented in various NPP-2006 designs of Atomproekt JSC.

To create a quantitative model of the energy supply of a «hydrogen city», the city of Innopolis, located in the Republic of Tatarstan, was chosen as the base. This young settlement can rightfully be considered a unique experimental platform for testing low-carbon solutions due to a combination of three factors. Factor one: the construction was carried out on an undeveloped territory, so there is no old, physically worn-out infrastructure. Factor two: the city is home to a data center of a major state-owned corporation, which consumes 20 MW of electricity on a 24/7 basis (this includes the energy consumption of cooling systems and uninterruptible power supplies). The third factor is that the climate is continental, which makes Innopolis a representative model for most regions of Russia, as well as for Eastern European countries and the North American continent.

The developed hybrid scheme is intended to replace the current power supply system. Its structure includes the following elements: photovoltaic installations with a total capacity of 36,6 MW (they are supposed to be installed on roofs and facades of buildings, on carports, as well as on land plots free of development); a 12 MW wind power plant; a 10 MW PEM type electrolysis system; a hydrogen storage tank; a 10 MW fuel cell battery A 25 MW combined-cycle power plant, which includes a 15 MW gas turbine with a combustion chamber adapted for operation on fuel mixtures with a hydrogen content in the range from 0 to 100 %. The electrical efficiency of this combined cycle plant is 56 % when powered by methane, and 52 % when powered by pure hydrogen. In the mode of combined electricity and heat generation, the corresponding figures are 86 % and 83 %.

The mathematical support of the work is a set of differential equations describing the energy balance. This model takes into account the stochastic nature of renewable energy generation, the kinetics of electrochemical reactions within the electrolyzer, and the thermodynamic principles of the steam-gas cycle. The accuracy of the model calculations has been verified using real-world data on solar radiation, wind conditions, and hourly electricity load profiles. During the experimental measurements, it was found that the actual values of the specific loads are 2,1-2,7 times lower than the regulatory values specified in SP 256.1325800.2016. This currently unused reserve of network infrastructure capacity can be utilized to connect the electrolyzer and charging stations without the need for reconstruction.

The results of numerical modeling have revealed a pronounced seasonal asymmetry. During the summer months, the excess production of renewable energy reaches 26 MWh per day, allowing for the production of up to 416 kilograms of hydrogen per hour. This hydrogen is stored for use during the winter. When winter sets in and renewable energy production becomes insufficient, the combined cycle plant provides up to 65 % of the daily consumption. It uses a mixture of natural gas with a 30 % hydrogen additive, which significantly reduces carbon dioxide emissions.

The proposed architectural scheme serves as a prototype for a carbon-neutral city of the future. It is suitable  for scaling to any settlements located in a continental climate zone and having critical IT infrastructure. In this context, Innopolis acts as a «living laboratory» – a prototype city where all the components of the hydrogen economy, including electricity generation, heat supply, transportation, data center, and housing and utilities, are integrated into a single ecosystem. It is important that this ecosystem is being created from scratch, without any costs for re-equipping existing communications.

Retrofitting existing natural gas thermal power plants (TPPs) for integrated hydrogen production requires minimizing the inherent thermodynamic penalty of steam extraction. This study develops a power loss factor (PLF)-based thermo-economic framework to analyze and optimize this trade-off. A validated model of a large-scale Russian TPP (TPP-22) is coupled with a modular high-temperature steam electrolysis (HTSE) system simulated in Aspen HYSYS. 

Two steam-condensate reintegration strategies are rigorously compared: a conventional steam-condenser scheme and a novel steam-heater scheme that redirects flow to the regenerative feedwater system. The steam-water cycle of the host TPP is modeled and validated using United Cycle against real operational data, achieving an error of less than 0.02 % after accounting for water injection for steam temperature control. The HTSE modules are simulated in Aspen HYSYS as an exact replica of the validated Idaho National Laboratory reference design. A comprehensive uncertainty quantification is performed, including sensitivity analysis (tornado diagram), seasonal performance assessment (summer/ winter modes), and SOEC degradation analysis over a 5-year period (0.5-0.75 % per 1,000 hours). Results show that the steam-heater configuration reduces the PLF from 1.7 % to 0.1 % in summer and from 5.6 % to 4.9 % in winter, preserving up to 14 MW of electrical output compared to the steam-condenser scheme. This improvement translates into a consistent reduction of the levelized cost of hydrogen (LCOH₂) by approximately 16-17 % under both 2021 and 2025 Russian economic conditions, yielding average LCOH2 values of 3.56-6.51 $/kg for hydrogen production rates of 0.2 kg/s per module. The specific CO2 emissions of the proposed system are 0.056 kg CO₂/kg H2, which is two orders of magnitude lower than grey hydrogen and significantly below green hydrogen from renewable electrolysis. The results provide a critical thermal design guideline, demonstrating that condensate return strategy is a decisive parameter for the efficiency and economic viability of repurposing thermal power assets for hydrogen co-generation.