Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Entropy Change in Reversible Processes

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.

Geometric Sequences

Geometric Sequences

In systems where values diminish by a constant proportion at each stage, the resulting sequence follows a geometric structure. Each new value in the sequence is obtained by applying a fixed multiplier to the preceding term. This regular, proportional decline type is often used to represent processes involving gradual loss, such as energy dissipation or reduction in amplitude over time.When analyzing the total effect of such a process across unlimited iterations, the series of values is referred...

The de Broglie Wavelength

The de Broglie Wavelength

In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...

BIBO stability of continuous and discrete -time systems

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.

Cyclic Processes And Isolated Systems

Cyclic Processes And Isolated Systems

A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state.
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each path...

Perpendicular-Axis Theorem

Perpendicular-Axis Theorem

The perpendicular-axis theorem states that the moment of inertia of a planar object about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two mutually perpendicular concurrent axes lying in the plane of the body.
Consider a circular disc of mass M and radius R lying along an x-y plane. The origin lies at the center of the disc, and the z-axis is perpendicular to the disc's plane. All three axes coincide at the disc's center. The moment of inertia of this...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Developing Topics.

Alzheimer's & dementia : the journal of the Alzheimer's Association·2025

Same author

SMAS: Structural MRI-based AD Score using Bayesian supervised VAE.

Computers in biology and medicine·2025

Same author

Educational attainment and cognitive behavioral therapy treatment outcome in late-life depression: A secondary analysis of a randomized controlled trial.

Journal of affective disorders·2025

Same author

Progress in the Treatment of Alzheimer's Disease Is Needed - Position Statement of European Alzheimer's Disease Consortium (EADC) Investigators.

The journal of prevention of Alzheimer's disease·2024

Same author

"Time Saved" Calculations to Improve Decision-Making in Progressive Disease Studies.

The journal of prevention of Alzheimer's disease·2024

Same author

Gaussian Process-based prediction of memory performance and biomarker status in ageing and Alzheimer's disease-A systematic model evaluation.

Medical image analysis·2023

Search research articles

Related Experiment Video

Updated: May 13, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Ergodicity breaking in geometric Brownian motion.

O Peters¹, W Klein

¹London Mathematical Laboratory, 14 Buckingham Street, WC2N 6DF London, United Kingdom. o.peters@lml.org.uk

Physical Review Letters

|March 26, 2013

Summary

Diversification can reconcile differing averages in Geometric Brownian motion (GBM) models. This study explores how diversification impacts ergodicity breaking in GBM, offering insights for financial and population dynamics.

Area of Science:

Complex systems modeling
Statistical physics
Mathematical finance

Background:

Geometric Brownian motion (GBM) models diverse systems, including financial markets and population dynamics.
Nonergodicity in GBM complicates statistical analysis, causing discrepancies between ensemble and time averages.
Individual GBM trajectories often collapse over time, contrasting with ensemble exponential growth.

Purpose of the Study:

To investigate the impact of diversification on ergodicity breaking in Geometric Brownian motion.
To analyze how diversification reconciles time and ensemble averages in non-ergodic systems.
To provide a framework for understanding diversification's role in complex systems.

Main Methods:

Analysis of Geometric Brownian motion with diversification.

More Related Videos

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

Related Experiment Videos

Last Updated: May 13, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

Application of ergodicity breaking concepts.

Comparison of time and ensemble averages.

Main Results:

Diversification was shown to reduce the gap between time and ensemble averages in GBM.
Ergodicity breaking effects were quantitatively analyzed in the context of diversification.
The study demonstrates a mechanism for stabilizing system behavior through diversification.

Conclusions:

Diversification is a key strategy for managing nonergodicity in GBM.
Understanding ergodicity breaking is crucial for accurate modeling of complex systems.
Findings have implications for financial risk management and population sustainability.