Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

3.1K
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.
3.1K
Continuous Charge Distributions01:17

Continuous Charge Distributions

7.8K
Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
The electric charge can also be subjected to an analogical...
7.8K
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

823
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....
823
Continuity Equation01:20

Continuity Equation

1.3K
The total amount of current flowing per unit cross-sectional area is called the current density. Hence, the current passing through a cross-sectional area can be written as the surface integral of the current density.
1.3K
Continuity Equation01:28

Continuity Equation

3.1K
The continuity equation asserts that the mass flow rate must remain constant for a steady flow of an incompressible fluid within a confined system. This principle applies to systems where fluid passes through varying cross-sectional areas, such as nozzles, syringes, and pipes.
The mass flow rate is expressed as:
3.1K
Reversible and Irreversible Processes01:14

Reversible and Irreversible Processes

5.4K
The thermodynamic processes can be classified into reversible and irreversible processes. The processes that can be restored to their initial state are called reversible processes. It is only possible if the process is in quasi-static equilibrium, i.e., it takes place in infinitesimally small steps, and the system remains at equilibrium However, these are ideal processes and do not occur naturally. An ideal system undergoing a reversible process is always in thermodynamic equilibrium within...
5.4K

You might also read

Related Articles

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

Sort by
Same author

Fractionally quantized recurrence detection times in monitored quantum many-body systems.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Telomeres in Lamin-A-depleted cells exhibit directed motion and dynamic coherence.

Biophysical journal·2026
Same author

Symmetry breaking of current response in disordered exclusion processes.

Physical review. E·2026
Same author

Tunable Anomalous Diffusion in Subrecoil-Laser-Cooled Atoms.

Physical review letters·2026
Same author

Density-independent transient caging in the high-density phase of motility-induced phase separation.

Physical review. E·2026
Same author

Observation-time-induced crossover from fluctuating diffusivity.

Physical chemistry chemical physics : PCCP·2026

Related Experiment Video

Updated: Dec 17, 2025

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
10:20

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

8.6K

Infinite invariant density in a semi-Markov process with continuous state variables.

Takuma Akimoto1, Eli Barkai2, Günter Radons3

  • 1Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan.

Physical Review. E
|June 25, 2020
PubMed
Summary

This study reveals the crucial role of an infinite invariant density in semi-Markov processes with fat-tailed distributions. This density governs the accumulation of state values near zero and influences time-averaged observables in anomalous diffusion models.

More Related Videos

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

14.9K
A Data-Driven Approach to Quantifying Immune States in Sepsis
07:42

A Data-Driven Approach to Quantifying Immune States in Sepsis

Published on: February 7, 2025

415

Related Experiment Videos

Last Updated: Dec 17, 2025

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
10:20

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

8.6K
Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

14.9K
A Data-Driven Approach to Quantifying Immune States in Sepsis
07:42

A Data-Driven Approach to Quantifying Immune States in Sepsis

Published on: February 7, 2025

415

Area of Science:

  • Statistical Physics
  • Stochastic Processes
  • Anomalous Diffusion Modeling

Background:

  • Semi-Markov processes are crucial for modeling systems with memory.
  • Anomalous diffusion models often involve complex state dynamics.
  • Fat-tailed interevent time distributions lead to unique process behaviors.

Purpose of the Study:

  • To investigate the role of a non-normalized steady state (infinite invariant density) in semi-Markov processes.
  • To analyze the accumulation of state values near zero in processes with fat-tailed interevent times.
  • To derive distributional limit theorems for time-averaged observables in nonstationary processes.

Main Methods:

  • Analysis of semi-Markov processes with fat-tailed interevent time distributions.
  • Derivation of scaling laws for state value density.
  • Development of distributional limit theorems for time-averaged observables.

Main Results:

  • Identified a fundamental role for infinite invariant density in semi-Markov processes.
  • Discovered two scaling laws describing state value accumulation near zero.
  • Provided exact expressions for the infinite invariant density.
  • Established distributional limit theorems for time-averaged observables.

Conclusions:

  • The infinite invariant density is essential for understanding nonstationary processes with fat-tailed distributions.
  • Universal behaviors in state value accumulation are described by the derived scaling laws.
  • The infinite invariant density dictates the distribution of time-averaged observables.