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Loschmidt’s Paradox, Extended to CPT Symmetry, Bypasses Second Law

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Journal of Applied Mathematics and Physics 2019年第12期7卷 3140-3175页

作者： George S. Levy entropic power Irvine California USA

Loschmidt’s paradox is extended by replacing its assumption of time reversibility with full CPT symmetry. Mobility is identified as a means for expressing collisions or dissipation, and the cross product of its gradient with the magnetic field, for expressing parity. Three phenomena incorporating such cross products are identified. The first is the cross product of the mobility gradient with the magnetic field. The second combines this cross product with the E cross B drift. The third is the reciprocal of the Nernst effect expressed as a cross product of the temperature gradient and the magnetic field. Simulations are conducted for testing Loschmidt’s extended paradox. Onsager’s exclusion of magnetic fields and rotation from reciprocals violates CPT symmetry and is unjustified. All three cross-product phenomena skew statistics in a fashion unanticipated by Boltzmann’s assumptions in his H-Theorem. CPT symmetric systems fall outside the assumptions of the theorem which is not rendered invalid but simply limited to its domain of applicability. Therefore, these systems do not violate the second law as Boltzmann defines it. They bypass it.

关键词： Second Law Boltzmann Loschmidt CPT Symmetry Entropy Nernst Effect H-Theorem Onsager Paradox Cross Product

Playing Rock, Paper, Scissors in Non-Transitive Statistical Thermodynamics

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Journal of Applied Mathematics and Physics 2017年第5期5卷 1174-1197页

作者： George S. Levy entropic power San Diego USA

Does non-transitivity in information theory have an analog in thermodynamics? A non-transitive game, “Swap”, is used as a toy thermodynamic model to explore concepts such as temperature, heat flow, equilibrium and entropy. These concepts, found to be inadequate for non-transitive thermodynamic, need to be generalized. Two kinds of temperatures, statistical and kinetic, are distinguished. Statistical temperature is a parameter in statistical distributions. Kinetic temperature is proportional to the expected kinetic energy based on its distribution. Identical for Maxwell-Boltzmann statistics, these temperatures differ in non-Maxwellian statistics when a force is present. Fourier’s law of conduction and entropy should be expressed using statistical temperature, not kinetic temperature. Kinetic temperature is always scalar but statistical temperature and statistical entropy in non-transitive systems have circulation, thereby allowing continuous and circular heat flow. Entropy is relative to underlying statistics, in analogy to the Kullback-Leibler divergence in information theory. The H-theorem, limited by assumptions of homogeneity and indistinguishability, only covers statistically homogeneous systems. The theorem does not cover non-transitive, statistically heterogeneous systems combining different distributions such as Maxwell-Boltzmann, biased half-Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein. The second law can be preserved if generalized by expressing it in terms of statistical temperature and statistical entropy.

关键词： Statistical Thermodynamics Non-Transitivity Second Law Detailed Balance Kinetic Temperature Statistical Temperature Non-Transitive Game Non-Transitive Thermodynamics Entropy Arrow of Time

Quantum Statistics in Physical Chemistry, the Law of Mass Action and Epicatalysis

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Open Journal of Physical Chemistry 2018年第4期8卷 81-99页

作者： George S. Levy entropic power Irvine CA USA

The law of mass action, based on maxwellian statistics, cannot explain recent epicatalysis experiments but does when generalized to non-maxwellian statistics. Challenges to the second law are traced to statistical heterogeneity that falls outside assumptions of homogeneity and indistinguishability made by Boltzmann, Gibbs, Tolman and Von Neumann in their H-Theorems. Epicatalysis operates outside these assumptions. Hence, H-Theorems do not apply to it and the second law is bypassed, not broken. There is no contradiction with correctly understood established physics. Other phenomena also based on heterogeneous statistics include non-maxwellian adsorption, the field-induced thermoelectric effect and the reciprocal Hall effect. Elementary particles have well known distributions such as Fermi-Dirac and Bose Einstein, but composite particles such as those involved in chemical reactions, have complex intractable statistics not necessarily maxwellian and best determined by quantum modeling methods. A step by step solution for finding the quantum thermodynamic properties of a quantum composite gas, that avoids the computational requirement of modeling a large number of composite particles includes 1) quantum molecular modeling of a few particles, 2) determining their available microstates, 3) producing their partition function, 4) generating their statistics, and 5) producing the epicatalytic parameter for the generalized law of mass action.

关键词： Adsorption Boltzmann Entropy Epicatalysis H-Theorem Heterogeneous Statistics Law of Mass Action Non-Maxwellian Quantum Thermodynamics Second Law

Evaluation of Buses in power Grids by Extended entropic Degree

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Evaluation of Buses in Power Grids by Extended Entropic Degr...

Erratum to “The Faraday Isolator, Detailed Balance and the Second Law” [Journal of Applied Mathematics and Physics, Vol. 5, No. 4, April 2017 PP. 889-899]

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作者： Chunchao Wu Xiaoliang Wang Fei Xue Xiaotong Xu Shaofeng Lu Lin Jiang Yujia Zhai SDIC Baiyin Wind power Co. LTD Xi’an Jiaotong-Liverpool University University of Liverpool

Complex network theory has been considered valuable in analyzing the security of networked infrastructures including power ***,the traditional pure topological assessment metrics ignore many characteristics in electrical *** most popular metrics for evaluation of nodes or buses in power grids are degree and *** integration of specific knowledge of electrical engineering,these metrics have been updated to entropic degree and e-betwenness in former ***,with consideration of local and global structural features,these two all have defects *** paper made integration of entropic degree and e-betweenness to develop a new concept as extended entropic degree by considering the e-betweenness of line as the weight in entropic *** new extended entropic degree can reflect both local and global structural features in evaluation of buses in power *** extended entropy degree was tested to verify the effectiveness in IEEE-30,IEEE-118,IEEE-300 and a United Kingdom distribution power *** results indicated that this new metric is more reasonable and effective in discovering structural features of buses in power grids.

关键词： Complex networks power system security power grid Degree entropic degree Line Betweenness

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Journal of Applied Mathematics and Physics 2017年第8期5卷 1537-1539页

作者： George S. Levy entropic power 130 Rockview Irvine CA 92612 USA

A Faraday isolator is shown to develop a temperature difference between its input and output, but still complies with the second law when all the heat carriers, in this case, photons are homogeneous and indistinguishable. This result is a consequence of the H-theorem which assumes homogeneity and indistinguishability of particles. However, when a thermal feedback path is added, in which heat carriers have physical properties different from the photons in the isolator, then a heterogeneous system is formed not covered by the H-theorem, and the second law is violated.

关键词： Faraday Isolator Detailed Balance Second Law Non-Maxwellian Entropy H-Theorem Statistical Mechanics Perpetual Motion Machine Statistical Symmetry Indistinguishability

The Faraday Isolator, Detailed Balance and the Second Law

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Journal of Applied Mathematics and Physics 2017年第4期5卷 889-899页

作者： George S. Levy entropic power 3980 Del Mar Meadows San Diego CA USA

关键词： Faraday Isolator Detailed Balance Second Law Non-Maxwellian Entropy H-Theorem Statistical Mechanics Perpetual Motion Machine Statistical Symmetry Indistinguishability

On-node lattices construction using partial Gauss–Hermite quadrature for the lattice Boltzmann method

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Chinese Physics B 2019年第5期28卷 175-180页

作者：叶欢锋干则成匡波杨燕华 School of Nuclear Science and Engineering Shanghai Jiao Tong University Department of Mathematics University of Michigan National Energy Key Laboratory of Nuclear power Software

A concise theoretical framework,the partial Gauss–Hermite quadrature(pGHQ),is established to construct on-node lattices of the lattice Boltzmann(LB)method under a Cartesian coordinate *** with the existing approaches,the pGHQ scheme has the following advantages:extremely concise algorithm,unifies the constructing procedure for symmetric and asymmetric on-node lattices,and covers a full-range quadrature degree of a given discrete velocity *** employ the pGHQ scheme to search the local optimal and asymmetric lattices for{n=3,4,5,6,7}moment degree equilibrium distribution discretization on the range[-10,10].The search reveals a surprising abundance of available *** a brief analysis,the discrete velocity set shows a significant influence on the positivity of equilibrium distributions,which is considered as one of the major impacts of the numerical stability of the LB ***,the results of the p GHQ scheme lay a foundation for further investigations to improve the numerical stability of the LB method by modifying the discrete velocity *** is also worth noting that pGHQ can be extended into the entropic LB model,even though it was proposed for the Hermite polynomial expansion LB theory.

关键词： equilibrium distribution discretization partial Gauss–Hermite quadrature

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Topological prime

Science China(Technological Sciences) 2020年第7期63卷 1314-1322页

作者： YANG XuXu YANG CanHui LIU JunJie YAO Xi SUO ZhiGang John A.Paulson School of Engineering and Applied Sciences Kavli Institute for Bionano Science and TechnologyHarvard UniversityCambridge MA 02138USA State Key Laboratory of Fluid power&Mechatronic System Key Laboratory of Soft Machines and Smart Devices of Zhejiang ProvinceDepartment of Engineering Mechanics and Center for X-MechanicsZhejiang UniversityHangzhou 310027China Department of Mechanics and Aerospace Engineering Southern University of Science and TechnologyShenzhen 518055China Key Lab for Special Functional Materials of Ministry of Education Henan UniversityKaifeng 475004China

This paper describes a general method, called topological prime, to stitch functional groups to a substrate of entropic polymer network. The precursor of a topological primer contains polymers, crosslinkers, and coupling agents. When the precursor is applied on the surface of the substrate, the crosslinkers link the primer polymers into a primer network, in topological entanglement with the substrate network, while the coupling agents link the primer network to the functional groups. The use of topological prime is demonstrated by priming a hydrophobic elastomer of an arbitrary shape for hydrophilic coating. We describe an approach that fulfills two fundamental requirements: wetting and adhesion. The coated elastomer maintains hydrophilicity and lubricity after stretch, scratch, swell, and slide. As a further demonstration, a hydrogel substrate is primed for hydrophobic coating. Topological prime opens an enormous space for applications in engineering and biomedicine.

关键词： elastomer hydrogel hydrophilic coating topological prime functional groups