Related Experiment Video
Updated: Jul 13, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Metabasin approach for computing the master equation dynamics of systems with broken ergodicity
John C Mauro1, Roger J Loucks, Prabhat K Gupta
1Science & Technology Division, Corning Incorporated, Corning, New York 14831, USA. mauroj@corning.com
The Journal of Physical Chemistry. A
|July 26, 2007
Summary
We developed a new method to simulate complex systems with broken ergodicity. This approach uses metabasins to efficiently compute dynamics, making simulations of challenging systems like glass-formers computationally feasible.
Area of Science:
- Computational physics
- Statistical mechanics
- Chemical dynamics
Background:
- Simulating systems with broken ergodicity is computationally challenging.
- Traditional methods struggle with long timescales and complex energy landscapes.
Purpose of the Study:
- To develop an efficient computational technique for systems with broken ergodicity.
- To enable the simulation of complex, realistic systems where direct integration is infeasible.
Main Methods:
- Partitioning systems into 'metabasins' with fast internal dynamics.
- Assuming equilibrium statistical mechanics within each metabasin.
- Computing inter-metabasin dynamics using a reduced set of master equations.
Main Results:
- The number of metabasins is dependent on system temperature and its time derivative.
- Simulation time steps are governed by the observation timescale, not fastest transitions.
- Validated against direct Euler integration on a model system.
- Demonstrated feasibility for a realistic glass-forming system (selenium).
Conclusions:
- The proposed technique significantly enhances computational efficiency for systems with broken ergodicity.
- This method opens possibilities for simulating complex materials and processes previously intractable.
- It provides a viable alternative to direct integration for challenging dynamic simulations.
Related Concept Videos
01:10Entropy 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.
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.
01:23Mechanistic Models: Compartment Models in Individual and Population Analysis
Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
01:24BIBO 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.
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.
01:21Mechanistic Models: Overview of Compartment Models
Mechanistic models, a category encompassing both physiological and compartmental modeling, differ from empirical models' approaches to incorporating known factors about the systems being modeled. Empirical models describe data with minimal assumptions, while mechanistic models aim to provide a robust description of available data by specifying assumptions and integrating known factors about the system. Compartmental analysis is a key example of a mechanistic model in pharmacokinetics and...
01:06Model Approaches for Pharmacokinetic Data: Distributed Parameter Models
Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...