A generalized Einstein relation is established for a drifted Brownian motion on a compact orientable Remannian manifole. The original form of such relation comes from an explicit formula of diffusion coeffcient by usi...A generalized Einstein relation is established for a drifted Brownian motion on a compact orientable Remannian manifole. The original form of such relation comes from an explicit formula of diffusion coeffcient by using the autocorrelation function of the velocity of the Einstein fluctuation theory of the diffusion process展开更多
The Stokes–Einstein–Debye(SED) relation in TIP5P water is tested with the original formula and its variants within the temperature range 240–390 K. The results indicate that although the variants explicitly break d...The Stokes–Einstein–Debye(SED) relation in TIP5P water is tested with the original formula and its variants within the temperature range 240–390 K. The results indicate that although the variants explicitly break down, the original SED relation is almost valid. Compared with the Stokes–Einstein relation, no explicit decoupling is observed in translational and rotational motion. Variation of the effective hydrodynamic radius is critical to testing the validity of the SED relation.展开更多
This paper presents an investigation of a DC glow discharge at low pressure in the normal mode and with Einstein＇s relation of electron diffusivity. Two-dimensional distributions in Cartesian geometry are presented i...This paper presents an investigation of a DC glow discharge at low pressure in the normal mode and with Einstein＇s relation of electron diffusivity. Two-dimensional distributions in Cartesian geometry are presented in the stationary state, including electric potential, electron and ion densities, longitudinal and transverse electrics fields as well as electron temperature. Our results are compared with those obtained in existing literature. The model used in this work is based on the first three moments of Boltzmann＇s equation. They serve as the continuity equation, the momentum transfer and the energy equations. The set of equations for charged particles presented in monatomic argon gas are coupled in a self-consistent way with Poisson＇s equation. A parametric study varying the cathode voltage, gas pressure, and secondary electron emission coefficient predicts many of the well-known features of DC discharges.展开更多
We employ the Green–Kubo(G-K)and Einstein relations to estimate the self-diffusion coefficients(denoted as D_(G)and D_(E),respectively)in two-dimensional(2D)strongly coupled dusty plasmas(SC-DPs)via equilibrium molec...We employ the Green–Kubo(G-K)and Einstein relations to estimate the self-diffusion coefficients(denoted as D_(G)and D_(E),respectively)in two-dimensional(2D)strongly coupled dusty plasmas(SC-DPs)via equilibrium molecular dynamics(EMD)simulations.D_(G)and D_(E)are computed for a broad domain of screening length(κ)and coupling parameters(Γ)along with different system sizes.It is observed that both D_(G)and D_(E)decrease linearly with increasing Г in warm liquid states and increase with increasingκ.In cold liquid states,the Einstein relation accurately predicts D_(E)in 2D SC-DPs because diffusion motion is close to normal diffusion,but the G-K relation provides overestimations of D_(G),because VACF indicates anomalous diffusion;thus,D_(G)is not accurate.Our new simulation outcomes reveal that D_(G)and D_(E)remain independent of system sizes.Furthermore,our investigations demonstrate that at higher temperatures,D_(G)and D_(E)converge,suggesting diffusion motion close to normal diffusion,while at lower temperatures,these two values diverge.We find reasonable agreement by comparing current and existing numerical,theoretical and experimental data.Moreover,when normalizing diffusion coefficients by the Einstein frequency and testing against the universal temperature scaling law,D_(G)deviates from theoretical curves at low temperatures and κ,whereas D_(E)only disagrees with theory at very smallκ(■0.10).These findings provide valuable insight into diagnosing dust component parameters within 2D DP systems and contribute to the broader understanding of diffusion processes in DP environments.展开更多
The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics...The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics, while enormous successful in physics, have been in an awkward situation of wanting a consistent dynamical understanding. Here we present from a formal point of view an exploration of the connection between thermodynamics and Darwinian dynamics and a few related topics. We first show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of Boltzmann-Gibbs type. In term of relative entropy the Second Law of thermodynamics is dynamically demonstrated without detailed balance condition, and is valid regardless of size of the system. In particular, the dynamical component responsible for breaking detailed balance condition does not contribute to the change of the relative entropy. Two types of stochastic dynamical equalities of current interest are explicitly discussed in the present approach： One is based on Feynman-Kac formula and another is a generalization of Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that Darwinian dynamics represents logically a simple and straightforward starting point for statistical mechanics and thermodynamics and is complementary to and consistent with conservative dynamics that dominates the physical sciences. Present exploration suggests the existence of a unified stochastic dynamical framework both near and far from equilibrium.展开更多
According to the general principle of non-equilibrium thermodynamics, we propose a set of macroscopic transport equations for the spin transport and the charge transport, In particular, the spin torque is introduced a...According to the general principle of non-equilibrium thermodynamics, we propose a set of macroscopic transport equations for the spin transport and the charge transport, In particular, the spin torque is introduced as a generalized ＇current density＇ to describe the phenomena associated with the spin non-conservation in a unified framework. The Einstein relations and the Onsager relations between different transport phenomena are established. Specifically, the spin transport properties of the isotropic non-magnetic and the isotropic magnetic two-dimensional electron gases are fully described by using this theory, in which only the macroscopic-spin-related transport phenomena allowed by the symmetry of the system are taken into account.展开更多
We study the stochastic motion of a Brownian particle driven by a constant force over a static periodic potential. We show that both the effective diffusion and the effective drag coefficient are mathematically well-d...We study the stochastic motion of a Brownian particle driven by a constant force over a static periodic potential. We show that both the effective diffusion and the effective drag coefficient are mathematically well-defined and we derive analytic expressions for these two quantities. We then investigate the asymptotic behaviors of the effective diffusion and the effective drag coefficient, respectively, for small driving force and for large driving force. In the case of small driving force, the effective diffusion is reduced from its Brownian value by a factor that increases exponentially with the amplitude of the potential. The effective drag coefficient is increased by approximately the same factor. As a result, the Einstein relation between the diffusion coefficient and the drag coefficient is approximately valid when the driving force is small. For moderately large driving force, both the effective diffusion and the effective drag coefficient are increased from their Brownian values, and the Einstein relation breaks down. In the limit of very large driving force, both the effective diffusion and the effective drag coefficient converge to their Brownian values and the Einstein relation is once again valid.展开更多
For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, providing convergence and stability information. In this paper, the converse is constructively prov...For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, providing convergence and stability information. In this paper, the converse is constructively proved that any dynamics with a Lyapunov function has a corresponding physical realization： a friction force, a Lorentz force, and a potential function. Such construction establishes a set of equations with physical meaning for Lyapunov function and suggests new approaches on the significant unsolved problem namely to construct Lyapunov functions for general nonlinear systems. In addition, a connection is found that the Lyapunov equation is a reduced form of a generalized Einstein relation for linear systems, revealing further insights of the construction.展开更多
The conceptual difficulties encountered in thermodynamics are well known and are certainly the reasons that have led the great physicist Arnold Sommerfeld, a long time ago, to say that understanding thermodynamics is ...The conceptual difficulties encountered in thermodynamics are well known and are certainly the reasons that have led the great physicist Arnold Sommerfeld, a long time ago, to say that understanding thermodynamics is not easy. The situation remains nearly the same today and is due to the fact that the tools used in thermodynamics, <em>i</em>.<em>e</em>. the equations, are not in good accordance with the laws of thermodynamics. Since the efficiency of the tools cannot be contested, it is probably the formulation of the laws that needs to be revised. On the basis of arguments already evoked in previous papers, the suggestion presented below is a contribution going in this sense and inserting the Einstein’s relation <em>E</em> = <em>mc</em><sup>2</sup> in the thermodynamic reasoning.展开更多
The first part of this paper is a condensed synthesis of the matter presented in several previous ones. It begins with an argumentation showing that the first and second laws of thermodynamics are incompatible with on...The first part of this paper is a condensed synthesis of the matter presented in several previous ones. It begins with an argumentation showing that the first and second laws of thermodynamics are incompatible with one another if they are not connected to relativity. The solution proposed consists of inserting the Einstein mass-energy relation into a general equation that associates both laws. The second part deals with some consequences of this new insight and its possible link with gravitation. Despite a slight modification of the usual reasoning, the suggested hypothesis leads to a simplification and extension of the thermodynamic theory and to the idea that relativity is omnipresent around us.展开更多
文摘A generalized Einstein relation is established for a drifted Brownian motion on a compact orientable Remannian manifole. The original form of such relation comes from an explicit formula of diffusion coeffcient by using the autocorrelation function of the velocity of the Einstein fluctuation theory of the diffusion process
基金Project supported by the National Natural Science Foundation of China (Grant No. 12104502)the Natural Science Foundation of Sichuan Province (Grant No. 2023YFG0308)the Fundamental Research Funds for the Central Universities (Grant No. 24CAFUC03057)。
文摘The Stokes–Einstein–Debye(SED) relation in TIP5P water is tested with the original formula and its variants within the temperature range 240–390 K. The results indicate that although the variants explicitly break down, the original SED relation is almost valid. Compared with the Stokes–Einstein relation, no explicit decoupling is observed in translational and rotational motion. Variation of the effective hydrodynamic radius is critical to testing the validity of the SED relation.
文摘This paper presents an investigation of a DC glow discharge at low pressure in the normal mode and with Einstein＇s relation of electron diffusivity. Two-dimensional distributions in Cartesian geometry are presented in the stationary state, including electric potential, electron and ion densities, longitudinal and transverse electrics fields as well as electron temperature. Our results are compared with those obtained in existing literature. The model used in this work is based on the first three moments of Boltzmann＇s equation. They serve as the continuity equation, the momentum transfer and the energy equations. The set of equations for charged particles presented in monatomic argon gas are coupled in a self-consistent way with Poisson＇s equation. A parametric study varying the cathode voltage, gas pressure, and secondary electron emission coefficient predicts many of the well-known features of DC discharges.
基金support of the Fundamental Research Funds for the Central Universities of China(Grant No.2019ZDPY16).
文摘We employ the Green–Kubo(G-K)and Einstein relations to estimate the self-diffusion coefficients(denoted as D_(G)and D_(E),respectively)in two-dimensional(2D)strongly coupled dusty plasmas(SC-DPs)via equilibrium molecular dynamics(EMD)simulations.D_(G)and D_(E)are computed for a broad domain of screening length(κ)and coupling parameters(Γ)along with different system sizes.It is observed that both D_(G)and D_(E)decrease linearly with increasing Г in warm liquid states and increase with increasingκ.In cold liquid states,the Einstein relation accurately predicts D_(E)in 2D SC-DPs because diffusion motion is close to normal diffusion,but the G-K relation provides overestimations of D_(G),because VACF indicates anomalous diffusion;thus,D_(G)is not accurate.Our new simulation outcomes reveal that D_(G)and D_(E)remain independent of system sizes.Furthermore,our investigations demonstrate that at higher temperatures,D_(G)and D_(E)converge,suggesting diffusion motion close to normal diffusion,while at lower temperatures,these two values diverge.We find reasonable agreement by comparing current and existing numerical,theoretical and experimental data.Moreover,when normalizing diffusion coefficients by the Einstein frequency and testing against the universal temperature scaling law,D_(G)deviates from theoretical curves at low temperatures and κ,whereas D_(E)only disagrees with theory at very smallκ(■0.10).These findings provide valuable insight into diagnosing dust component parameters within 2D DP systems and contribute to the broader understanding of diffusion processes in DP environments.
基金The project supported in part by USA NIH Grant under HG002894
文摘The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics, while enormous successful in physics, have been in an awkward situation of wanting a consistent dynamical understanding. Here we present from a formal point of view an exploration of the connection between thermodynamics and Darwinian dynamics and a few related topics. We first show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of Boltzmann-Gibbs type. In term of relative entropy the Second Law of thermodynamics is dynamically demonstrated without detailed balance condition, and is valid regardless of size of the system. In particular, the dynamical component responsible for breaking detailed balance condition does not contribute to the change of the relative entropy. Two types of stochastic dynamical equalities of current interest are explicitly discussed in the present approach： One is based on Feynman-Kac formula and another is a generalization of Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that Darwinian dynamics represents logically a simple and straightforward starting point for statistical mechanics and thermodynamics and is complementary to and consistent with conservative dynamics that dominates the physical sciences. Present exploration suggests the existence of a unified stochastic dynamical framework both near and far from equilibrium.
基金Project supported by the National Key Basic Research Special Foundation of China (Grant No 2006CB921300)the National Natural Science Foundation of China (Grant No 10604063)
文摘According to the general principle of non-equilibrium thermodynamics, we propose a set of macroscopic transport equations for the spin transport and the charge transport, In particular, the spin torque is introduced as a generalized ＇current density＇ to describe the phenomena associated with the spin non-conservation in a unified framework. The Einstein relations and the Onsager relations between different transport phenomena are established. Specifically, the spin transport properties of the isotropic non-magnetic and the isotropic magnetic two-dimensional electron gases are fully described by using this theory, in which only the macroscopic-spin-related transport phenomena allowed by the symmetry of the system are taken into account.
文摘We study the stochastic motion of a Brownian particle driven by a constant force over a static periodic potential. We show that both the effective diffusion and the effective drag coefficient are mathematically well-defined and we derive analytic expressions for these two quantities. We then investigate the asymptotic behaviors of the effective diffusion and the effective drag coefficient, respectively, for small driving force and for large driving force. In the case of small driving force, the effective diffusion is reduced from its Brownian value by a factor that increases exponentially with the amplitude of the potential. The effective drag coefficient is increased by approximately the same factor. As a result, the Einstein relation between the diffusion coefficient and the drag coefficient is approximately valid when the driving force is small. For moderately large driving force, both the effective diffusion and the effective drag coefficient are increased from their Brownian values, and the Einstein relation breaks down. In the limit of very large driving force, both the effective diffusion and the effective drag coefficient converge to their Brownian values and the Einstein relation is once again valid.
基金Project supported by the National Basic Research Program of China(Grant No.2010CB529200)the National Natural Science Foundation of China(Grant Nos.61073087 and 91029738)
文摘For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, providing convergence and stability information. In this paper, the converse is constructively proved that any dynamics with a Lyapunov function has a corresponding physical realization： a friction force, a Lorentz force, and a potential function. Such construction establishes a set of equations with physical meaning for Lyapunov function and suggests new approaches on the significant unsolved problem namely to construct Lyapunov functions for general nonlinear systems. In addition, a connection is found that the Lyapunov equation is a reduced form of a generalized Einstein relation for linear systems, revealing further insights of the construction.
文摘The conceptual difficulties encountered in thermodynamics are well known and are certainly the reasons that have led the great physicist Arnold Sommerfeld, a long time ago, to say that understanding thermodynamics is not easy. The situation remains nearly the same today and is due to the fact that the tools used in thermodynamics, <em>i</em>.<em>e</em>. the equations, are not in good accordance with the laws of thermodynamics. Since the efficiency of the tools cannot be contested, it is probably the formulation of the laws that needs to be revised. On the basis of arguments already evoked in previous papers, the suggestion presented below is a contribution going in this sense and inserting the Einstein’s relation <em>E</em> = <em>mc</em><sup>2</sup> in the thermodynamic reasoning.
文摘The first part of this paper is a condensed synthesis of the matter presented in several previous ones. It begins with an argumentation showing that the first and second laws of thermodynamics are incompatible with one another if they are not connected to relativity. The solution proposed consists of inserting the Einstein mass-energy relation into a general equation that associates both laws. The second part deals with some consequences of this new insight and its possible link with gravitation. Despite a slight modification of the usual reasoning, the suggested hypothesis leads to a simplification and extension of the thermodynamic theory and to the idea that relativity is omnipresent around us.
