Economic Cycles of Carnot Type

Abstract

Originally, the Carnot cycle was a theoretical thermodynamic cycle that provided an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference by the application of work to the system. The first aim of this paper is to introduce and study the economic Carnot cycles concerning Roegenian economics, using our thermodynamic–economic dictionary. These cycles are described in both a Q−P diagram and a E−I diagram. An economic Carnot cycle has a maximum efficiency for a reversible economic “engine”. Three problems together with their solutions clarify the meaning of the economic Carnot cycle, in our context. Then we transform the ideal gas theory into the ideal income theory. The second aim is to analyze the economic Van der Waals equation, showing that the diffeomorphic-invariant information about the Van der Waals surface can be obtained by examining a cuspidal potential.

Information Geometry in Roegenian Economics

“…Let us characterise the geometry of the statistical Roegenian manifold that arises from the equilibrium distribution of an ideal income (see [ 16 ]) of noninteracting economic actors.…”

“…Note that the partition function in the canonical ensemble is from which one can calculate the Helmholtz free energy and thus obtain the equation of state satisfied by a classical ideal income (see [ 16 ]).…”

“…Let P be the price level, Q be the volume of goods, and I be internal politics stability. Here, we shall extend the model to include economic actors’ interactions, which leads to the economic Van der Waals equation of state (see also [ 16 ]) where N is the total number of economic actors and are constants determined by the properties of each actor. The “monetary policies as liquidity or consumption—income” transition occurs at the critical point where price level P , volume of goods Q , and the internal politics stability I assume the values …”

“…We have been inspired from information geometry in Thermodynamics (see [ 1 ]) to produce an information geometry in Roegenian economics [ 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ].…”

“…Generally, the information geometry approach [ 1 , 2 , 16 , 17 , 18 , 19 , 20 ] studies the differential geometric structure of statistical models. Refs.…”