Demonstration of Onsager reciprocal relations

In summary, the Onsager reciprocal relations are a set of mathematical relationships proposed by Lars Onsager in the 1920s that describe the symmetry and reversibility of physical processes in thermodynamic systems. They are important in understanding and predicting the behavior of complex systems, and are represented by linear equations that relate fluxes and forces. These relations are derived using statistical mechanics and the principle of detailed balance, and have real-world applications in fields such as materials science, chemical engineering, and biology. They are used to study transport phenomena and design efficient processes and devices, as well as to understand biological processes such as enzyme kinetics and ion channels in cells.
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Hello everyone,

I am working on the Onsager reciprocal relations, more precisely on the demonstration of those relations. I try to understand the Onsager original paper (1931) but it's really not easy (although he says that the examples are "extremely simple"). I was wondering if any of you knew a good textbook that demonstrates those relations or maybe an article that follows the original paper with more details.

Thank you for your help!
 
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S. R. de Groot, P. Mazur, Non-equilibrium thermodynamics, Dover
 

1. What are Onsager reciprocal relations?

The Onsager reciprocal relations, also known as the Onsager's reciprocity postulates, are a set of mathematical relationships that describe the symmetry and reversibility of physical processes in systems that are in a state of thermodynamic equilibrium. These relations were first proposed by Lars Onsager, a Norwegian-American physicist, in the 1920s.

2. Why are Onsager reciprocal relations important?

Onsager reciprocal relations are important because they provide a fundamental understanding of the underlying physical processes in thermodynamic systems. They also allow us to make predictions about the behavior of complex systems, such as materials and chemical reactions, by simplifying the mathematical calculations involved.

3. What is the mathematical representation of Onsager reciprocal relations?

The mathematical representation of Onsager reciprocal relations is a set of linear equations that relate the fluxes and forces in a system. In simple terms, these equations state that the rate of change of a particular physical property, such as temperature or concentration, is proportional to the driving force or gradient of that property.

4. How are Onsager reciprocal relations derived?

Onsager reciprocal relations are derived using statistical mechanics and the principle of detailed balance. This involves considering the microscopic behavior of individual particles within a system and how they interact with each other to produce macroscopic properties. By assuming a state of thermodynamic equilibrium, the equations for the fluxes and forces can be derived.

5. What are some real-world applications of Onsager reciprocal relations?

Onsager reciprocal relations have a wide range of applications in various fields, including materials science, chemical engineering, and biology. They are used to study transport phenomena, such as heat and mass transfer, and to design efficient processes and devices. They are also used in the development of new materials and the understanding of biological processes, such as enzyme kinetics and ion channels in cells.

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