Related Experiment Video
Updated: Aug 5, 2026
10:02
Submillisecond Conformational Changes in Proteins Resolved by Photothermal Beam Deflection
Published on: February 18, 2014
Asymptotic Thermodynamics for Chemical Reaction Networks with Fast-Slow Kinetics
1School of Computer and Big Data, Minjiang University, Fuzhou 350108, China.
Entropy (Basel, Switzerland)
|July 28, 2026
Summary
This study introduces asymptotic expansions for nonequilibrium thermodynamics in chemical reaction networks (CRNs). The method rigorously analyzes energy and entropy balances in complex, multiscale systems.
Area of Science:
- Chemical kinetics
- Thermodynamics
- Mathematical modeling
Background:
- Chemical reaction networks (CRNs) often exhibit complex kinetics with multiple timescales.
- Understanding nonequilibrium thermodynamics is crucial for analyzing these systems.
- Existing methods may struggle with the multiscale nature of CRNs.
Purpose of the Study:
- To systematically derive asymptotic expansions for nonequilibrium thermodynamics in CRNs.
- To apply singular perturbation theory to analyze fast-slow kinetics.
- To develop a rigorous framework for energy and entropy balance in multiscale CRNs.
Main Methods:
- Systematic derivation of asymptotic expansions using singular perturbation theory.
- Obtaining first and second laws of thermodynamics for the asymptotic expansion model.
- Deriving composite expansions for enthalpy, entropy, entropy production rate, and relative entropy.
- Analyzing convergence orders based on local Lipschitz properties.
Main Results:
- Composite expansions capture long-time trends (outer parts) and fast dynamics (inner parts).
- Enthalpy shows convergence similar to kinetic variables.
- Entropy, relative entropy, and entropy production rate exhibit reduced convergence orders due to logarithmic terms near zero concentrations.
- Validated on the reversible Michaelis-Menten reaction, yielding analytical expansions.
- Numerical simulations confirm accuracy and reveal higher-order convergence for entropy production rate.
Conclusions:
- Composite expansion is a rigorous tool for analyzing energy and entropy balances in multiscale CRNs.
- The method provides physically consistent approximations.
- Understanding convergence properties is key for accurate thermodynamic analysis.
Related Concept Videos
02:24Predicting Reaction Outcomes
Kinetics describes the rate and path by which a reaction occurs. In contrast, thermodynamics deals with state functions and describes the properties, behavior, and components of a system. It is not concerned with the path taken by the process and cannot address the rate at which a reaction occurs. Although it does provide information about what can happen during a reaction process, it does not describe the detailed steps of what appears on an atomic or a molecular level. On the other hand,...
01:25Transition State Theory
Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their...
01:29Reaction Mechanisms: Rate-limiting Step Approximation
The rate-determining step, or RDS, in a chemical reaction is the slowest step that determines the overall reaction rate. It is identified by using the observed rate law and typically involves approximation methods like the RDS approximation or the steady-state approximation.In the RDS approximation, also known as the rate-limiting-step or equilibrium approximation, the reaction mechanism consists of one or more reversible reactions near equilibrium, followed by a slower RDS, and then one or...
01:26Reaction Mechanisms: The Steady-State Approximation
The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...
03:08Rate-Determining Steps
Relating Reaction Mechanisms
In a multistep reaction mechanism, one of the elementary steps progresses significantly slower than the others. This slowest step is called the rate-limiting step (or rate-determining step). A reaction cannot proceed faster than its slowest step, and hence, the rate-determining step limits the overall reaction rate.
The concept of rate-determining step can be understood from the analogy of a 4-lane freeway with a short-stretch of traffic-bottleneck caused due to...
In a multistep reaction mechanism, one of the elementary steps progresses significantly slower than the others. This slowest step is called the rate-limiting step (or rate-determining step). A reaction cannot proceed faster than its slowest step, and hence, the rate-determining step limits the overall reaction rate.
The concept of rate-determining step can be understood from the analogy of a 4-lane freeway with a short-stretch of traffic-bottleneck caused due to...
01:26Reversible or Opposing Reactions
Reversible or opposing reactions play a crucial role in understanding the dynamic nature of chemical processes. While kinetics focuses on how reactions proceed, thermodynamics emphasizes that most reactions do not reach completion. Instead, a reverse reaction starts occurring over time, and when its rate equals that of the forward reaction, a dynamic equilibrium is established.For example, consider a simple chemical process where A forms B reversibly. The rate constants for the forward and...