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Related Concept Videos

Entropy Change in Reversible Processes01:10

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.
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
Reversible and Irreversible Processes01:14

Reversible and Irreversible Processes

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...
Uncertainty: Overview00:59

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
BIBO stability of continuous and discrete -time systems01:24

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.

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Related Experiment Video

Updated: Jun 5, 2026

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
10:22

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Published on: September 7, 2019

Observation uncertainty in reversible Markov chains.

Philipp Metzner1, Marcus Weber, Christof Schütte

  • 1Department of Mathematics and Computer Science, Free University Berlin, Arnimallee 6, D-14195 Berlin, Germany. metzner@math.fu-berlin.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces an efficient Monte Carlo Markov chain framework for uncertainty assessment in Markov models, crucial for simplifying complex processes. The method aids in analyzing model parameters and applications like molecular conformation identification.

Related Experiment Videos

Last Updated: Jun 5, 2026

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
10:22

Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements

Published on: September 7, 2019

Area of Science:

  • Computational Chemistry
  • Statistical Modeling
  • Data Science

Background:

  • Real-life processes often require simplified models capturing essential dynamics.
  • Markov models are suitable for memoryless dynamics, with parameters estimated via Bayesian inference from time series data.

Purpose of the Study:

  • To propose an efficient Monte Carlo Markov chain (MCMC) framework for assessing the uncertainty of Markov models and related observables.
  • To develop a Gibbs sampler for sampling transition matrix distributions under reversibility and/or sparsity constraints.

Main Methods:

  • Development of an efficient MCMC framework.
  • Implementation of a Gibbs sampler for Bayesian inference.
  • Application of the framework to analyze Markov model uncertainty.
  • Utilizing Robust Perron Cluster Analysis (PCCA+) for molecular conformation identification.

Main Results:

  • Demonstration of the sampling scheme's performance across various model examples.
  • Successful uncertainty analysis of Markov models.
  • Application to identify trialanine molecule conformations.

Conclusions:

  • The proposed MCMC framework provides an efficient method for Markov model uncertainty quantification.
  • The Gibbs sampler effectively handles constraints on transition matrices.
  • The approach is applicable to complex problems such as molecular dynamics analysis.