12 February 2020

On Equilibrium (1970-1979)

"A precise, all-encompassing definition is difficult to frame, but the general meaning of 'equilibrium' is that a system has settled down to the point where its macroscopic properties are unchanging with time. In practice there is seldom any doubt whether a system has reached equilibrium or not. And there is always a test of sorts: do the macroscopic properties, given further 'aging'' of the system, change discernibly?" (Ralph Baierlein, "Atoms and Information Theory: An Introduction to Statistical Mechanics", 1971)

"A system is in equilibrium when the forces constituting it are arranged in such a way as to compensate each other, like the two weights pulling at the arms of a pair of scales." (Rudolf Arnheim, "Entropy and Art: An Essay on Disorder and Order", 1971)

"When we know that a physical system is in equilibrium, know the environment, and know the molecular constitution, we are still very far from knowing the quantum-mechanical state that should be used to describe the system. We may conclude that the state should be one of the energy eigenstates, but which of many is still an open question. A statistical description is the best we can hope to achieve. If we supplement our knowledge with information enabling us to force an expectation value calculation of the energy to yield a specified numerical value, we are certainly better off. Nonetheless, this addition still leaves us without a determination of the probability distribution." (Ralph Baierlein, "Atoms and Information Theory: An Introduction to Statistical Mechanics", 1971)

"When matter is becoming disturbed by non-equilibrium conditions it organizes itself, it wakes up. It happens that our world is a non-equilibrium system." (Ilya Prigogine, "Thermodynamics of Evolution", 1972)

"In an isolated system, which cannot exchange energy and matter with the surroundings, this tendency is expressed in terms of a function of the macroscopic state of the system: the entropy." (Ilya Prigogine, "Thermodynamics of Evolution", 1972)

"The evolution of a physicochemical system leads to an equilibrium state of maximum disorder." (Ilya Prigogine, "Thermodynamics of Evolution", 1972)

"The functional order maintained within living systems seems to defy the Second Law; nonequilibrium thermodynamics describes how such systems come to terms with entropy." (Ilya Prigogine, "Thermodynamics of Evolution", 1972)

"There is little point in demanding minor concessions and relaxations of the abstract, timeless general equilibrium. The light it can throw on human affairs is throw by its most austere and formal version. We are not concerned to ask: How could it possibly work? The useful question is: What does its logical structure imply?" (George L S Shackle, "Epistemics and Economics", 1972)

"Chance is commonly viewed as a self-correcting process in which a deviation in one direction induces a deviation in the opposite direction to restore the equilibrium. In fact, deviations are not 'corrected' as a chance process unfolds, they are merely diluted." (Amos Tversky, "Judgment Under Uncertainty: Heuristics and Biases", 1974)

"Equilibrium is a figment of the human imagination." (Kenneth Boulding, Toward a General Social Science, 1974)

"The vector equilibrium is the true zero reference of the energetic mathematics. Zero pulsation in the vector equilibrium is the nearest approach we will ever know to eternity and god: the zero phase of conceptual integrity inherent in the positive and negative asymmetries that propagate the differentials of consciousness." (Buckminster Fuller, "Synergetics: Explorations in the Geometry of Thinking", 1975)

"The notion that the 'balance of nature' is delicately poised and easily upset is nonsense. Nature is extraordinarily tough and resilient, interlaced with checks and balances, with an astonishing capacity for recovering from disturbances in equilibrium. The formula for survival is not power; it is symbiosis." (Sir Eric Ashby, [Encounter] 1976)

"In any system governed by a potential, and in which the system's behavior is determined by no more than four different factors, only seven qualitatively different types of discontinuity are possible. In other words, while there are an infinite number of ways for such a system to change continuously (staying at or near equilibrium), there are only seven structurally stable ways for it to change discontinuously (passing through non-equilibrium states)." (Alexander Woodcock & Monte Davis, "Catastrophe Theory", 1978)

"We know, in other words, the general conditions in which what we call, somewhat misleadingly, an equilibrium will establish itself: but we never know what the particular prices or wages are which would exist if the market were to bring about such an equilibrium." (Friedrich Hayek, "Unemployment and monetary policy: government as generator of the ‘business cycle’", 1979)

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