scholarly journals Thermal dynamic phase transition of Reissner-Nordström Anti-de Sitter black holes on free energy landscape

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Ran Li ◽  
Kun Zhang ◽  
Jin Wang
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Free Energy ◽  
First Passage Time ◽  
Energy Landscape ◽  
Planck Equation ◽  
Passage Time ◽  
Free Energy Landscape ◽  
De Sitter ◽  
First Passage

Abstract We explore the thermodynamics and the underlying kinetics of the van der Waals type phase transition of Reissner-Nordström anti-de Sitter (RNAdS) black holes based on the free energy landscape. We show that the thermodynamic stabilities of the three branches of the RNAdS black holes are determined by the underlying free energy landscape topography. We suggest that the large (small) RNAdS black hole can have the probability to switch to the small (large) black hole due to the thermal fluctuation. Such a state switching process under the thermal fluctuation is taken as a stochastic process and the associated kinetics can be described by the probabilistic Fokker-Planck equation. We obtained the time dependent solutions for the probabilistic evolution by numerically solving Fokker-Planck equation with the reflecting boundary conditions. We also investigated the first passage process which describes how fast a system undergoes a stochastic process for the first time. The distributions of the first passage time switching from small (large) to large (small) black hole and the corresponding mean first passage time as well as its fluctuations at different temperatures are studied in detail. We conclude that the mean first passage time and its fluctuations are related to the free energy landscape topography through barrier heights and temperatures.

scholarly journals First-passage time distribution for a random walker on a random forcing energy landscape

2010 ◽  
Vol 2010 (09) ◽  
pp. P09005 ◽  
Author(s):  
Michael Sheinman ◽  
Olivier Bénichou ◽  
Raphaël Voituriez ◽  
Yariv Kafri
Keyword(s):  
Time Distribution ◽  
First Passage Time ◽  
Energy Landscape ◽  
Passage Time ◽  
First Passage ◽  
Random Walker ◽  
Random Forcing

First-Passage Time for Oscillators With Nonlinear Damping

1978 ◽  
Vol 45 (1) ◽  
pp. 175-180 ◽  
Author(s):  
J. B. Roberts
Keyword(s):  
First Passage Time ◽  
Digital Simulation ◽  
Planck Equation ◽  
Passage Time ◽  
Nonlinear Damping ◽  
First Passage ◽  
One Dimensional ◽  
Fokker Planck Equation ◽  
First Passage Failure ◽  
Fokker Planck

A simple numerical scheme is proposed for computing the probability of first passage failure, P(T), in an interval O-T, for oscillators with nonlinear damping. The method depends on the fact that, when the damping is light, the amplitude envelope, A(t), can be accurately approximated as a one-dimensional Markov process. Hence, estimates of P(T) are found, for both single and double-sided barriers, by solving the Fokker-Planck equation for A(t) with an appropriate absorbing barrier. The numerical solution of the Fokker-Planck equation is greatly simplified by using a discrete time random walk analog of A(t), with appropriate statistical properties. Results obtained by this method are compared with corresponding digital simulation estimates, in typical cases.

First passage time distribution of a Wiener process with drift concerning two elastic barriers

1996 ◽  
Vol 33 (01) ◽  
pp. 164-175 ◽  
Author(s):  
Marco Dominé
Keyword(s):  
Explicit Expression ◽  
Wiener Process ◽  
Time Distribution ◽  
First Passage Time ◽  
Planck Equation ◽  
Passage Time ◽  
Special Choice ◽  
First Passage ◽  
Special Cases ◽  
Reflecting Barriers

We solve the Fokker-Planck equation for the Wiener process with drift in the presence of elastic boundaries and a fixed start point. An explicit expression is obtained for the first passage density. The cases with pure absorbing and/or reflecting barriers arise for a special choice of a parameter constellation. These special cases are compared with results in Darling and Siegert [5] and Sweet and Hardin [15].

scholarly journals First-passage times in protein folding: exploring the native-like states vs. overcoming the free energy barrier

2021 ◽  
Author(s):  
Sergei F. Chekmarev
Keyword(s):  
Free Energy ◽  
Protein Folding ◽  
Energy Barrier ◽  
First Passage Time ◽  
Passage Time ◽  
Free Energy Barrier ◽  
Native State ◽  
First Passage ◽  
Single Exponential ◽  
Passage Times

All first-passage time distributions are essentially single-exponential. The first-passage time to reach the native state may be determined by the time to find the native state among native-like ones.

scholarly journals THERMODYNAMIC GEOMETRY OF THE BORN–INFELD–ANTI-DE SITTER BLACK HOLES

2011 ◽  
Vol 26 (18) ◽  
pp. 3091-3105 ◽  
Author(s):  
PENG CHEN
Keyword(s):  
Black Holes ◽  
Heat Capacity ◽  
Black Hole ◽  
Free Energy ◽  
Thermodynamic Potential ◽  
De Sitter ◽  
Invariant Metric ◽  
Four Dimensions ◽  
Nonlinear Generalization ◽  
Thermodynamic Geometry

Thermodynamic geometry is applied to the Born–Infeld–anti-de Sitter black hole (BIAdS) in the four dimensions, which is a nonlinear generalization of the Reissner–Nordström–AdS black hole (RNAdS). We compute the Weinhold as well as the Ruppeiner scalar curvature and find that the singular points are not the same with the ones obtained using the heat capacity. Legendre-invariant metric proposed by Quevedo and the metric obtained by using the free energy as the thermodynamic potential are obtained and the corresponding scalar curvatures diverge at the Davies points.

The Free Energy for Rotating and Charged Black Holes and Banados, Teitelboim and Zanelli Black Holes

2018 ◽  
Vol 73 (11) ◽  
pp. 1061-1073 ◽  
Author(s):  
N.A. Hussein ◽  
D.A. Eisa ◽  
T.A.S. Ibrahim
Keyword(s):  
Black Holes ◽  
Heat Capacity ◽  
Black Hole ◽  
Free Energy ◽  
Quantum Correction ◽  
Kerr Black Hole ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Charged Black Holes ◽  
Thermodynamic Variables

AbstractThis paper aims to obtain the thermodynamic variables (temperature, thermodynamic volume, angular velocity, electrostatic potential, and heat capacity) corresponding to the Schwarzschild black hole, Reissner-Nordstrom black hole, Kerr black hole and Kerr-Newman-Anti-de Sitter black hole. We also obtained the free energy for black holes by using three different methods. We obtained the equation of state for rotating Banados, Teitelboim and Zanelli black holes. Finally, we used the quantum correction of the partition function to obtain the heat capacity and entropy in the quantum sense.

scholarly journals The flight of the hornbill: drift and diffusion in arboreal avian movement

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ankit Vikrant ◽  
Janaki Balakrishnan ◽  
Rohit Naniwadekar ◽  
Aparajita Datta
Keyword(s):  
Diffusion Coefficients ◽  
Animal Movement ◽  
Anthropogenic Activities ◽  
First Passage Time ◽  
Mechanistic Model ◽  
Planck Equation ◽  
Passage Time ◽  
First Passage ◽  
Human Settlements ◽  
Fokker Planck

AbstractCapturing movement of animals in mathematical models has long been a keenly pursued direction of research1. Any good model of animal movement is built upon information about the animal’s environment and the available resources including whether prey is in abundance or scarce, densely distributed or sparse2. Such an approach could enable the identification of certain quantities or measures from the model that are species-specific characteristics. We propose here a mechanistic model to describe the movement of two species of Asian hornbills in a resource-abundant heterogenous landscape which includes degraded forests and human settlements. Hornbill telemetry data was used to this end. The birds show a bias both towards features of attraction such as nesting and roosting sites as well as possible bias away from points of repulsion such as human presence. These biases are accounted for with suitable potentials. The spatial patterns of movement are analyzed using the Fokker–Planck equation, which helps explain the variation in movement of different individuals. Search times to target locations were calculated using first passage time equations dual to the Fokker–Planck equations. We also find that the diffusion coefficients are larger for breeding birds than for non-breeding ones—a manifestation of repeated switching of directions to move back to the nest from foraging sites. The degree of directedness towards nests and roosts is captured by the drift coefficients. Non-breeding hornbills show similar values of the ratio of the two coefficients irrespective of the fact that their movement data is available from different seasons. Therefore, the ratio of drift to diffusion coefficients is indicative of an individual’s breeding status, as seen from available data. It could possibly also characterize different species. For all individuals, first passage times increase with proximity to human settlements, in agreement with the premise that anthropogenic activities close to nesting/roosting sites are not desirable.

scholarly journals First Passage Time Memory Lifetimes for Simple, Multistate Synapses

2017 ◽  
Vol 29 (12) ◽  
pp. 3219-3259 ◽  
Author(s):  
Terry Elliott
Keyword(s):  
Optimality Conditions ◽  
Signal To Noise Ratio ◽  
First Passage Time ◽  
Planck Equation ◽  
Memory Systems ◽  
Passage Time ◽  
Memory Storage ◽  
First Passage ◽  
Firing Properties ◽  
Superior Approach

Memory models based on synapses with discrete and bounded strengths store new memories by forgetting old ones. Memory lifetimes in such memory systems may be defined in a variety of ways. A mean first passage time (MFPT) definition overcomes much of the arbitrariness and many of the problems associated with the more usual signal-to-noise ratio (SNR) definition. We have previously computed MFPT lifetimes for simple, binary-strength synapses that lack internal, plasticity-related states. In simulation we have also seen that for multistate synapses, optimality conditions based on SNR lifetimes are absent with MFPT lifetimes, suggesting that such conditions may be artifactual. Here we extend our earlier work by computing the entire first passage time (FPT) distribution for simple, multistate synapses, from which all statistics, including the MFPT lifetime, may be extracted. For this, we develop a Fokker-Planck equation using the jump moments for perceptron activation. Two models are considered that satisfy a particular eigenvector condition that this approach requires. In these models, MFPT lifetimes do not exhibit optimality conditions, while in one but not the other, SNR lifetimes do exhibit optimality. Thus, not only are such optimality conditions artifacts of the SNR approach, but they are also strongly model dependent. By examining the variance in the FPT distribution, we may identify regions in which memory storage is subject to high variability, although MFPT lifetimes are nevertheless robustly positive. In such regions, SNR lifetimes are typically (defined to be) zero. FPT-defined memory lifetimes therefore provide an analytically superior approach and also have the virtue of being directly related to a neuron's firing properties.

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