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

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...

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.

Alternative Sets of Equilibrium Equations

Alternative Sets of Equilibrium Equations

When analyzing the behavior of structures, engineers often rely on the concept of equilibrium. This refers to the state where all forces and moments acting on a system balance each other, resulting in no net movement or rotation. In many cases, equilibrium can be described by a set of standard equations. However, in some situations, alternative sets of equilibrium equations must be used to describe the system's behavior accurately.
One example of such a situation can be observed in a...

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.

Transmission-Line Differential Equations

Transmission-Line Differential Equations

Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...

Separable Differential Equations

Separable Differential Equations

A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...

You might also read

Related Articles

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

Sort by

Same author

Reply to: Prostate-Specific Membrane Antigen Positron Emission Tomography and Radiometabolic Therapies in Metastatic Castration-Resistant Prostate Cancer.

Journal of clinical oncology : official journal of the American Society of Clinical Oncology·2026

Same author

Local treatment of the primary tumor in mHSPC in the ARPI era: incremental value or overtreatment?

Expert review of anticancer therapy·2026

Same author

EMETPRO: a multicentric, international, retrospective analysis evaluating patients with metastatic hormone-sensitive prostate cancer with early progression.

Prostate cancer and prostatic diseases·2026

Same author

Validation of a large language model as a decision tool for drug interaction in prostate cancer: A comparative study against UpToDate. Meet-URO 5/25 - GENIE study.

Journal of geriatric oncology·2026

Same author

Detection of Homologous Recombination Repair Gene Mutations by Tumor Tissue and Circulating Tumor DNA Testing in Prostate Cancer in the Phase III PROpel Trial.

JCO precision oncology·2026

Same author

Nivolumab plus ipilimumab for chemotherapy-refractory metastatic castration-resistant prostate cancer: results from the randomized portion of the phase 2 CheckMate 650 trial.

Nature communications·2026

Search research articles

Related Experiment Video

Updated: Jul 22, 2026

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

Ergodicity breaking in well-behaved generalized Langevin equations.

Giuseppe Procopio¹, Chiara Pezzotti¹, Massimiliano Giona¹

¹Sapienza Università di Roma, Dipartimento di Ingegneria Chimica, Materiali, Ambiente La , Via Eudossiana 18, 00184 Roma, Italy.

Physical Review. E

|April 18, 2025

Summary

Ergodicity breaking in Generalized Langevin Equations (GLEs) is explained by dissipative stability and stochastic realizability boundaries. This phenomenon is absent in viscoelastic fluids if Kubo's fluctuation-dissipation theory holds.

More Related Videos

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

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Related Experiment Videos

Last Updated: Jul 22, 2026

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

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

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Area of Science:

Statistical Mechanics
Rheology
Non-equilibrium Physics

Background:

Generalized Langevin Equations (GLEs) are crucial for modeling complex systems with memory effects.
Ergodicity breaking is a significant phenomenon observed in certain physical systems, challenging standard statistical mechanics assumptions.
The Plyukhin model and viscoelastic fluid rheology present distinct cases for studying ergodicity breaking.

Purpose of the Study:

To explain the phenomenon of ergodicity breaking in GLEs using the concepts of dissipative stability and stochastic realizability.
To investigate the conditions under which ergodicity breaking occurs or is prevented in systems with nonvanishing friction factors.
To provide a physical interpretation of ergodicity breaking in the context of hydromechanic theories and fluid-inertial effects.

Main Methods:

Application of dissipative stability and stochastic realizability concepts to analyze GLEs.
Examination of the Plyukhin model with a generalized Debye kernel.
Analysis of systems with dissipative kernels characterized by real-valued relaxation rates (viscoelastic fluids).
Consideration of Kubo's fluctuation-dissipation theorem.

Main Results:

Ergodicity breaking in GLEs occurs at the boundary of dissipative stability, coinciding with stochastic realizability for models like the Plyukhin model.
In viscoelastic fluids, where stochastic realizability is within dissipative stability, ergodicity breaking is precluded if Kubo's theory holds.
A hydromechanic interpretation attributes ergodicity breaking to a dissipationless fluid-inertial effect, leading to superdiffusion.

Conclusions:

Dissipative stability and stochastic realizability provide a framework for understanding ergodicity breaking in GLEs.
The rheological properties of the medium significantly influence the occurrence of ergodicity breaking.
A fluid-inertial effect offers a physical explanation for superdiffusion observed in certain ergodicity-breaking scenarios.