An Economy Viewed as a Far-from-Equilibrium System from the Perspective of Algorithmic Information Theory

Abstract

This paper, using Algorithmic Information Theory (AIT), argues that once energy resources are considered, an economy, like an ecology, requires continuous energy to be sustained in a homeostatic state away from the decayed state of its (local) thermodynamic equilibrium. AIT identifies how economic actions and natural laws create an ordered economy through what is seen as computations on a real world Universal Turing Machine (UTM) that can be simulated to within a constant on a laboratory UTM. The shortest, appropriately coded, programme to do this defines the system's information or algorithmic entropy. The computational behaviour of many generations of primitive economic agents can create a more ordered and advanced economy, able to be specified by a relatively short algorithm. The approach allows information flows to be tracked in real-world computational processes where instructions carried in stored energy create order while ejecting disorder. Selection processes implement the Maximum Power Principle while the economy trends towards Maximum Entropy Production, as tools amplify human labour and interconnections create energy efficiency. The approach provides insights into how an advanced economy is a more ordered economy, and tools to investigate the concerns of the Bioeconomists over long term economic survival.

Algorithmic Entropy and Landauer’s Principle Link Microscopic System Behaviour to the Thermodynamic Entropy

“…Devine [ 22 , 23 , 27 ] uses the above argument to establish the entropy cost of maintaining stability in a far-from-equilibrium system at . The system is maintained by accessing stored energy and ejecting waste.…”

“…For example, Devine [ 20 ] has used AIT to show there is no need to define a fourth law of thermodynamics to explain order in the universe, as has been postulated by the intelligent design community ([ 21 ]). More recently, algorithmic entropy has been used to track the emergence of order in far-from-equilibrium biological and economic systems [ 22 , 23 ].…”

“…In the natural world, bits are computational instructions, embodied in the physical laws that specify the interactions between different real world states. As is discussed later in Section 6 , Landauer’s principle [ 26 ] can be used to establish the thermodynamic cost of transferring bits out of a system and within a system [ 22 , 23 , 27 ] for a real-world reversible process. For a system to be stable in a homeostatic far-from-equilibrium set of configurations, both the energy flows into and out of the system, as well as the bit flows in and out, must balance.…”

Landauer’s Principle a Consequence of Bit Flows, Given Stirling’s Approximation

“…Later the argument tightened when erasure was seen to be the reduction in the number of bits specifying a microstate of a system and, for a quantum system, the change in its Von Neumann entropy as discussed in Section 5. Nevertheless, for these reasons it is unclear how valid the principle is for regimes where the assumptions do not hold, particularly as Devine [3,4] used the principle to identify the thermodynamic cost of maintaining a system distant from equilibrium in terms of entropy flows.…”

“…As the argument applies to systems distant from equilibrium, it justifies the use of Landauer's principle to track bit flows into and out of the non-equilibrium system as used by Devine [3,4]. By being able to do so, AIT offers an approach to statistical thermodynamics which is easy to visualize and which offers new insights, as these computational bits are real entities linked to energy through the temperature.…”