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laws of nature.......

Symmetry, Broken-Symmetry and the First and Second Laws ofThermodynamics.


The laws of thermodynamics are special laws that sit above the ordinary laws of nature as laws about laws or laws upon which the other laws depend (Swenson & Turvey, 1991).

It can be successfully shown that without the first and second laws, which express symmetry properties of the world, there could be no other laws at all.


The first law or the law of energy conservation which says that all real-world processes involve transformations of energy, and that the total amount of energy is always conserved expresses time-translation symmetry.

It means, there is something that unifies the world (constitutes it as a continuum) which if you go forward or backward in time remains entirely the same.

It is, in effect, through this conservation or out of it that all real-world dynamics occurs, yet the first law itself is entirely indifferent to these changes or dynamics.

As far as the first law is concerned, nothing changes at all, and this is just the definition of a symmetry, something that remains invariant, indifferent or unchanged given certain transformations, and the remarkable point with respect to the first law is that it refers to that which is conserved (the quantity of energy) or remains symmetric under all transformations.

Although intuited at least as early as the work of the Milesian physicists, and in modern times particularly by Leibniz, the first law is taken to have been first explicitly "discovered" in the first part of the last century by Mayer, then Joule, and later Helmholz with the demonstration of the equivalence of heat and other forms of energy, and completed in this century with Einsteins's demonstration that matter is also a form of energy.


Figure shows a famous experiment devised by Joule to demonstrate the equivalence of matter and energy.
fig - Comics/Fantasy/Anime

Entropy and the Second Law of Thermodynamics The second law of thermodynamics (the entropy law or law of entropy) was formulated in the middle of the last century by Clausius and Thomson following Carnot's earlier observation that, like the fall or flow of a stream that turns a mill wheel, it is the "fall" or flow of heat from higher to lower temperatures that motivates a steam engine. The key insight was that the world is inherently active, and that whenever an energy distribution is out of equilibrium a potential or thermodynamic "force" (the gradient of a potential) exists that the world acts spontaneously to dissipate or minimize. All real-world change or dynamics is seen to follow, or be motivated, by this law. So whereas the first law expresses that which remains the same, or is time-symmetric, in all real-world processes the second law expresses that which changes and motivates the change, the fundamental time-asymmetry, in all real-world process. Clausius coined the term "entropy" to refer to the dissipated potential and the second law, in its most general form, states that the world acts spontaneously to minimize potentials (or equivalently maximize entropy), and with this, active end-directedness or time-asymmetry was, for the first time, given a universal physical basis. The balance equation of the second law, expressed as S > 0, says that in all natural processes the entropy of the world always increases, and thus whereas with the first law there is no time, and the past, present, and future are indistinguishable, the second law, with its one-way flow, introduces the basis for telling the difference. in the fig: A glass of liquid at temperature TI is placed in a room at temperature TII such that . The disequilibrium produces a field potential that results in a flow of energy in the form of heat from the glass to the room so as to drain the potential until it is minimized (the entropy is maximized) at which time thermodynamic equilibrium is reached and all flows stop. refers to the conservation of energy in that the flow from the glass equals the flow of heat into the room.

picture by fantafabulous

fig4:Boltzmann's View of the Second Law as a Law of Disorder: The active macroscopic nature of the second law posed a direct challenge to the "dead" mechanical world view which Boltzmann tried to meet in the latter part of the last century by reducing the second law to a law of probability following from the random collisions of mechanical particles (efficient cause (see Swenson (1990)). Following the lead of Maxwell who had modeled gas molecules as colliding billiard balls, Boltzmann argued that the second law was simply a consequence of the fact that since with each collision nonequilibrium distributions would become increasingly disordered leading to a final state of macroscopic uniformity and microscopic disorder. Because there are so many more possible disordered states than ordered ones, he concluded, a system will almost always be found either in the state of maximum disorder or moving towards it.

picture by fantafabulous

fig5 : Two time slices from the Bénard experiment. When the gradient of the potential (the "force") between source (the heated surface below) and the sink (the cooler air at the top) is below a critical threshold (left) the flow of heat is produced by the random collision of the molecules (conduction), and the system is in the disordered or "Boltzmann regime", and the surface of the system is smooth, homogeneous, and symmetrical. When the force is above the critical threshold (right), however, the symmetry of the system is broken and autocatakinetic order spontaneously arises as random microscopic fluctuations are amplified to macroscopic levels and "Benard cells" fill the container as hundreds of millions of molecules begin moving together (for more detailed discussion see e.g., Swenson, 1989a,b, c, 1992, 1997a).

picture by fantafabulous
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