Equilibrium Principle Research Articles

Design and Experimental Study on the Torque Balancing Mechanism of a Satellite-Borne Two-Axis Rotary Table

With the rapid development of science and technology, high-resolution remote sensing cameras are now widely used in various fields. At the beginning of camera attitude adjustment, residual torque due to state changes can affect platform stability and lead to the degradation of imaging quality. This paper analyzes the effect of external disturbances on the attitude of the satellite platform according to the Newton–Euler method. In order to effectively realize the self-balancing of the torque of the remote sensing camera rotary table and eliminate the influence of the residual torque on the stability of the satellite platform, this study designs a torque balancing mechanism for the two-axis rotary table of a remote sensing camera based on the first-generation balancing mechanism. Firstly, this paper provides a detailed analysis of the mechanism equilibrium principle from the theoretical point of view based on the theories related to momentum moment theorem and momentum moment conservation law. Then, the dynamics model of the torque balancing mechanism is built, and the dynamics simulation analysis is carried out in this paper. The analysis results show that compared with the first-generation torque balancing mechanism, the residual torque of the second-generation torque balancing mechanism is reduced by 66.67%, the peak value of the residual torque is reduced by 57.55%, the mass of the balancing flywheel is reduced by 74.14%, and the torque balancing time is reduced by 42.86%. Finally, two torque balancing mechanism prototypes were fabricated at equal scale for test verification in this paper. The test results show that compared with the first-generation torque balancing mechanism, the residual torque of the second-generation test prototype is reduced by 40%, the peak of the residual torque is reduced by 25%, the mass of the balancing flywheel is reduced by 60.34%, and the torque balancing time is reduced by 51.06%. There are some differences between the simulation analysis and the experimental results, but the overall trend is consistent with the theory. Through theoretical derivation, simulation analysis and experimental verification, the correctness and feasibility of the proposed second-generation torque balancing mechanism are fully confirmed, which has certain reference significance and engineering application value for the torque self-balancing scheme of rotary tables.

Iterative Backpropagation Method for Efficient Gradient Estimation in Bilevel Network Equilibrium Optimization Problems

Network optimization or network design with an embedded traffic assignment (TA) to model user equilibrium principle, sometimes expressed as bilevel problems or mathematical programs with equilibrium constraints (MPEC), is at the heart of transportation planning and operations. For applications to large-scale multimodal networks with high dimensional decision variables, the problem is nontrivial, to say the least. General-purpose algorithms and problem-specific bilevel formulations have been proposed in the past to solve small problems for demonstration purposes. Research gap, however, exists in developing efficient solution methods for large-scale problems in both static and dynamic contexts. This paper proposes an efficient gradient estimation method called Iterative Backpropagation (IB) for network optimization problems with an embedded static TA model. IB exploits the iterative structure of the TA solution procedure and simultaneously calculates the gradients while the TA process converges. IB does not require any additional function evaluation and consequently scales very well with higher dimensions. We apply the proposed approach to origin-destination (OD) estimation, an MPEC problem, of the Hong Kong multimodal network with 49,806 decision variables, 8,797 nodes, 18,207 links, 2,684 transit routes, and 165,509 OD pairs. The calibrated model performs well in matching the link counts. Specifically, the IB-gradient based optimization technique reduces the link volume squared error by 98%, mean absolute percentage error (MAPE) from 95.29% to 21.23%, and the average GEH statistics from 24.18 to 6.09 compared with the noncalibrated case. The framework, even though applied to OD estimation in this paper, is applicable to a wide variety of optimization problems with an embedded TA model, opening up an efficient way to solve large-scale MPEC or bilevel problems. Funding: The study is supported by IVADO Postdoctoral Fellowship scheme 2021, HSBC 150th Anniversary Charity Programme HKBF17RG01, National Science Foundation of China (71890970, 71890974), General Research Fund (16212819, 16207920) of the HKSAR Government, and the Hong Kong PhD Fellowship.

An Improved Incremental Procedure for the Ground Reaction Based on Hoek-Brown Failure Criterion in the Tunnel Convergence-Confinement Method

The purpose of this study is to introduce the Hoek–Brown nonlinear failure criterion into the convergence–confinement method (CCM), which is based on the linear failure criterion, and implant it into the ground reaction curve (GRC) in this theory. Based on consistent and rigorous theoretical analysis and according to the mechanical relationships, the principle of equilibrium, the material constitutive law, and the strain/displacement compatibility equation are used to deduce the closed-form analytical solution of the stress/displacement of the rock mass in the plastic region and to complete the simulation and interpretation of the nonlinear behavior of surrounding rock due to the advancing excavation of a circular tunnel. In this paper, confinement loss is regarded as the concept of increment in numerical analysis, and the calculation process and analysis steps of the explicit analysis method (EAM) are proposed. This method can not only realize the calculation of analytical solutions but can also be performed using simple spreadsheets. In addition, to verify the feasibility of this calculation method, this study uses published data to verify the validity of the analytical solution implemented by the incremental procedure and to study the influence of nonlinear failure criteria on the GRC, especially the mechanical behavior at the intrados of the tunnel and the distributions of tress/displacement on the cross-section of the tunnel. A comparison between the published results and the proposed solution in this study reveals consistent and favorable trends.

Structural synthesis of the reconfigurable legged mobile lander for strong geometry-physical interaction with extraterrestrial environment

To design the engineering prototype of reconfigurable legged mobile lander (ReLML) for strong geometry-physical interaction with extraterrestrial environment, this paper proposes a tailored structural synthesis methodology unifying kinematic geometry and statics. Compared with our preceding works, three inbuilt operation modes are first integrated: adjusting mode is a totally new mode defined as three rotations (3R) with a strong geometrical adaptation to hostile terrain; landing mode is redefined as two rotations one translation (2R1T), inherits Chang'E lander to survive from strong impact interaction; roving mode turns into the other 2R1T motion for good motion/force interactivity. The interaction characteristics (motion, force, energy) between ReLML and environment are extracted to derive output finite motions and instantaneous wrenches of leg end-effector, following the principles of optimal force system equilibrium and work efficiency. The motion and force synergistic syntheses of metamorphic limb and joint are implemented to design and assemble mechanical generators. The ReLML can serve the alien base construction and adjustable launch bracket. The unified structural synthesis methodology of kinematic geometry and statics is universal and effective for designing parallel mechanisms and reconfigurable mechanisms, especially for strong physical interaction scenarios.

The advanced concepts for septal l-strut re-designing in septorhinoplasty for better strength and stability by considering of center of gravity.

This study contributes to the multidisciplinary understanding of septal L-strut reshaping and introduces innovative surgical design concepts based on engineering principles of static equilibrium. The objective is to enhance structural strength and stability, ultimately leading to improved surgical outcomes. Finite element analysis is employed to model the three-dimensional septal cartilage in septoplasty. A significant contribution of this work is the introduction of an innovative redesigns for the septal L-strut structure. These redesigns represent the first-ever attempt to incorporate the center of gravity theory into the modeling of the septal L-strut. Our findings emphasize the significance of attaining a lower center of gravity in the design of the septal L-strut, as it contributes to optimal core strength and stability. To achieve this, we recommend widening the caudal septum and shaping the interior fillet corner to its maximum size, taking into account its specific shape. Notably, the utilization of a standard 20x20 mm septal L-strut, the C-shaped technique, and the septal support graft technique provide superior strength due to enhanced basement support. To enhance surgical outcomes in septal L-strut procedures, design modifications are proposed to improve strength and stability, resulting in optimized performance. Recommendations include widening the caudal septum and incorporating fillet shapes in the geometry to lower the center of gravity.

An Analysis of Qisas and Diyat Laws, Inadequately Encompassed the Islamic Gist as Fused in Judicial System of Pakistan

The Qisas and Diyat is product of Islamic jurisprudence. The laws in Pakistan with distinct applicability of conceptual approach of Qisas and Diyat laws in trails are inadequately address the purposes of criminal justice along with consequences of vast judicial dircretion in Qisas and Diyat cases will not serving the purpose of administering justice. The Holy Quran hasn’t provided dictionary definition of justice, but it establishes conceptual approach to the principle of equilibrium, parity, righteous, proper assessing, veracity, individual capacity and progress and the accepted mandate. The key form of justice is the egalitarianism of human personalities being valued as Human beings, evidently indicated in the Holy injunctions of and even stressed in the last Holy Sermon of (PBUH). The Qisas and Diyat is product of Islamic jurisprudence. The laws in Pakistan with distinct applicability of conceptual approach of Qisas and Diyat laws in trails are inadequately addressed the purposes of criminal justice along with consequences of vast judicial discretion in Qisas and Diyat cases will not serve the purpose of administering justice. The Holy Quran hasn’t provided a dictionary definition of justice, but it establishes a conceptual approach to the principle of equilibrium, parity, righteousness, proper assessing, veracity, individual capacity and progress and the accepted mandate. The key form of justice is the egalitarianism of human personalities being valued as Human beings, evidently indicated in the Holy injunctions of and even stressed in the last Holy Sermon of (PBUH). The Qisas and Diyat laws, as pooled in Pakistan Penal Code, 1860, have not been argued and debated adequately and hence contain imperfections, tend to bring imbalance and introduce crimes like violence against women, vani, swara etc. The aim of the analysis is to address the shortcomings and loopholes prevailing in the criminal justice system by advancing solutions and concept clarity related to the institution of aqilah.

A new source finding and tracking analysis approach for the active reflector of five-hundred-meter aperture spherical telescope

The FAST (Five-hundred-meter Aperture Spherical Telescope) is the world’s largest single-aperture radio telescope. During operation, FAST needs to follow the observed celestial body to adjust displacements, which can be divided into two processes: the source finding and tracking. In this paper, a new numerical method based on Vector Form Intrinsic Finite Element (VFIFE) is proposed to simulate the source finding and tracking process for FAST’s active reflector. The basic principle of static equilibrium and calculation flow of the sourcing and tracking analysis is proposed, and the finite element program is compiled to analyze the displacement process of the reflector cable-net structure. Then, six typical test conditions are selected to simulate the sourcing and tracking displacement process. The obtained final form in the equilibrium state adheres to the target configuration, demonstrating the applicability of the suggested approach and the correctness of calculation findings. In addition, the change in the actuator length and the structural force distribution can be simultaneously derived. These values serve as a vital theoretical foundation for FAST’s practical operation and regulation.

S, Fe dual doped and precisely regulated CoP porous nanoneedle arrays for efficient hydrogen evolution at 3 A cm−2

Transition metal phosphides (TMPs) have been proved as promising catalysts for the hydrogen evolution reaction (HER) and oxygen evolution reaction (OER). However, CoP has a strong hydrogen adsorption energy, resulting in a slow Heyrovsky step in the HER. Herein, the solid phase FeS is ionized into S and Fe ions and doped into cobalt precursor during the hydrothermal process based on the precipitation dissolution equilibrium principle, and the doping strategy precisely regulated the atomic ratio of metal/P. The optimized S, Fe-CoP@IF one-dimensional porous nanoneedles structure exhibit excellent HER performance, which only required 82.3 mV and 200.1 mV to achieve 100 mA cm−2 and 3 A cm−2 together with high currents stability for 100 h. It also has better OER performance, with 260 mV reaching 100 mA cm−2. Further simulated industrial test for S, Fe-CoP@IF in alkaline anion-exchange membrane (AEM) cells show that only 1.75 V is required to attain 500 mA cm−2. Density functional theory (DFT) calculations confirmed that the dual-doping further modulates the electronic structure of CoP, reduces the Gibbs free energy for hydrogen adsorption. This work provides the possibility to further improve the catalytic activity of cobalt phosphide and apply it to industrial applications.

Quantification of Surface Tension Effects and Nucleation-and-Growth Rates during Self-Assembly of Biological Condensates.

Liquid-solid and liquid-liquid phase separation (PS) drives the formation of functional and disease-associated biological assemblies. Principles of phase equilibrium are here employed to derive a general kinetic solution that predicts the evolution of the mass and size of biological assemblies. Thermodynamically, protein PS is determined by two measurable concentration limits: the saturation concentration and the critical solubility. Due to surface tension effects, the critical solubility can be higher than the saturation concentration for small, curved nuclei. Kinetically, PS is characterized by the primary nucleation rate constant and a combined rate constant accounting for growth and secondary nucleation. It is demonstrated that the formation of a limited number of large condensates is possible without active mechanisms of size control and in the absence of coalescence phenomena. The exact analytical solution can be used to interrogate how the elementary steps of PS are affected by candidate drugs.

Optimal intersection design and signal setting in a transportation network with mixed HVs and CAVs

It is widely recognized that human-driven vehicles (HVs) and connected and autonomous vehicles (CAVs) are expected to coexist and share the urban traffic infrastructure in the transportation network for a long time. To fully utilizes CAVs’ potential to reduce congestion in the transitional period, this study proposes and addresses the intersection design and signal setting problem in the transportation network with mixed HVs and CAVs. Due to the difference in terms of communication technology and autonomous driving technology for HVs and CAVs, three types of intersections have been proposed to amplify the efficiency-improvement benefit from CAVs by separating CAVs from HVs in a temporal or local-spatial dimension: the conventional signalized intersection, the novel signalized intersection with a dedicated CAV phase and dedicated CAV approaches, and the intelligent signal-free intersection. The problem is to determine the spatial layout of different types of intersections in the transportation network, the cycle time, and green time duration for each phase of signalized intersections that minimize the total travel cost, in which the route choice behavior of heterogeneous travelers has been respected based on the user equilibrium principle. A mixed-integer nonlinear programming model is developed to formulate the proposed intersection design and signal setting problem based on the link-node modeling method, in which the path enumeration is avoided. Then, by employing various linearization techniques (e.g., disjunctive constraints, logarithmic transformation, piecewise linearization with logarithmic-sized binary variables and constraints, outer-approximation technique), the proposed model can be further transformed into a relaxed sub-problem in the form of mixed-integer linear programming. A globally optimal solution algorithm embedding with solving a sequence of relaxed sub-problems and nonlinear mixed complementarity problems is proposed to converge to a global optimum. The results of numerical experiments illustrate that the proposed methodology can significantly improve the performance of the whole network. Moreover, it consistently outperforms the optimization model considering only conventional signalized intersections under various CAV market penetration rates.

Hydrogen adsorption in nanopores: Molecule-wall interaction mechanism

Reduction in the utilization of carbon-based fossil energy is the inevitable pathway to fulfill the net-zero CO2 emission target. Hydrogen, one of favorable clean energy sources, becomes a heat topic at present while its safe and efficient storage remains a challenging issue. The majority of related research focus on the hydrogen injection into salt cavern as well as depleted oil/gas reservoirs, where hydrogen is highly compressed under high pressure. In this research, an alternative approach that stores hydrogen into nanopores using the essential adsorption property is investigated, and so does its advantage over traditional high-pressure injection method. First of all, a mechanical model for density distribution of nanoconfined hydrogen is established by the chemical potential equilibrium principle, in which both intermolecular interactions and molecule-wall interactions are taken into account. Additionally, shift of critical properties taking place in nanopores is coupled as well. Then, the nanoconfined hydrogen adsorption behavior is presented, influence of atmosphere parameters, like pressure and temperature, as well as nanopore physical properties, like pore size and strength the pore wall imposes on hydrogen molecules, are identified. The proposed model can reach excellent agreements with hydrogen adsorption data collected from the existed experiments and molecular simulation, clarifying its reliability. Results show that (a) Adsorption phase thickness approaches 0.5 nm, indicating 1–2 adsorption layers are formed, which is insensitive to pressure or temperature variation; (b) Nanoconfined hydrogen density is able to achieve as great as 7 times bulk-hydrogen density at relatively low pressure, suggesting nanopores could store more hydrogen molecules than the traditional high-pressure injection method; (c) Modifying nanopore surface chemistry to intensify molecule-wall interaction strength is a desirable method to dramatically improve nanoconfined hydrogen adsorption capacity. The research lays a fundamental framework to shed light on hydrogen adsorption from a microscopic viewpoint.

Thermodynamic analysis of carbon deposition in the preparation of hydrogen-rich reducing gas for direct reduction processes

Hydrogen-rich reducing gas (H2RG) is a key fuel in the emerging carbon–neutral steel industry including gas-based direct reduction (DR) processes. If the preparation parameters in gas reforming are not properly controlled, carbon deposition can occur and it will affect the normal operation of this H2RG preparation process. Therefore, it is necessary to control the carbon deposition during the H2RG preparation process. In this paper, for the first time, a generic “Mass balance and chemical equilibrium diagram for H-C-O system” is proposed for determining the preparation parameters of the process and meanwhile controlling H2/CO ratio in the final gas composition. Then, by applying the phase rule and equilibrium principle of multi-reaction coexistence system, this diagram is used to determine the relationships between the carbon deposition curve and several key parameters including H2/CO ratio, preparation temperature, and total pressure and further determine the region of carbon deposition under the given conditions. For example, under the conditions of 1 atm, H2/CO = 2.0, 600 °C, the critical H2O/CH4 ratio is 2.0. That is, carbon deposition will occur if the H2O/CH4 ratio is less than 2.0 and otherwise not under such conditions. Then, the effect of the preparation parameters on the final gas composition is studied. This diagram provides an effective and handy tool for both proper preparation of H2RG without carbon deposition and meeting the requirements of the given DR process for the carbon–neutral steel industry.

Diagnosis of wind turbine systematic yaw error through nacelle anemometer measurement analysis

The power produced by a wind turbine can be considerably affected by the presence of systematic errors, which are particularly difficult to diagnose. This study deals with wind turbine systematic yaw error and proposes a novel point of view for diagnosing and quantifying its impact on the performance. The keystone is that, up to now in the literature, the effect of the yaw error on the nacelle wind speed measurements of the affected wind turbine has been disregarded. Given this, in this work a new method based on the general principle of flow equilibrium is proposed for the diagnosis of such type of error. It is based on recognizing that a misaligned wind turbine measures the wind speed differently with respect to when it is aligned. The method is shown to be effective for the diagnosis of two test cases, about which an independent estimate of the yaw error is available from upwind measurements (spinner anemometer). A data-driven generalization of the concept of relative performance is then formulated and employed for estimating how much the systematic yaw error affects wind turbine performance. It is shown that the proposed method is more appropriate than methods employing wind speed measurements (like the power curve), which are biased by the presence of the error. The results of this study support that SCADA-collected data can be very useful to diagnose wind turbine systematic yaw error, provided that a critical analysis about their use is done.

Non-unimodal and non-concave relationships in the network Macroscopic Fundamental Diagram caused by hierarchical streets

Unimodal, concave relationships between average network productivity and accumulation or density aggregated across spatially compact regions of urban networks—so called network Macroscopic Fundamental Diagrams (MFDs)—have recently been shown to exist on homogeneous street networks. When present, MFD relationships facilitate the modeling of traffic congestion at a regional level and have led to the development of various regional traffic control strategies. However, real street networks are not homogeneous—they generally have a hierarchical structure where some streets (e.g., arterials) promote higher mobility than others (e.g., local roads). This paper examines how the presence of hierarchical roadway structures may potentially cause non-unimodal patterns in a network's MFD. These are observed using three types of tools: analytical models of simple network structures, simulations of various idealized roadway networks, and empirical data. The impacts of street hierarchy depend on how vehicles use different roadway types to move within the network; i.e., their routing strategy. The findings suggest that the presence of roadway hierarchies may lead to MFDs that have non-unimodal or non-concave patterns on the free-flow branch when vehicles route themselves according to user equilibrium principles, which is closest to what would be observed in realistic situations. Such patterns are contrary to what is traditionally assumed in most MFD-based modeling frameworks. However, the unimodal and concave MFD should be expected under system optimal routing conditions that maximize network productivity for a given traffic state.

Traffic assignment in urban transportation network problem with emission constraints in China: a cooperative game theory

Traffic assignment in urban transport planning is the process of allocating traffic flows in a network. Traditionally, traffic assignment can reduce travel time or travel costs. As the number of vehicles increases and congestion causes increased emissions, environmental issues in transportation are gaining more and more attention. The main objective of this study is to address the issue of traffic assignment in urban transport networks under an abatement rate constraint. A traffic assignment model based on cooperative game theory is proposed. The influence of vehicle emissions is incorporated into the model. The framework consists of two parts. First, the performance model predicts travel time based on the Wardrop traffic equilibrium principle, which reflects the system travel time. No travelers can experience a lower travel time by unilaterally changing their path. Second, the cooperative game model gives link importance ranking based on the Shapley value, which measures the average marginal utility contribution of links of the network to all possible link coalitions that include the link, and assigns traffic flow based on the average marginal utility contribution of a link with system vehicle emission reduction constraints. The proposed model shows that traffic assignment with emission reduction constraints allows more vehicles in the network with an emission reduction rate of 20% than traditional models.

Coordinated operation of coupled transportation and power distribution systems considering road solar generation

The emerging photovoltaic (PV) integration technology called solar road (SR) gives road infrastructure the possibility of not only carrying traffic loads but also generating electricity. The versatility of SR leads to the nexus between transportation network (TN) and power distribution network (PDN). Along with the increasing penetration of electric vehicles (EVs), the installation of SR can promote the reliance of transportation and electrical networks to a higher degree. In order to cope with the severe challenges brought by SR and EV to the TN-PDN coordinated operation, this paper suggests a traffic-power coordinated operation model incorporating road solar generation (TPOSR), where the impact of the traffic flow and SR on the coupled network is studied. Specifically, the user equilibrium (UE) principle is adopted to describe the traffic flow distribution in TN, while the Distflow model is employed to model the power flow in PDN. In TN, the SRs serve as links that let the vehicles through. Moreover, from the perspective of PDN, the SR output model considering traffic shading effect is proposed, based on traffic assignment problem (TAP) and traffic flow theory. In the proposed TPOSR model, we assume the independent system operator, a public organization, can imposes road tolls and dispatch generators to promote coordinated operation of the coupled network. Numerical results demonstrate the effectiveness of the proposed TPOSR for reducing social costs and improving SR performance.

DIRECT MARTENSITIC TRANSFORMATIONS OF LOW-CARBON STEELS

The proposed model is based on the use of the principle of detailed equilibrium, which occurs during phase transitions of the crystal lattice. This theory complements the theory of Landau phase transitions in crystalline media, as well as the theory of crystallization of matter by Kolmogorov and Avrami. In the proposed theory, martensitic transformations are described by equations of induced transitions between two energy levels, which correspond to the number of particles of the original phase with low energy (austenite) and the number of particles of the transformed phase with higher energy (martensite). The source of transformations are particles of the third kind – phonons, the number of which is related to the induced transitions of particles between energy levels and depends on the transformation temperature. The conclusions of the proposed theory quantitatively correspond to the experimental data for phase transformations of low-carbon steels.

Analisis Penerapan Etika Bisnis Islam Dalam Proses Pembuatan ‎Tempe Di Desa Resam Lapis ‎ Kec. Bantan Kab. Bengkalis ‎

This research was conducted with the aim of finding out how tempe management is viewed from the perspective of Islamic business ethics for tempe entrepreneurs in Resam Lapis Village. The research location will be carried out at Home Industry which is in Resam Lapis Village, Bantan District. The type of research carried out is field research. The research approach used in this research is descriptive qualitative. The population that will be taken in this study is all tempe production houses in Resam Lapis Village. In collecting data, the method that the author uses is observation by going directly to the tempe-making home industry to observe directly, interviews conducted directly with the owners of the tempe-making home industry and collecting documentation from interviews and observations in the form of writing, photos, archives, and so on related to the application of Islamic business ethics carried out by the tempe-making home industry. This study uses qualitative data analysis methods. Qualitative analysis is an effort made by working with data, finding patterns, sorting it into manageable units, determining what is important and what is learned and deciding what others can tell. The results of the study found that the implementation of Islamic business ethics in Home Industry Tempe Nursiah has been implemented, namely the principle of unity, the principle of free will, the principle of responsibility and the principle of truth (virtue and honesty). However, there is one principle that is not implemented, namely the principle of equilibrium.

Design and Modeling of a Hybrid Soft Robotic Manipulator With Compliant Mechanism

The recent surge of interest in soft robotics has prompted many interesting soft robotic manipulator designs to be proposed. However, current soft robotic manipulators mainly focus on bending and rotation, while elongation has not received attention due to the limited extension/contraction range or the inextensibility of the backbone. This will adversely affect the application of soft robotic manipulators. In this letter, we introduce a hybrid soft robotic manipulator capable of controllable elongation and give a modeling method based on equilibrium principles and assuming a priori deformed configuration. The hybrid soft manipulator consists of a multi-chamber soft body and a rod-driven compliant mechanism, wherein the compliant mechanism provides a push-pull drive to constrain the motion of the manipulator. The model is a modeling framework for a multi-chamber soft robotic manipulator that depicts the relationship between pressures, bending, rotation, and elongation. We experimentally verify the model and demonstrate the potential of the hybrid soft manipulator for point tracking, by comparing it with the soft manipulator without driving rods.

AXIOMATIC PRINCIPLES AND DETAILED BALANCE

This article presents an analysis of scientific papers and research on axiomatic principles and detailed balance, we are convinced that even today, in accordance with modern requirements, there is still a need to address axiomatic principles and detailed balance, methods and methods for their study. As mentioned earlier, the axiomatics of statistical physics is reduced to the principle of equal probability of the existence of an equilibrium closed physical system in all microstates accessible to it. This postulate, in turn, suggests that the time-averaged probability of the direct and reverse transition of the system between two selected groups of microstates in the accessible region of the phase space must be the same in both directions (this follows from the definition of an equilibrium state, which contains the requirement of stationarity). In fairness, it should be noted that the principle of detailed balance is not a consequence of the axiomatic principles of statistical physics, and therefore, strictly speaking, is not required to be applied within the framework of this axiomatics. There are situations and outcomes we have given in this article, when the principle of equal probability of available microstates in a closed system is satisfied, but the principle of detailed statistical equilibrium is not.