temperature, T. Thus, one definition of entropy change is dS = dQ/T. In classical
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temperature, T. Thus, one definition of entropy change is dS = dQ/T. In classical
contexts, dS is expressed in units of heat called Joules per degree of absolute
temperature in units Kelvin, the temperature in Centigrade plus 273.16°. The best-
known physical image involves the heat-energy transfer to and from heat baths
called reservoirs as intermediate actions of the work of the heat driven engine
executing what has come to be known as the Carnot Cycle. The same formulation
emerges in this more concrete context: the heat, Q, transfer, dQ, at a particular
absolute temperature, T, dQ/T, has been used to define an entropy change, dS =
dQ/T related to some not-need-to-know-about specific alteration(s) in a system’s
internal physical properties.
lf one allows some loose thinking about heat-induced increases in the
Statistical randomness of molecular motion in the above reservoir that is associated
with the loss of useable energy, the positive entropy change, dS > 0, is vaguely
relatable to the kinds of information entropies to be discussed below. If a gas
trapped in an insulated, physically isolated, closed cylinder is allowed to expand
infinitely slowly, reversibly, called adiabatically, pushing up the piston that closed off
its end, the gas will become cooler, energy having been expended doing the work of
lifting the piston. Defined as an isolated system (of course no where in the real, non-
laboratory, world can this condition of absent exchanges of energy or matter with
the environment be found), it is a reversible process, because returning the energy
of the work by, again, infinitely slowly pushing down on the piston and compressing
the gas to its original volume, returns it to its former temperature-defined energy
state. In this historically prominent thought-toy of physics, there has been a
reversible change in energy but no changes in the entropy, dS = 0. The gas’s heat,
temperature (and energy and volume) can be completely restored in this
metaphysically mythic classical thermodynmical tale of an entropy-conserving,
reversible process.
While fixed entropy and independence of the specific path is the case for the
above noted abstract reversible cycle, in the real, irreversible orbits of most physical
and all biological systems, entropy increases, dS > 0. Walter Nernst’s 1907 heat
theorem yields a zero point from which to determine a difference measure in the
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