## ABSTRACT

The theory of the present chapter and those of Chapters 12 and 13 are developed close to equilibrium. Since the entropy increases in an irreversible process, the entropy production in time is an essential quantity of interest. Assuming a simple system of two compartments with an internal contact through which heat can flow, the rate of entropy production dS/dt is caused by heat flow dQ/dt (called flux; denoted J) due to a small temperature difference, 1/T
_{1} − 1/T
_{2} (called force or affinity; denoted X). Onsager assumes the linear relation J = LX, where L is a phenomenological coefficient independent of time; thus, dS/dT = LX
^{2}. In the case of two irreversible processes (mixing), J
_{1} = L
_{11 × 1} + L
_{12 × 2 }and J
_{2} = L
_{21 × 1} + L
_{22 × 2}, Onsager has derived the reciprocal relations for the interference coefficients, L
_{12} = L
_{21}, and more generally, L_{ik}
= L_{ki}
. The derivation of L_{ik}
= L_{ki}
is also based on the assumption that the decay of a macroscopic disturbance close to equilibrium can be described by the decay of a microscopic fluctuation in equilibrium statistical mechanics. Therefore, a treatment of fluctuations (due to Einstein) is presented, where their distribution is approximated by a Gaussian. Another necessary ingredient is the principle of detailed balance, which is derived as well. The chapter ends by discussing steady states and the principle of minimum entropy production. Some specific examples are discussed.