Thermodynamics Far from Equilibrium: from Glasses to Black Holes

Thermodynamics is the old science that describes the flow of energy in systems with many atoms. Works started by Carnot, Kelvin and Clausius showed that these laws are very general. This universality led to the formulation of the first and second law of thermodynamics, that apply to a vast amount of systems, such as gases and crystals. During half a century there was still a problem with the application to glasses. In this field there were classical paradoxes related to the so-called Ehrenfest relations and Prigogine-Defay ratio. The solution of this problem is discussed below. Due to its inherent non-equilibrium nature a glass is far from equilibrium. To describe it in a thermodynamic treatment one has to take into account at least one additional system parameter, the self-generated effective temperature, and its conjugate variable, the configurational entropy . After having realized how thermodynamics should be formulated for glasses, we have investigated the situation for black holes . For this problem various aspects of the dynamics are known, and it was generally expected that the laws for black hole dynamics would coincide with the laws of black hole thermodynamics. We nevertheless felt that the proper connection between black hole dynamics and standard thermodynamics had not been made, and this will be clarified below. Two years have passed since our letter on the black hole thermodynamics appeared . Till now the reaction of workers in gravitation was reserved, though researchers in other areas were attracted by its unifying concept. We feel that the blame should be put on the lack of basic thermodynamic training in physics teaching programs. Indeed, for many scholars thermodynamics is not much more than Gibbsian equilibrium thermodynamics. If asked “what is the second law?” the answer is often dU = TdS − pdV , which, however, is the combination of the first law (dU = d̄Q +d̄W with d̄W = −pdV for a fluid) and the second law in case of equilibrium, where the heat added to the system satisfies d̄Q = TdS. When mentioning the issue of thermodynamics of a black hole isolated from matter to people working in gravitation, a standard reaction is: “But I can put it in an insulating box, and then I can apply equilibrium thermodynamics”. To us it is worrisome that such an unrealistic setup is considered to be a satisfactory explanation of the