Entropy theory (1850):

the heat-powered steam engines of the 17th & 18th centuries converted less than 2% of their input into useful work output; physicists investigated this lost energy.  Between 1803 & 1824 L. Carnot & his son Sadi proposed the Carnot cycle, stating that in any machine, accelerations & shocks represent losses of moment of activity (work) & provided the first rudimentary statement of the 2nd law of thermodynamics & the allied concept of 'transformation-energy' or entropy.  The Scottish mechanical engineer Rankin studied steam engines; in 1849 he found the relationship between saturated vapour pressure & temperature.  He established relationships between the temperature, pressure & density of gases & made reference to the thermodynamic quantity itself in 1850 (naming it “thermodynamic function” and “heat-potential”).  Clausius (1822-1888) was a German physicist & mathematician & founder of thermodynamics; his restatement of Carnot's principle gave the theory of heat a sounder basis.  His "On the Moving Force of Heat" (1850), stated the basic ideas of the 2nd law of thermodynamics.  In 1865 he introduced the concept of entropy.

 

the old dynamic physics:

reference to the Classical physics of Newton, Galileo, pre-1900 which predate Modern Physics of the early 20th century

 

The First Law:

reference to the First law of Thermodynamics

and see above page 417

 

“elementary disorder":

in thermodynamics, entropy is often described using the words order or disorder.  Perfect internal disorder describes thermodynamic equilibrium.  In this context disorder means energy dispersal.  Entropy is a measure of energy dispersal or energy spread at a specific temperature. Changes in entropy can be quantitatively related to the distribution or the spreading out of the energy of a thermodynamic system, divided by its temperature.  The idea that the 2nd law of thermodynamics or "entropy law" is a law of disorder (or that dynamically ordered states are "infinitely improbable") is due to L. Boltzmann (1844-1906).

 

calculus of Probabilities:

reference to statistical mechanics, a mathematical framework used in physics, that applies statistical methods & probability theory to large assemblies of microscopic entities.  It assumes no natural laws, but explains the macroscopic behaviour of nature from the behaviour of such ensembles.  It arose out of the development of classical thermodynamics & successful explained macroscopic physical properties (e.g. temperature, pressure or heat capacity) in terms of microscopic parameters that fluctuate about average values, characterized by probability distributions.  From statistical mechanics evolved statistical physics, which uses methods of probability theory & statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems.