# Thermodynamic isomorphisms

In human thermodynamics, thermodynamic isomorphisms are derived or made up equations, alluded to be thermodynamical, on the superficial premise that they have the same general mathematical shape. The majority of these types of isomorphism equations have essentially nothing to do with thermodynamics, but are surface scratching attempts to appear thermodynamical.

Examples
A simple example would be American mathematician Harold Davis’ 1941 modelling of a person’s budget in the differential form: [1]

$dI = dS + dE \,$

where I is income, S is savings, and E is expenditure, which according to Johannes Lisman (1949) is an attempt to formulate a first law of thermodynamics: [2]

$dQ = dU + dA \,$

where Q is heat supplied, U is internal energy, and A is external work done. The classic example is John Neumann’s circa 1949 suggestion to Claude Shannon to call Ralph Hartley’s 1928 logarithmic equation for the transmission of information, in the form of high and low voltage (1s and 0s) pulses, in telegraph wires:

H = n log S

By the name “entropy” since Max Planck (1901) was using a similar equation to describe the entropy of a physical body in thermodynamics:

S = k log W

These examples, as with most isomorphism attempts, are purely baseless. A recent example of thermodynamics isomorphisms are the theories of English engineering business consultant John Bryant, as captured in the 2009 book Thermoeconomics: a Thermodynamic Approach to Economics. An example being the empty jumps of extrapolation, that the Watt indicator diagram describing pressure-volume work of a piston and cylinder :

W = PdV

where W is the work done, P is the pressure, and V is change in volume of the body in question, translates, in economic systems, to a description of the price P of a product plotted against the volume V per unit time of the product flowing through the system, such that the

W = PV

where W is the work value of that particular product or good per unit time, coming out of the economic system. This last example seems to be based on nothing more than the fact that the different quantities start with the same letter. [3] In the correct view, conceptions of social pressure (or social volume) or economic pressure (or economic volume) of working systems of human molecules, e.g. Russia, become greatly more complicated, the exchange of goods in the system acting as a secondary field particle of the exchange force involved in the human chemical reactions in the system or in other descriptions a factor of the activation energy.

Etymology
This category of equations seems to have been named in 1966 by American economist Paul Samuelson, who called such equations in economics, by the name “economic isomorphisms”, as he would receive numerous versions of such equations in the monthly mail, as he has commented. [4]

Action thermodynamics,
Unitless thermodynamics

References
1. Davis, Harold T. (1941). The Theory of Econometrics (pg. 171-76). Bloomington.
2. Lisman, Johannes H.C. (1949). “Econometrics and Thermodynamics: A Remark on Davis’ Theory of Budgets” (abs), Econometrica, XVII, 59-62.
3. Bryant, John (2009). Thermoeconomics: A Thermodynamic Approach to Economics (ch. 1: Introduction; ch. 3: Thermodynamic Principles; ch. 5: Money). VOCAT International Ltd.
4. Samuelson, Paul. (1966). "Thermodynamics and Economic Isomorphisms", The Collected Scientific Papers, 2: 203-219, 1966, MIT Press; in: Global Econometrics, F.G. Adams-Hickman, B.G. Hickman, eds., MIT Press, Cambridge, 1983.