La relación de reciprocidad de Onsager expresa la igualdad de ciertas relaciones entre flujos y fuerzas en sistemas termodinámicos fuera de equilibrio pero en los que existe noción de equilibrio termodinámico local. Como ejemplo, se observa que las diferencias de temperatura en un sistema conducen a que el calor fluya desde la zona más caliente del sistema hacia la más fría. Del mismo modo, las diferencias de presión conducen a que la materia fluya desde la zona de más alta presión hacia la de más baja presión. Puede observarse experimentalmente que cuando ambas varían, temperatura y presión, las diferencias de presión pueden causar flujos de calor y las diferencias de temperatura pueden causar flujos de materia. Y lo que es aún más sorprendente, el flujo de calor por unidad de presión de diferencia y la densidad de materia que fluye por unidad de temperatura de diferencia son iguales. Lars Onsager, químico-físico estadounidense de origen noruego (1903-76), realizó la demostración de que ésta era una relación necesaria utilizando la física estadística en 1929. Por ello recibió el Premio Nobel de Química en 1968. Existen similares relaciones recíprocas entre diferentes pares de fuerzas y flujos en diferentes sistemas físicos. La teoría desarrollada por Onsager es mucho más general que el ejemplo anterior y con ella se pueden tratar más de dos fuerzas termodinámicas al mismo tiempo. La relación de reciprocidad de Onsager ha sido postulada en ocasiones como la «cuarta ley de la termodinámica».

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In thermodynamics, the Onsager reciprocal relations express the equality of certain ratios between flows and forces in thermodynamic systems out of equilibrium, but where a notion of local equilibrium exists. "Reciprocal relations" occur between different pairs of forces and flows in a variety of physical systems. For example, consider fluid systems described in terms of temperature, matter density, and pressure. In this class of systems, it is known that temperature differences lead to heat flows from the warmer to the colder parts of the system; similarly, pressure differences will lead to matter flow from high-pressure to low-pressure regions. What is remarkable is the observation that, when both pressure and temperature vary, temperature differences at constant pressure can cause matter flow (as in convection) and pressure differences at constant temperature can cause heat flow. Perhaps surprisingly, the heat flow per unit of pressure difference and the density (matter) flow per unit of temperature difference are equal. This equality was shown to be necessary by Lars Onsager using statistical mechanics as a consequence of the time reversibility of microscopic dynamics (microscopic reversibility). The theory developed by Onsager is much more general than this example and capable of treating more than two thermodynamic forces at once, with the limitation that "the principle of dynamical reversibility does not apply when (external) magnetic fields or Coriolis forces are present", in which case "the reciprocal relations break down". Though the fluid system is perhaps described most intuitively, the high precision of electrical measurements makes experimental realisations of Onsager's reciprocity easier in systems involving electrical phenomena. In fact, Onsager's 1931 paper refers to thermoelectricity and transport phenomena in electrolytes as well-known from the 19th century, including "quasi-thermodynamic" theories by Thomson and Helmholtz respectively. Onsager's reciprocity in the thermoelectric effect manifests itself in the equality of the Peltier (heat flow caused by a voltage difference) and Seebeck (electrical current caused by a temperature difference) coefficients of a thermoelectric material. Similarly, the so-called "direct piezoelectric" (electrical current produced by mechanical stress) and "reverse piezoelectric" (deformation produced by a voltage difference) coefficients are equal. For many kinetic systems, like the Boltzmann equation or chemical kinetics, the Onsager relations are closely connected to the principle of detailed balance and follow from them in the linear approximation near equilibrium. Experimental verifications of the Onsager reciprocal relations were collected and analyzed by D. G. Miller for many classes of irreversible processes, namely for thermoelectricity, electrokinetics, transference in electrolytic solutions, diffusion, conduction of heat and electricity in anisotropic solids, thermomagnetism and galvanomagnetism. In this classical review, chemical reactions are considered as "cases with meager" and inconclusive evidence. Further theoretical analysis and experiments support the reciprocal relations for chemical kinetics with transport. For his discovery of these reciprocal relations, Lars Onsager was awarded the 1968 Nobel Prize in Chemistry. The presentation speech referred to the three laws of thermodynamics and then added "It can be said that Onsager's reciprocal relations represent a further law making a thermodynamic study of irreversible processes possible." Some authors have even described Onsager's relations as the "Fourth law of thermodynamics".

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