SolarEnergy

HeatDissipation

System of Accounts for Global Entropy Production (SAGE-P): the

Mirror Image of GDP

IIASA workshop on Complex System Modeling: Laxenburg, Austria

28-30 August 2006

The Second Law of thermodynamics

states all spontaneous chemical and physical change increases the

entropy of the universe and this tends towards a maximum

Ayers

‘Entropy Acounting’ is an arbitrary statistical measure of order/disorder

in any well-defined dissipative structure.*production is creation of product and

given a negative sign.*consumption is the destruction product

and given a positive sign.

*production - consumption = system’s surplus/deficit product.

Adam Smith conceived the economy as flow-fund ‘provisioning’ system where the stock is

composed of fixed and circulating capital where the economic output assumes a physical stock reserved for immediate

consumption Abstract products, qua services, while necessary

to maintain order, security, distribution and distractions, were not considered part of the

wealth of Nations because services could not an accumulate and disappeared the instant they

were producedAdam Smith, Inquiry into Nature and Cause of the

Wealth of Nations, 1775

So great a part of the circulating capital being continually withdrawn from it, in order to be placed in the other two branches of the general stock of society; it must in its turn require continual supplies without which it would soon cease to exist. These supplies are principally drawn from three sources, the produce of the land, of mines, and of fisheries. These afford continual supplies of provisions and materials, of which part is afterwards wrought into finished work, and by which are replaced the provisions, materials and finished work continually withdrawn from circulating capital. Adam Smith, 1775

Adam Smith’s entropy flow concept of value

Of all parts of the stock, either of an individual, or of a society, reserved for immediate consumption, what is laid out in houses is most slowly consumed. A stock of clothes may last several years: a stock of furniture half a century or a century: but a stock of houses, well built and properly taken care of, may last many centuries. Though the period of their total consumption, however, is more distant, they are still as really a stock reserved for immediate consumption as either clothes or household furniture.

Income is a flow through a period of time and not, like capital, as a fund at an instant in time, ... consisting of abstract services and not, like capital, of concrete wealth. The income from any instrument is thus the flow of services rendered by the instrument. The income of a community is the total flow of services from all its instruments. The income of an individual is the flow of services yielded to him from his property.

Irving Fisher, 1905, The Nature of Capital and Income

The objective of economic policy should not be to maximize consumption or production, but rather minimize it, i.e. to enable us to maintain our capital stock with as little consumption and production as possible. It is not the increase in consumption or production that makes us rich, but the increase in capital, and any invention which enables us to enjoy a given stock of capital and a smaller amount of consumption and production, out-go or income, so much the gain.

Kenneth Boulding, 1949, Income of Wealth, Review of Economic Studies

The Second Law of thermodynamic and the economic process

The significant fact for the economist is that the new science of thermodynamics began as a physics of economic value and, basically, can still be regarded as such. The Entropy Law itself emerges as the most economic of all natural laws. It is in...the primary science of matter that the fundamental nonmechanistic nature of the economic process fully reveals itself.

Nicolas Georgescu-Roegen, The Entropy Law and the Economic Process, 1971

The Mecca of the economist lies in economic biology rather than economic dynamics. But biological conceptions are more complex than those of mechanics; a volume on Foundations must therefore give a relatively large place to mechanical analogies; and the frequent use of the term "equilibrium," which suggests something of a statical analogy.

Alfred Marshall, Principles of Economics, eigth edition,

1920

The General Equilibrium State Condition

A situation where all markets in an economy aresimultaneously in equilibrium and prices and

quantities do not change

The optimum state condition (also assumed the most efficient allocation of scarce resources) exists when:* no single firm can dominate the market* free entry & exit from the market* perfect information for both the buyer and the seller

A living organism continually increases its entropy -or, as you might say, produces positive entropy -thus tends to approach the dangerous state of maximum entropy, which is death.

A living organism continually increases its entropy -or, as you might say, produces positive entropy -thus tends to approach the dangerous state of maximum entropy, which is death.

The Concept of Entropy ProductionThe Concept of Entropy Production

Erwin Schrödinger, 1944, “What is Life & Mind and Matter”

Erwin Schrödinger, 1944, “What is Life & Mind and Matter”

What an organism feeds upon is negative entropy. Or, to put it less paradoxically, the essential thing in metabolism is that the organism succeeds in freeing itself from all the entropy it cannot help producing while alive.

What an organism feeds upon is negative entropy. Or, to put it less paradoxically, the essential thing in metabolism is that the organism succeeds in freeing itself from all the entropy it cannot help producing while alive.

The Concept of Negative Entropy The Concept of Negative Entropy

Erwin Schrödinger, 1944, “What is Life & Mind and Matter”

Erwin Schrödinger, 1944, “What is Life & Mind and Matter”

The Economy defined as an open thermodynamic system

The Economy defined as an open thermodynamic system

An open, as opposed to isolated system, exchange matter and energy with the ambient environment, expressed as the transfer of entropy across system boundaries, (deS) and

distinguished from the entropy produced within the system, diS. The difference between diS and

deS describe the net rate of dissipation of system

structure, net P = diS - deS = 0 infers Steady-

State or production = consumption, > 0 infers surplus or production > consumption, < 0 infers deficit or production < consumption

An open, as opposed to isolated system, exchange matter and energy with the ambient environment, expressed as the transfer of entropy across system boundaries, (deS) and

distinguished from the entropy produced within the system, diS. The difference between diS and

deS describe the net rate of dissipation of system

structure, net P = diS - deS = 0 infers Steady-

State or production = consumption, > 0 infers surplus or production > consumption, < 0 infers deficit or production < consumption

accounting numeraire & identities

computable objects: physical & abstract

Functions: production, consumption &capital accumulation

Mapping: natural systems on formal systems& vice versa

SAGE-P is a set of integrated economic accounts expressed as dissipative structures, accounting identites, and limit functions of:

*Production, *Consumption,

*Accumulation and *Trade with the rest-of-the-world.

The balance sheets are expressed as net values of entropy production.

SAGE-P is a set of integrated economic accounts expressed as dissipative structures, accounting identites, and limit functions of:

*Production, *Consumption,

*Accumulation and *Trade with the rest-of-the-world.

The balance sheets are expressed as net values of entropy production.

G-R Flow-Fund Model

Factors of production are divided into two categories: 1. the fund elements enters and leaves the process with its efficiency intact and represent the agents of the process, (i.e., production coefficients): Fund Elements =

2. the flow elements are distinguished either as inputs or outputs of the process which are used or acted upon. Flow Elements =

3. the activities of the fund is represented by a time integral of service flow from the

4. The analytical representation of the Process:

where the i subscript represents input or output and represents both inputs and outputs.

G-R Flow-Fund Model

Factors of production are divided into two categories: 1. the fund elements enters and leaves the process with its efficiency intact and represent the agents of the process, (i.e., production coefficients): Fund Elements =

2. the flow elements are distinguished either as inputs or outputs of the process which are used or acted upon. Flow Elements =

3. the activities of the fund is represented by a time integral of service flow from the

4. The analytical representation of the Process:

where the i subscript represents input or output and represents both inputs and outputs.

αC

iE (t)

αS (t) αC

0

T

iE (t);0

T

αS (t);

α

Joint Economic/ Ecological Products

Joint Economic/ Ecological Products

• Type 1 input, assume the I/O coefficients of ‘low entropy’ flows into the production function, (factors of production);

• Type 2 output, assume the output vector of ‘high entropy’ flows to satisfy the demand function, plus waste residuals;

• Type 3 stock, assume the accumulated ‘low entropy fund’ (i.e., natural, economic and cultural capital).

• Type 1 input, assume the I/O coefficients of ‘low entropy’ flows into the production function, (factors of production);

• Type 2 output, assume the output vector of ‘high entropy’ flows to satisfy the demand function, plus waste residuals;

• Type 3 stock, assume the accumulated ‘low entropy fund’ (i.e., natural, economic and cultural capital).

Joint Economic EcoProducts Joint Economic EcoProducts • Products are complex physical and/or abstact

object, the properties of which exhibit degrees of ‘jointness’ ranging from zero (no discernible ecoproduct) to one, (no discernible econproduct).

• Production functions are complex (metabolic) physical and/or abstract processes, the properties of which exhibit degrees of jointness in the coefficients of mass inflow and outflow balances.

• The mapping of ecosystem functions on economic functions and its inverse, results in the Cartesian ‘joint product’ of the flow vector of entropy production.

• Products are complex physical and/or abstact object, the properties of which exhibit degrees of ‘jointness’ ranging from zero (no discernible ecoproduct) to one, (no discernible econproduct).

• Production functions are complex (metabolic) physical and/or abstract processes, the properties of which exhibit degrees of jointness in the coefficients of mass inflow and outflow balances.

• The mapping of ecosystem functions on economic functions and its inverse, results in the Cartesian ‘joint product’ of the flow vector of entropy production.

SYSTEM OFACCOUNTS FOR ENTROPYPRODUCTIONSAGE-P

FIXED CAPITALCycling Systems(AtmosphereHydrosphereLithosphere)& Minerals & Fossil Fuels

LOW ENTROPY STOCKSCIRCULATING CAPITALReproductive Resources(Natural, Economic andSocial/Cultural)

PRODUCTIONFUNCTION Transformation of Low EntropyStocks inro HighEntropy Products

CONSUMPTIONFUNCTIONTransformation of low entropy stocks into waste residuals

RATE OF REPLENISHMENTRATE OF CONSUMPTIONLOW ENTROPY FUNDSolar Energy InputHeat DissipationOutputSAGE-P and Entropy Production Accounting

Ecosystem Production Function, (Somatic)Human Production Function, (Exosomatic)Œconomy of NatureŒconomy of Man

Industrial Revolution circa. 1750sOIKONOMIA and the Exosomatic Revolution

Production Function StructureSpatial Structure Figure 1: Hierarchical Classification of Ecosystems Production

Functions and Spatial (Nesting) Structure Adapted from Allen and Hoekstra .(1991) &Level 2Level 4Canadian Ecosystem ClassificationEcozone Ecoprovince Ecoregion Ecodistrict Ecotype Ecoelement Ecosection Level 1