Entropic Dynamics on Gibbs Statistical Manifolds

Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles. Here, we develop the entropic dynamics of a system, the state of which is described by a probability distribution. Thus, the dynamics unfolds on a statistical manifold that is automatically endowed by a metric structure provided by information geometry. The curvature of the manifold has a significant influence. We focus our dynamics on the statistical manifold of Gibbs distributions (also known as canonical distributions or the exponential family). The model includes an “entropic” notion of time that is tailored to the system under study; the system is its own clock. As one might expect that entropic time is intrinsically directional; there is a natural arrow of time that is led by entropic considerations. As illustrative examples, we discuss dynamics on a space of Gaussians and the discrete three-state system.     

Increased Entropic Brain Dynamics during DeepDream-Induced Altered Perceptual Phenomenology

In recent years, the use of psychedelic drugs to study brain dynamics has flourished due to the unique opportunity they offer to investigate the neural mechanisms of conscious perception. Unfortunately, there are many difficulties to conduct experiments on pharmacologically-induced hallucinations, especially regarding ethical and legal issues. In addition, it is difficult to isolate the neural effects of psychedelic states from other physiological effects elicited by the drug ingestion. Here, we used the DeepDream algorithm to create visual stimuli that mimic the perception of hallucinatory states. Participants were first exposed to a regular video, followed by its modified version, while recording electroencephalography (EEG). Results showed that the frontal region’s activity was characterized by a higher entropy and lower complexity during the modified video, with respect to the regular one, at different time scales. Moreover, we found an increased undirected connectivity and a greater level of entropy in functional connectivity networks elicited by the modified video. These findings suggest that DeepDream and psychedelic drugs induced similar altered brain patterns and demonstrate the potential of adopting this method to study altered perceptual phenomenology in neuroimaging research.     

A Note on Friedmann Equation of FRW Universe in DeformedHo\v{r}ava-Lifshitz Gravity from Entropic Force

With entropic interpretation of gravity proposed by Verlinde, we obtain the Friedmann equation of the Friedmann-Robertson-Walker universe for the deformed Ho\v{r}ava-Lifshitz gravity. It is shown that, when the parameter of Ho\v{r}ava-Lifshitz gravityω→∝, the modified Friedmann equation will go back to the one in Einstein gravity. This results may imply that the entropic interpretation of gravity is effective for the deformed Ho\v{r}ava-Lifshitz gravity.     

Phase Transition in Modified Newtonian Dynamics (MONDian) Self-Gravitating Systems

We study the statistical mechanics of binary systems under the gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems in the microcanonical and canonical ensembles, we show that in the microcanonical systems, unlike the Newtonian gravity, there is a sharp phase transition, with a high-temperature homogeneous phase and a low-temperature clumped binary one. Defining an order parameter in the canonical systems, we find a smoother phase transition and identify the corresponding critical temperature in terms of the physical parameters of the binary system.     

Entropic Dynamics: Quantum Mechanics from Entropy and Information Geometry

Entropic Dynamics (ED) is a framework in which Quantum Mechanics (QM) is derived as an application of entropic methods of inference. The magnitude of the wave function is manifestly epistemic: its square is a probability distribution. The epistemic nature of the phase of the wave function is also clear: it controls the flow of probability. The dynamics is driven by entropy subject to constraints that capture the relevant physical information. The central concern is to identify those constraints and how they are updated. After reviewing previous work I describe how considerations from information geometry allow us to derive a phase space geometry that combines Riemannian, symplectic, and complex structures. The ED that preserves these structures is QM. The full equivalence between ED and QM is achieved by taking account of how gauge symmetry and charge quantization are intimately related to quantum phases and the single‐valuedness of wave functions.     

Analysis of Chaotic Dynamics by the Extended Entropic Chaos Degree

The Lyapunov exponent is the most-well-known measure for quantifying chaos in a dynamical system. However, its computation for any time series without information regarding a dynamical system is challenging because the Jacobian matrix of the map generating the dynamical system is required. The entropic chaos degree measures the chaos of a dynamical system as an information quantity in the framework of Information Dynamics and can be directly computed for any time series even if the dynamical system is unknown. A recent study introduced the extended entropic chaos degree, which attained the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. Moreover, an improved calculation formula for the extended entropic chaos degree was recently proposed to obtain appropriate numerical computation results for multidimensional chaotic maps. This study shows that all Lyapunov exponents of a chaotic map can be estimated to calculate the extended entropic chaos degree and proposes a computational algorithm for the extended entropic chaos degree; furthermore, this computational algorithm was applied to one and two-dimensional chaotic maps. The results indicate that the extended entropic chaos degree may be a viable alternative to the Lyapunov exponent for both one and two-dimensional chaotic dynamics.     

熵测不准关系与光场的熵压缩

用熵作为光场量子涨落的量度,根据熵测不准关系,建立了熵压缩的概念,具体研究了光场与原子相互作用时的熵压缩,结果显示,熵压缩实现了对光场压缩效应的高灵敏量度。     

Entropic destruction of heavy quarkonium with hyperscaling violation

We study the entropic destruction of heavy quarkonium in strongly coupled theories with an anisotropic scaling symmetry in time and a spatial direction. We consider Lifshitz and hyperscaling violation theories, which are covariant under a generalized Lifshitz scaling symmetry with the dynamical exponent z and hyperscaling violation exponent \begin{document}$ \theta$\end{document}. It is shown that the entropic force depends on the parameters of these theories. In particular, increasing z decreases the entropic force, thus reducing the quarkonium dissociation, while increasing \begin{document}$ \theta$\end{document} has the opposite effect.     

The difference between Newtonian and relativistic forces

This paper discusses a new turn in the 148-year old electrodynamic force law controversy between the 1822 Ampère force law of the Newtonian electrodynamics and Grassmann's 1845 law which has become the electrodynamic force law of relativistic electromagnetism. Faced with the infallibility of Ampère's empirical law, defenders of relativity theory now argue that Ampère's law is equivalent to the relativistic law. This paper demonstrates that, far from being equivalent, the laws require two different mechanics of solid bodies, disagree on internally generated stresses, and predict different force distributions.     

AFM针尖-测试面接触分子动力学研究

针对AFM针尖-测试面的接触问题,利用分子动力学模拟针尖同测试面间的"跳跃粘附"和"颈缩分离"过程;分析接触力同接触间隙的关系及测试面压力分布;发现分离过程滞后粘附过程;得到接触力大小只与接触区域附近少数原子层有关,且接触区域近处原子受压力、远处受拉力的结论;讨论测试面位错半径同接触力和接触间隙的关系.     

The Entropic Uncertainty Relation for Two Qubits in the Cavity‐Based Architecture

Based on a simple cavity‐engineered architecture, the dynamics of quantum memory–assisted entropic uncertainty relation (QMA‐EUR) for two qubits initially prepared in a generic Werner state is investigated. The effects of cavity decay rate, qubit–cavity couplings, and cavity–cavity couplings on the uncertainty are explored. It is found that the damped oscillation of uncertainty can be induced by the increase of two types of coupling strengths mentioned above. It is demonstrated that the maximum value of uncertainty is closely related to the purity of the initial state. The uncertainty can be either increased or decreased, depending on the threshold value of coupling strength between the two cavities. Finally, in agreement with a recent observation, an asynchronous relation between uncertainty and mixedness is found during the initial time evolution.     

Modified Friedmann Equations on the Brane from Entropic Force

The well-known area relation of the black hole entropy can be modified from the inclusion of quantum effects, motivated from the loop quantum gravity. Applying this modified entropy-area relation to brane cosmology, we derive the modified cosmological equations governing the evolution of the universe on the brane. We adopt the viewpoint that interprets gravity as an entropic force caused by the changes in the information when a material body moves away from the holographic screen.     

近距离牛顿反平方定律实验检验进展

为了统一描述自然界的四种基本相互作用,科学家提出了很多理论模型,其中很多理论认为牛顿反平方定律在近距离下会发生偏离,或存在其他的非牛顿引力作用,而理论的正确与否需要高精度的实验检验.国际上很多研究组在不同间距下采用不同的技术对反平方定律进行了高精度的实验检验,本文重点介绍华中科技大学引力中心采用密度调制法分别在亚毫米与微米范围进行的实验研究进展.在亚毫米范围采用精密扭秤技术,在对牛顿引力进行双补偿、抑制电磁干扰后,结合零实验与非零实验结果,在作用程为70—300μm区间对Yukawa形式的破缺给出国际上精度最高的限制.在微米范围采用悬臂梁作为弱力传感器,通过测量金球和密度调制吸引质量间水平力的变化来检验非牛顿引力是否存在,实验结果不需进行Casimir力和静电力背景扣除,是此间距下不依赖于Casimir力和静电力理论计算模型的两个结果之一.     

Entropic Uncertainty in Neutrino and Meson Systems

The dynamics of quantum‐memory‐assisted entropic uncertainty for the closed neutrino system in the context of two flavor oscillations and the meson system within the framework of open quantum system are investigated. It is found that the entropic uncertainty exists in close relation with the quantum correlation, and growing quantum correlation can decrease the uncertainty. The oscillatory behaviors of entropic uncertainty in neutrino system brought about by neutrino oscillating property are different from the decaying behaviors of entropic uncertainty in meson system induced by the meson decaying nature. In addition, the entropic uncertainty is always equal to its lower bound in the two subatomic systems. This study would throw light on the particle behavior characteristics of high energy physics, and may be useful to the tasks of quantum information‐processing implemented with subatomic system since the uncertainty principle plays vital role in quantum information science and technology.     

Entropic noise induced stability and double entropic stochastic resonance induced by correlated noises

For the activated dynamics of a Brownian particle moving in a confined system with the presence of entropic barriers, this paper investigates a periodic driving and correlations between two noises. Within the two-state approximation, the explicit expressions of the mean first passage time (MFPT) and the spectral power amplification (SPA) are obtained, respectively. Based on the numerical computations, it is found that: (i) The MFPT as a function of the noise intensity exhibits a maximum with the positive correlations between two noises (λ>0), this maximum for MFPT shows the characteristic of the entropic noise induced stability (ENIS) effect. The intensity λ of correlations between two noises can enhance the ENIS effect. (ii) The SPA as a function of the noise intensity exhibits a double-peak by tuning the noise correlation intensity λ, i.e., the existence of a double-peak behaviour is the identifying characteristic of the double entropic stochastic resonance phenomenon.     

The structure of the Newtonian limit

We consider a smooth one-parameter family of four-dimensional manifolds X,≥0, each one endowed with a covariant metric g. It is assumed that g is a Lorentz metric for each >0, i.e., the signature of g is (+,−,−,−) for >0, while the limit metric g₀ on X₀ is assumed to be degenerated of rank 1, i.e., the signature of g₀ is (+,0,0,0). We characterize when the limit manifold X₀ inherits the geometric structure of a Newtonian gravitation. The limit manifold X₀ is a Newtonian gravitation if and only if there exist the limits of the Levi-Civita connection , the curvature operator and the contravariant Einstein tensor G² as →0. Moreover, the existence of these limits is characterized in terms of the Taylor expansion of the family {g} with respect to the parameter .     

Letter: Gravitational Potential in the Palatini Formulation of Modified Gravity

General Relativity has so far passed almost all the ground-based and solar-system experiments. Any reasonable extended gravity models should consistently reduce to it at least in the weak field approximation. In this work we derive the gravitational potential for the Palatini formulation of the modified gravity of the L(R) type which admits a de Sitter vacuum solution. We argue that the Newtonian limit is always obtained in those class of models and the deviations from General Relativity are very small for a slowly moving source.     

Entropic Resonant Activation and StochasticResonance Driven by Non-Gaussian Noise

The transition rate and stochastic resonance (SR) of a Brownian particle moving in a confined system under the presence of entropic barriers are investigated when the system is driven by non-Gaussian noise. The explicit expressions of the transition rate and the spectral power amplification (SPA) are obtained, respectively. The effects of the parameter q indicating the departure from the Gaussian noise and the correlation timeτ of the non-Gaussian noise on the transition rate and the SPA are discussed. Research results show that: (i) The transition rate as a function of the noise strength exhibits a maximum. This maximum for transition rate identifies the phenomenon of entropic resonant activation (ERA), the parameter q and the noise correlation timeτ weaken the ERA of the system; (ii) The curves of SPA appear a transition from one peak to double-peak, and then to one peak again as the noise correlation timeτ of non-Gaussian noise increases.