Equilibrium State Research Articles

Entropy and Thermodynamic Temperature in Nonequilibrium Classical Thermodynamics as Immediate Consequences of the Hahn–Banach Theorem: II Properties

In a companion article it was shown in a certain precise sense that, for any thermodynamical theory that respects the Kelvin–Planck second law, the Hahn–Banach theorem immediately ensures the existence of a pair of continuous functions of the local material state—a specific entropy (entropy per mass) and a thermodynamic temperature—that together satisfy the Clausius–Duhem inequality for every process. There was no requirement that the local states considered be states of equilibrium. This article addresses questions about properties of the entropy and thermodynamic temperature functions so obtained: To what extent do such temperature functions provide a faithful reflection of “hotness”? In precisely which Kelvin–Planck theories is such a temperature function essentially unique, and, among those theories, for which is the entropy function also essentially unique? What is a thermometer for a Kelvin–Planck theory, and, for the theory, what properties does the existence of a thermometer confer? In all of these questions, the Hahn–Banach Theorem again plays a crucial role.

Nonlinear evolution characteristics and seepage mechanical model of fluids in broken rock mass based on the bifurcation theory

With the deep extension of coal mining in China, fault water inrush has become one of the major disasters threatening the safety production of coal mine. Based on the control equations of steady state and non-Darcy seepage in fractured rock mass, the multi-parameter nonlinear dynamic seepage equations of fractured rock mass are established in this paper. Based on the nonlinear dynamics theory, the function of the state variable in the system is derived, and the influence of the gradual change of non-Darcy flow factors on the structural stability of seepage system is studied. The research achievements show that there are three branches in the equilibrium state of the seepage system. Specifically, the stability of the equilibrium state changes abruptly near the limit parameter. The seepage dynamic system of fractured rock mass has the delayed bifurcation, and the coal mine disaster such as fault water inrush occurs easily at the bifurcation point. The research results are of great significance to enrich the theory of fault water inrush in coal mine, and to reveal the disastrous mechanism of fault water inrush and guide its prevention and control technology in coal mine, which can provide the theoretical reference for predicting the water seepage stability in fractured rock mass.

Equilibrium States of Endomorphisms of $\mathbb{P}^{k}$: Spectral Stability and Limit Theorems

AbstractWe establish the existence of a spectral gap for the transfer operator induced on $\mathbb{P}^{k} = \mathbb{P}^{k} (\mathbb{C})$ by a generic holomorphic endomorphism and a suitable continuous weight and its perturbations on various functional spaces, which is new even in dimension one. Thanks to the spectral gap, we establish an exponential speed of convergence for the equidistribution of the backward orbits of points towards the conformal measure and the exponential mixing. Moreover, as an immediate consequence, we obtain a full list of statistical properties for the equilibrium states: CLT, Berry-Esseen Theorem, local CLT, ASIP, LIL, LDP, almost sure CLT. Many of these properties are new even in dimension one, some even in the case of zero weight function (i.e., for the measure of maximal entropy).

Near Equilibration Times in the Diffusion-Controlled Adsorption.

A model of the Frumkin isotherm following adsorption on the surface of the rotating disk is developed with the purpose to calculate the time that is needed for the establishment of the near equilibrium state between the amount of adsorbate and the bulk concentration of surfactant. The "near" is quantified as 99% of the proper equilibrium surface coverage. The near equilibration time depends on the bulk concentration and on the coefficient of molecular attraction in the adsorbed layer. In the vicinity of the inflection point of the isotherm, this time exhibits sharp spike. It is caused by the diminished flux that increases surface coverage very slowly but continues for a long time. Eventually, both the flux and the surface coverage increase with time drastically under the influence of the exponential part of the Frumkin isotherm.

Tracking the Dimensionality Transition from a Three Dimensional Single Crystal to a Two Dimensional Perovskite

AbstractThis work carefully studied the transition from 3D perovskite to 2D perovskite. Our system includes single crystals (SCs) of MAPbBr3, which were dipped in a solution of barrier molecules. Three monoammonium cations and one di‐ammonium cation were studied. Absorbance and cathodoluminescence were used to follow the formation of low‐dimensional perovskite on the SC surface. Quantitative nuclear magnetic resonance and scanning electron microscopy assist in quantitatively tracking the exchange process. We followed the barrier molecules′ concentration during the exchange process and their penetration depth into the 3D single crystal. The short aliphatic chain penetrates much farther into the crystal (ca. 450 μm) than the long aliphatic chain barrier molecule. In contrast, the process time is the opposite: the long aliphatic chain requires 5 days to achieve an equilibrium state compared with 15 days for the short aliphatic chain. Ab initio calculations indicate that the exchange process initiates due to the methylammonium vacancies on the surface, and the process is inhibited by the interactions between the −NH3 group and the PbBr2 planes. This work sheds light on the kinetics and thermodynamics of the transition from 3D to 2D perovskites, which is important for stabilizing the hybrid perovskites.

Multidimensional Electrochemistry Decodes the Operando Mechanism of Hydrogen Oxidation

AbstractBeing an efficient approach to the utilization of hydrogen energy, the hydrogen oxidation reaction (HOR) is of particular significance in the current carbon‐neutrality time. Yet the mechanistic picture of the HOR is still blurred, mostly because the elemental steps of this reaction are rapid and highly entangled, especially when deviating from the thermodynamic equilibrium state. Here we report a strategy for decoding the HOR mechanism under operando conditions. In addition to the wide‐potential‐range I–V curves obtained using gas diffusion electrodes, we have applied the AC impedance spectroscopy to provide independent and complementary kinetic information. Combining multidimensional data sources has enabled us to fit, in mathematical rigor, the core kinetic parameter set in a 5‐D data space. The reaction rate of the three elemental steps (Tafel, Heyrovsky, and Volmer reactions), as a function of the overpotential, can thus be distilled individually. Such an undocumented kinetic picture unravels, in detail, how the HOR is controlled by the elemental steps on polarization. For instance, at low polarization region, the Heyrovsky reaction is relatively slow and can be ignored; but at high polarization region, the Heyrovsky reaction will surpass the Tafel reaction. Additionally, the Volmer reaction has been the fastest within overpotentials of interest. Our findings not only offer a better understanding of the HOR mechanism, but also lay the foundation for the development of improved hydrogen energy utilization systems.

Research on the Postural Stability of Underwater Bottom Platforms with Different Burial Depths

The bottom platform is an important underwater sensor that can be used in communications, early warning, monitoring, and other fields. It may be affected by earthquakes, winds, waves, and other loads in the working environment, causing changes in posture and affecting its sensing function. Therefore, it is of practical engineering significance to analyze the force conditions and posture changes in the bottom platform. In order to solve the problem of postural stability of the underwater bottom platform, this paper establishes a fluid and structural simulation model of the underwater bottom platform. First, computational fluid dynamics (CFD) technology is used to solve the velocity distribution and forces in the watershed around the bottom platform under a 3 kn ocean current, where the finite element method (FEM) numerical calculation method is used to solve the initial equilibrium state of the bottom platform after it is buried. On this basis, this paper calculates the forces on the bottom platform and the posture of the bottom platform at different burial depths under the action of ocean currents. Additionally, the effects of different burial depths on the maximum displacement, deflection angle, and postural stability of the bottom platform are studied. The calculation results show that when the burial depth is greater than 0.6 m, and the deflection angle of the bottom platform under the action of the 3 kn sea current is less than 5°, the bottom platform can maintain a stable posture. This paper could be used to characterize the postural stability of underwater bottom platforms at different burial depths for the application of underwater sensors in ocean engineering.

Quantum tachyonic preheating, revisited

In certain models of inflation, the postinflationary reheating of the Universe is not primarily due to perturbative decay of the inflaton field into particles, but proceeds through a tachyonic instability. In the process, long-wavelength modes of an unstable field, which is often distinct from the inflaton itself, acquire very large occupation numbers, which are subsequently redistributed into a thermal equilibrium state. We investigate this process numerically through quantum real-time lattice simulations of the Kadanoff-Baym equation, using a 1/N-NLO truncation of the 2PI-effective action. We identify the early-time maximum occupation number, the “classical” momentum range, the validity of the classical approximation and the effective IR temperature, and study the kinetic equilibration of the system and the equation of state.

Multidimensional Electrochemistry Decodes the Operando Mechanism of Hydrogen Oxidation.

Being an efficient approach to the utilization of hydrogen energy, the hydrogen oxidation reaction (HOR) is of particular significance in the current carbon-neutrality time. Yet the mechanistic picture of the HOR is still blurred, mostly because the elemental steps of this reaction are rapid and highly entangled, especially when deviating from the thermodynamic equilibrium state. Here we report a strategy for decoding the HOR mechanism under operando conditions. In addition to the wide-potential-range I-V curves obtained using gas diffusion electrodes, we have applied the AC impedance spectroscopy to provide independent and complementary kinetic information. Combining multidimensional data sources has enabled us to fit, in mathematical rigor, the core kinetic parameter set in a 5-D data space. The reaction rate of the three elemental steps (Tafel, Heyrovsky, and Volmer reactions), as a function of the overpotential, can thus be distilled individually. Such an undocumented kinetic picture unravels, in detail, how the HOR is controlled by the elemental steps on polarization. For instance, at low polarization region, the Heyrovsky reaction is relatively slow and can be ignored; but at high polarization region, the Heyrovsky reaction will surpass the Tafel reaction. Additionally, the Volmer reaction has been the fastest within overpotentials of interest. Our findings not only offer a better understanding of the HOR mechanism, but also lay the foundation for the development of improved hydrogen energy utilization systems.

Indigenous and colonial influences on Amazonian forests

Societal Impact StatementGlobal climate models that incorporate carbon sources and sinks usually consider that forest uptake of carbon is in a state of equilibrium. Both historical and paleoecological records suggest that this is commonly not the case for Amazonia. Here, the impacts of colonial practices on Amazonian Indigenous peoples and forests are reviewed. Human activities affect forests' successional stages, trajectories, and species composition. By increasing the spatial coverage of paleoecological records that focus on pre‐ and post‐Columbian periods, the long‐term interactions between humans and Amazonian forests and their role in affecting Earth's climate may be better understood.SummaryLegacy effects left by the activities of Indigenous people in Amazonia are well known. Although severe, widespread, and recently occurring, the impacts left post‐1492 CE have been less investigated. We review the impact of colonial practices on Indigenous peoples and Amazonian forests. We suggest that forests comprise the sum of their past events, in a mosaic of different cumulative successional trajectories depending on the type, frequency, intensity, and timing of human influence. In regions with a history of minimal human influence, old‐growth species sensitive to fire would be the dominant landscape. In regions with high pre‐Columbian and low colonial influence, old‐growth forests carrying pre‐Columbian ecological legacies would be prevalent. Regions occupied by Indigenous groups post‐1492 CE would also carry similar ecological legacies. In regions influenced by the Jesuits, mid‐successional forests are expected to be enriched with cacao trees. In regions of latex extraction during the rubber boom, mid‐growth forests would present high abundances of early and mid‐successional species and depletion of some species. In deforested areas, we expect early successional forests with influence of exotic useful species. This patchwork of history probably plays a large role in shaping today's forests, and the biodiversity and carbon dynamics documented within them. Paleoecological work focusing on the last millennium, although scarce, has the potential to detect these mosaics of past human influence, and they should be considered when estimating forest ages and successional stages across the basin.

Effect analysis on passive and active regeneration performance of catalytic diesel particulate filters at the equilibrium point in the presence of ash layer

AbstractCatalytic diesel particulate filters (CDPF) form the main post‐processing devices for the diesel engines. Particulates trapped by CDPF can be oxidized by nitrogen dioxide (NO2) and oxygen (O2). The CDPF passive and active regeneration model on platinum‐based catalyst in the presence of ash layer, including the mass, momentum, and enthalpy balances of the gas and the solid phase, the gas diffusion, and the kinetic of the soot oxidation reaction is performed and validated by the bench test. The effects of different temperatures on CDPF passive and active regeneration at the equilibrium point are analyzed. Further, the effective analysis of ash loading and ash layer distribution on the equilibrium state is conducted. The research on CDPF passive and active regeneration at the equilibrium point in the presence of ash layer provides a theoretical basis for CDPF application.

Mechanism of stress transmission and feasibility of mining the lower coal seam under repeated mining in close-multiple coal seams

Mining in an upper coal seam results in the redistribution of vertical stress within a lower coal seam until a new equilibrium state is attained. Close-multiple coal seams mining faces the occurrence of multi-goafs and a complex stress environment. Based on a case study of close-multiple coal seams with repeated mining in the Qianjiaying coal mine, a stress distribution model of the floor in the coal seam striking range was established by optimizing the load form of the abutment pressure. The floor stress state after primary and repeated mining of upper coal seams was analyzed in a visual and quantitative manner. The concentrations of vertical stress, horizontal stress, and shear stress are all located in the floor under the coal rib after primary and repeated mining. The curve of stresses gradually levels off as the depth of the floor increases, indicating a diminishing influence of mining-induced stress from the upper coal seam. Based on the stress analysis by numerical simulations, the overall lower coal seam remains in a state of large-scale stress relief. Stress relief occurred twice under repeated mining, which indicates that the lower coal seam has favorable mining feasibility. The results of the study can provide scientific guidance to prevent mining accidents.

Sediment DNA Records the Critical Transition of Bacterial Communities in the Arid Lake

It is necessary to predict the critical transition of lake ecosystems due to their abrupt, non-linear effects on social-economic systems. Given the promising application of paleolimnological archives to tracking the historical changes of lake ecosystems, it is speculated that they can also record the lake’s critical transition. We studied Lake Dali-Nor in the arid region of Inner Mongolia because of the profound shrinking the lake experienced between the 1300 s and the 1600 s. We reconstructed the succession of bacterial communities from a 140-cm-long sediment core at 4-cm intervals and detected the critical transition. Our results showed that the historical trajectory of bacterial communities from the 1200 s to the 2010s was divided into two alternative states: state1 from 1200 to 1300 s and state2 from 1400 to 2010s. Furthermore, in the late 1300 s, the appearance of a tipping point and critical slowing down implied the existence of a critical transition. By using a multi-decadal time series from the sedimentary core, with general Lotka-Volterra model simulations, local stability analysis found that bacterial communities were the most unstable as they approached the critical transition, suggesting that the collapse of stability triggers the community shift from an equilibrium state to another state. Furthermore, the most unstable community harbored the strongest antagonistic and mutualistic interactions, which may imply the detrimental role of interaction strength on community stability. Collectively, our study showed that sediment DNA can be used to detect the critical transition of lake ecosystems.

Methodological bases for balanced development of the food supply of the population

A retrospective analysis of the economic theories of marginal utility, general economic equilibrium, spatial economics, production factors, and organization theory was carried out from the position of forming the methodological basis for the emergence of the theory of balanced development of food supply for the population. The substantive aspects of the critical concepts of the identified theories are detailed in their influence on the formation and formation of the methodology for food supply to the population, including maintaining a balanced and equilibrium state in the conditions of continuous influence of external factors on food systems. For each identified theory, provisions have been established that determine the relationship with the methodology of the area under study. It has been established that the emergence of the theory and methods of balanced development of food supply for the population is a natural stage in the evolution of economic science in the context of increasing the role and importance of man in the modern economy. The methodological grounds identified are the need to achieve and maintain a balanced human diet, ensure coordination and maintain a balance of social and economic interests of consumers and food producers, ensure a balanced state of food production and consumption, maintain a balance of resource capabilities and future food needs of people, prevent the emergence of imbalances in the food sector. The work results can be used to develop new conceptual frameworks for developing the domestic agro-industrial complex and allow us to form a more holistic and detailed understanding of the specifics and features of achieving balanced agri-food sector development.

Limited effect of the confluence angle and tributary gradient on Alpine confluence morphodynamics under intense sediment loads

Abstract. Confluences are dynamic morphological nodes that are found in all river networks. In mountain regions, they are influenced by hydraulic and sedimentary processes that occur in steep channels during extreme events in small watersheds. Sediment transport in the tributary channel and aggradation in the confluence can be massive, potentially causing overbank flooding and sedimentation into adjacent settlement areas. Previous works dealing with confluences have mainly focused on lowland regions, and those that have focused on mountain areas have used sediment concentrations and channel gradients that are largely under-representative of mountain river conditions. The presented work contributes to filling this research gap with 45 experiments that use a large-scale physical model. Geometric model parameters, the applied grain size distribution, and the considered discharges represent the conditions at 135 confluences in South Tyrol (Italy) and Tyrol (Austria). The experimental program allowed for a comprehensive analysis of the effects of (i) the confluence angle, (ii) the tributary gradient, (iii) the channel discharges, and (iv) the tributary sediment concentration. In contrast to most research dealing with confluences, results indicate that, in the presence of an intense tributary sediment supply and a small tributary-to-main-channel discharge ratio (0.1), the confluence angle does not have a decisive effect on confluence morphology. Adjustments to the tributary channel gradient yielded the same results. A reoccurring range of depositional geomorphic units was observed in which a deposition cone transitioned to a bank-attached bar. The confluence morphology and tributary channel gradient rapidly adjusted, tending towards an equilibrium state to accommodate both water discharges and the sediment load from the tributary. Statistical analyses demonstrated that the confluence morphology was controlled by the combined channel discharge and the depositional or erosional extent was controlled by the sediment concentration. Applying conclusions drawn from lowland confluence dynamics could misrepresent depositional and erosional patterns and the related flood hazard at mountain river confluences.

Quantum-classical correspondence in spin-boson equilibrium states at arbitrary coupling

Abstract The equilibrium properties of nanoscale systems can deviate significantly from standard thermodynamics due to their coupling to an environment. We investigate this here for the θ-angled spin-boson model, where we first derive a compact and general form of the classical equilibrium state including environmental corrections to all orders. Secondly, for the quantum spin-boson model we prove, by carefully taking a large spin limit, that Bohr's quantum-classical correspondence persists at all coupling strengths. This shows, for the first time, the validity of the quantum-classical correspondence for an open system and gives insight into the regimes where the quantum system is well-approximated by a classical one. Finally, we provide the first classification of the coupling parameter regimes for the spin-boson model, from weak to ultrastrong, both for the quantum case and the classical setting. Our results shed light on the interplay of quantum and mean force corrections in equilibrium states of the spin-boson model, and will help draw the quantum to classical boundary in a range of fields, such as magnetism and exciton dynamics.

Competitive adsorption mechanisms of multicomponent gases in kaolinite under electric fields: A molecular perspective

The investigation of the competitive adsorption mechanisms of gas mixtures within the inorganic nanopores of shale influenced by an electric field holds paramount importance for improving shale gas recovery and enhancing CO2 storage efficiency. This study employs molecular dynamics (MD) simulations to investigate the competitive adsorption mechanisms of gas mixtures on kaolinite surfaces. Subsequently, the engineering parameters governing electric field-enhanced CO2 sequestration and enhanced gas recovery (CS-EGR) are explored and optimized. In the absence of an electric field, the analysis reveals that water molecules exhibit the highest adsorption capacity in a ternary H2O–CO2–CH4 mixture, resulting in the formation of a water film of a specific thickness. CO2 displays a superior adsorption capability over CH4. As the CO2 volume injected into the reservoir increases, CH4 undergoes desorption due to the dominant adsorption effect of CO2. However, the efficiency of CO2 displacing CH4 diminishes significantly. The introduction of an electric field alters the equilibrium state of the gas mixture, leading to a further increase in CO2 adsorption and enhancing its selectivity relative to that of CH4 by 33%. These findings lay the foundation for the practical implementation of electric field-enhanced CS-EGR in shale reservoirs.

Concerning for the solvent-polarity-dependent conformational equilibrium and ESIPT mechanism in Pz3HC system: A novel insight

In this report, we propose a new insight into the interaction between the solvent-polarity-dependent conformational equilibrium and excited state intramolecular proton transfer (ESIPT) behavior of Pz3HC system in four different polar solvents (polarity order: ACN > THF > TOL > CYC). Using quantum chemistry method, we first announce a coexistence mechanism between Pz3HC-1 and Pz3HC-3 in the ground state in four solvents based on the Boltzmann distribution. In particular, Pz3HC-1 is the principal configuration in non-polar solvent, but Pz3HC-3 is the principal configuration in polar solvent. In addition, the simulated fluorescence spectra interprets the negative solvatochromism effect of Pz3HC-1 and Pz3HC-3 in four solvents. The evidence from intramolecular hydrogen bonding (IHB) parameters and electronic perspective collectively confirms the light-induced IHB enhancement and intramolecular charge transfer (ICT) properties in Pz3HC-1 and Pz3HC-3, which raises the likelihood of the ESIPT process. Combining the calculation of potential energy curve (PEC) and intrinsic reaction coordinate (IRC), we demonstrate that the ESIPT ease of Pz3HC-1 in different polar solvents obeys the order of CYC > TOL > THF > ACN, while the order of ESIPT ease in Pz3HC-3 is opposite. Notably, the ESIPT process of Pz3HC-3 in CYC solvent is accompanied by the twisted intramolecular charge transfer (TICT) process. In addition, we also reveal that the enol* and keto* fluorescence peaks of Pz3HC-3 in CYC solvent are quenched by ISC and TICT process, respectively. Our work not only provides a satisfactory explanation of the novel dynamics mechanism for Pz3HC system, but also brings light to the design and application of new sensing molecules in the future.

Casein-quaternary chitosan complexes induced the soft assembly of egg white peptide and curcumin for ulcerative colitis alleviation

Soft assembly of peptide and curcumin (Cur) molecules enables functional integration by finding dynamic equilibrium states through non-covalent interactions. Herein, we developed two soft assembly systems, curcumin-egg white peptides (Cur-EWP) aggregations (AGs) and Cur-EWP-casein-quaternary chitosan (Cur-EWP-CA-QC) nanoparticles (NPs) to comparatively investigate their therapeutic effects on ulcerative colitis in mice and elucidate their underlying mechanism. Results revealed that Cur-EWP AGs, despite gastrointestinal tract instability, exhibited a propensity for swift accumulation within the colorectal region, enriching mucus-associated and short-chain fatty acid (SCAF)-producing bacteria, restoring the intestinal barrier damage. Whereas, Cur-EWP-CA-QC NPs, benefiting from their remarkable stability and exceptional mucosal adsorption properties, not only enhanced permeability of Cur and EWP in the small intestine to activate the immune response and boost tight junction protein expression but also, in their unabsorbed state, regulated the intestinal flora, exerting potent anti-inflammatory activity. Soft assembly of peptides and hydrophobic nutraceuticals could synergize biological activities to modulate chronic diseases.

Streamlining Protein Fractional Synthesis Rates Using SP3 Beads and Stable Isotope Mass Spectrometry: A Case Study on the Plant Ribosome.

Ribosomes are an archetypal ribonucleoprotein assembly. Due to ribosomal evolution and function, r-proteins share specific physicochemical similarities, making the riboproteome particularly suited for tailored proteome profiling methods. Moreover, the structural proteome of ribonucleoprotein assemblies reflects context-dependent functional features. Thus, characterizing the state of riboproteomes provides insights to uncover the context-dependent functionality of r-protein rearrangements, as they relate to what has been termed the ribosomal code, a concept that parallels that of the histone code, in which chromatin rearrangements influence gene expression. Compared to high-resolution ribosomal structures, omics methods lag when it comes to offering customized solutions to close the knowledge gap between structure and function that currently exists in riboproteomes. Purifying the riboproteome and subsequent shot-gun proteomics typically involves protein denaturation and digestion with proteases. The results are relative abundances of r-proteins at the ribosome population level. We have previously shown that, to gain insight into the stoichiometry of individual proteins, it is necessary to measure by proteomics bound r-proteins and normalize their intensities by the sum of r-protein abundances per ribosomal complex, i.e., 40S or 60S subunits. These calculations ensure that individual r-protein stoichiometries represent the fraction of each family/paralog relative to the complex, effectively revealing which r-proteins become substoichiometric in specific physiological scenarios. Here, we present an optimized method to profile the riboproteome of any organism as well as the synthesis rates of r-proteins determined by stable isotope-assisted mass spectrometry. Our method purifies the r-proteins in a reversibly denatured state, which offers the possibility for combined top-down and bottom-up proteomics. Our method offers a milder native denaturation of the r-proteome via a chaotropic GuHCl solution as compared with previous studies that use irreversible denaturation under highly acidic conditions to dissociate rRNA and r-proteins. As such, our method is better suited to conserve post-translational modifications (PTMs). Subsequently, our method carefully considers the amino acid composition of r-proteins to select an appropriate protease for digestion. We avoid non-specific protease cleavage by increasing the pH of our standardized r-proteome dilutions that enter the digestion pipeline and by using a digestion buffer that ensures an optimal pH for a reliable protease digestion process. Finally, we provide the R package ProtSynthesis to study the fractional synthesis rates of r-proteins. The package uses physiological parameters as input to determine peptide or protein fractional synthesis rates. Once the physiological parameters are measured, our equations allow a fair comparison between treatments that alter the biological equilibrium state of the system under study. Our equations correct peptide enrichment using enrichments in soluble amino acids, growth rates, and total protein accumulation. As a means of validation, our pipeline fails to find "false" enrichments in non-labeled samples while also filtering out proteins with multiple unique peptides that have different enrichment values, which are rare in our datasets. These two aspects reflect the accuracy of our tool. Our method offers the possibility of elucidating individual r-protein family/paralog abundances, PTM status, fractional synthesis rates, and dynamic assembly into ribosomal complexes if top-down and bottom-up proteomic approaches are used concomitantly, taking one step further into mapping the native and dynamic status of the r-proteome onto high-resolution ribosome structures. In addition, our method can be used to study the proteomes of all macromolecular assemblies that can be purified, although purification is the limiting step, and the efficacy and accuracy of the proteases may be limited depending on the digestion requirements. Key features • Efficient purification of the ribosomal proteome: streamlined procedure for the specific purification of the ribosomal proteome or complex Ome. • Accurate calculation of fractional synthesis rates: robust method for calculating fractional protein synthesis rates in macromolecular complexes under different physiological steady states. • Holistic ribosome methodology focused on plants: comprehensive approach that provides insights into the ribosomes and translational control of plants, demonstrated using cold acclimation [1]. • Tailored strategies for stable isotope labeling in plants: methodology focusing on materials and labeling considerations specific to free and proteinogenic amino acid analysis [2].