Irreversible processes, equilibrium Onsager reciprocal relations

Thermodynamics for non-equilibrium processes is referred to as irreversible thermodynamics. The scientific field of irreversible thermodynamics was established during the early 1900 s. There are three major reasons why irreversible thermodynamics is important for non-equilibrium systems. In the first place special attention is paid to the validity of the classical thermodynamic relations outside equilibrium (i.e., simple systems). In the second place the theory gives a description of the coupled transport processes (i.e., the Onsager reciprocal relations). In the third place the theory quantifies the entropy that is produced during transport. Irreversible thermodynamics can also be used to assess the second law efficiency of how valuable energy resources are exploited. 

The usual emphasis on equilibrium thermodynamics is somewhat inappropriate in view of the fact that all chemical and biological processes are rate-dependent and far from equilibrium. The theory of non-equilibrium or irreversible processes is based on Onsager s reciprocity theorem. Formulation of the theory requires the introduction of concepts and parameters related to dynamically variable systems. In particular, parameters that describe a mechanism that drives the process and another parameter that follows the response of the systems. The driving parameter will be referred to as an affinity and the response as a flux. Such quantities may be defined on the premise that all action ceases once equilibrium is established. 

Fortunately, several simplifications can be made (Nye, 1957). Transport phenomena, for example, are processes whereby systems transition from a state of nonequilibrium to a state of equilibrium. Thus, they fall within the realm of irreversible or nonequilibrium thermodynamics. Onsager s theorem, which is central to nonequilibrium thermodynamics, dictates that as a consequence of time-reversible symmetry, the off-diagonal elements of a transport property tensor are symmetrical (i.e., xy = X/,-). This is known as a reciprocal relation. The Norwegian physical chemist Lars Onsager (1903-1976) was awarded the 1968 Nobel Prize in Chemistry for reciprocal relations. Thus, the tensor above can be rewritten as... 

An irreversible process involves the natural movement of a system from a non-equilibrium state to an equilibrium state without intervention, thus it is a spontaneous process. Basically thermodynamics can tell us the direction in which a process will occur, but can say nothing about the speed (rate) of the process. Onsager might be counted as the founder of the field with his papers from in 1931 entitled Reciprocal relations in irreversible processes, Phys. Rev., vol. 37, pp. 405-426 Phys. Rev., vol. 38, pp. 2265-2279. 

Reciprocal relations have been the first results in the thermodynamics of irreversible processes to indicate that this was not some ill-defined no-man s-land but a worthwhile subject of study whose fertility could be compared with that of equilibrium thermodynamics. Equilibrium thermodynamics was an achievement of the nineteenth century, nonequilibrium thermodynamics was developed in the twentieth century, and Onsager s relations mark a crucial point in the shift of interest away from equilibrium toward nonequilibrium. 

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