Title: Optimal processes in macro systems (thermodynamics and economics)
1Optimal processesin macro systems
(thermodynamics and economics)
- A.M. Tsirlin and V. Kazakov
2Macro Systems thermodynamics, economics,
segregated systems
- Extensive variables
- V, U, , N0, N
- Intensive variables
- T, m, P, , p, c
Equation of state
3Irreversibility and kinetics
- Natural processes
- Irreversibility measure,
- dissipation
- S, s
4Structure of MM of the macrosystem
5Workout example
thermodynamics
microeconomics
Irreversible DS gt 0, A 0 Reversible DS 0, A gt 0 Irreversible ? gt 0, E 0 Reversible ? 0, E gt 0
6Major problems
- Minimal dissipation processes .
- Stationary state of an open system that includes
intermediary. - Intermediarys limiting possibilities in close,
open and non-stationary macro systems. - Qualitative measure of irreversibility in
microeconomics. - Realizability area of macro system.
7Irreversibility measure in microeconomic systems
Economic agent N?Rn1 Resources and capital (N0) endowments
Economic agent pi(N) Estimate of i-th resource (equilibrium price)
Wealth function S(N) exists such that
8voluntariliness principle
dSi ? 0, i1,2 If p1i and p2i have different
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9Capital dissipation
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- s g(c,p)(cp) capital dissipation (trading
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10Minimal dissipation processes in thermodynamics
For ? a( p )g( p, u ) We get
11Minimal dissipation processes in thermodynamics
Heat transfer p T1, u T2
12Minimal dissipation processes in thermodynamics
13Minimal dissipation processes in thermodynamics
If
14Stationary state of open macro system
- Thermodynamics
- n power, p1iTi
- q heat,
- g mass,
- p intensive variables
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15If g 0, qij aij(Ti Tj), then
If m 2, T1 T, T2 T, then
limiting power
For g AX Prigogines extremal principle holds
for any u (A Onsager matrix).
16Stationary states of open macro systems
- Microeconomics
- ui prices,
- p estimates
17If gij aij(pj pj), gi ai(ui pj), then
If m 2, p1 p, p2 p, then
Analogy of Prigogine extremal principle for g
AD (Dijpi pj) A symmetric.
18Optimal processes
- Availability Amax(t)?
- Control u(t) (u1, , um),
- h(t) (h1,,hm), hi 0, 1
- k number of conditions on final state.
- Statements
- .u(t) "h are minimal dissipation processes,
- For reservoirs u(t), h(t) are piece-wise
constant function that takes not more than k1
values. - Systems entropy is piece-wise linear function
"q, g
19If
exergy
20Separation systems
21Microeconomics. Profitability ?
- E? analogous of exergy .
- t given
- c(t) obeys conditions of minimal dissipation
during all contacts - ?
- obeys the conditions
22Realizability area
Thermodynamics (heat engine)
23Realizability area
Microeconomics (intermediary)
24Optimal processes in macro systems
(thermodynamics and economics)
- e-mail tsirlin_at_sarc.botik.ru
- vladimir.kazakov_at_uts.edu.au