The Concept of Irreversibility in Statistical Mechanics

The interaction between concepts of irreversibility and the development of non-equilibrium statistical mechanics is discussed with particular reference to certain 'paradoxes' that retarded this development A recently evolved attitude towards the general problem of irreversibility may be considered responsible for a number of practical advances in this field. My subject is the interaction between concepts of irreversibility and the development of non-equilibrium statistical mechanics. In particular, I will discuss certain 'paradoxes' that seriously retarded this development, and how these paradoxes are viewed in modern work. Then I will describe an attitude towards the general problem of irreversibility, evolved in the last ten or fifteen years, that in my opinion is responsible for a number of important practical advances in non-equilibrium statistical mechanics. Everyone knows what irreversibility is. On a primitive level, we know that fire burns wood to ashes, that men grow old and die, and that taxes will increase. On a more advanced level, we know that irreversibility is associated with an inevitable increase of entropy. We know from experience that we are unable to construct devices to decrease the total entropy of our local environment. Whatever we are able to do, the entropy increases. Our experience is summarized in the second law of thermodynamics. On a still more advanced level, the irreversible increase of entropy is given a cosmic generality and a deep philosophical significance. Here, the standard view is summarized in the famous statement by Clausius:'... die Entropie der Welt strebt cinem Maximum zu'. In this form. the second law of thermodynamics is often used to discuss the approach of the entire universe to a state of thermal equilibrium, or to support our intuition that the flow of time has an 'arrow' attached to it. Many of the difficulties that arise in the statistical mechanical theory of irreversibility can be traced to the sweeping generality of the third view of irreversibility that we have just referred to. At this level, there seems to be a fundamental contradiction between the second law and mechanics. The main point I want to make here is that these difficulties can be avoided by taking a more modest point of view, in which the second law merely summarizes certain human experiences. I do not say that one must take the