Lars Onsager's paper, "Reciprocal Relations in Irreversible Processes," derived a general reciprocal relation applicable to transport processes such as heat and electricity conduction and diffusion. The derivation is based on the assumption of microscopic reversibility, which involves considering certain average products of fluctuations. The key result is that different irreversible processes must be compared in terms of entropy changes, as expressed by the relation \( S = k \log W \). For linear relations between rates and "forces," a quadratic dissipation function is introduced, and the symmetry conditions demanded by microscopic reversibility lead to the condition \( \dot{S}(\alpha, \dot{\alpha}) - \Phi(\dot{\alpha}, \dot{\alpha}) = \text{maximum} \). This condition determines the rates of the processes for given initial conditions. The paper also discusses the statistical significance of the entropy and the dissipation function, and it formulates reciprocal relations for non-reversible systems, such as those with external magnetic fields or Coriolis forces. The results provide a theoretical foundation for understanding the symmetry and reversibility in irreversible processes.Lars Onsager's paper, "Reciprocal Relations in Irreversible Processes," derived a general reciprocal relation applicable to transport processes such as heat and electricity conduction and diffusion. The derivation is based on the assumption of microscopic reversibility, which involves considering certain average products of fluctuations. The key result is that different irreversible processes must be compared in terms of entropy changes, as expressed by the relation \( S = k \log W \). For linear relations between rates and "forces," a quadratic dissipation function is introduced, and the symmetry conditions demanded by microscopic reversibility lead to the condition \( \dot{S}(\alpha, \dot{\alpha}) - \Phi(\dot{\alpha}, \dot{\alpha}) = \text{maximum} \). This condition determines the rates of the processes for given initial conditions. The paper also discusses the statistical significance of the entropy and the dissipation function, and it formulates reciprocal relations for non-reversible systems, such as those with external magnetic fields or Coriolis forces. The results provide a theoretical foundation for understanding the symmetry and reversibility in irreversible processes.