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Optimal processes in macro systems (thermodynamics and economics)

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Optimal processes in macro systems (thermodynamics and economics) A.M. Tsirlin and V. Kazakov Macro Systems: thermodynamics, economics, segregated systems Extensive ... – PowerPoint PPT presentation

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Title: Optimal processes in macro systems (thermodynamics and economics)


1
Optimal processesin macro systems
(thermodynamics and economics)
  • A.M. Tsirlin and V. Kazakov

2
Macro Systems thermodynamics, economics,
segregated systems
  • Extensive variables
  • V, U, , N0, N
  • Intensive variables
  • T, m, P, , p, c

Equation of state
3
Irreversibility and kinetics
  • Natural processes
  • Irreversibility measure,
  • dissipation
  • S, s

4
Structure of MM of the macrosystem
5
Workout 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
6
Major problems
  1. Minimal dissipation processes .
  2. Stationary state of an open system that includes
    intermediary.
  3. Intermediarys limiting possibilities in close,
    open and non-stationary macro systems.
  4. Qualitative measure of irreversibility in
    microeconomics.
  5. Realizability area of macro system.

7
Irreversibility 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
8
voluntariliness principle
dSi ? 0, i1,2 If p1i and p2i have different
signs that it is not less than 2 flows.


0
p
p
g
p
p
,
)
,
(
  • For
  • capital extraction

2
1
2
1
ö
æ
å

ç
-


p
p
N
p
N
p
S
,
const
,
,

ç
0
0
0
i
i
i
???
ø
è
i
-

N
N
p
S
)
(
0
0
0
?
9
Capital dissipation
t ?? t fixed
  • s g(c,p)(cp) capital dissipation (trading
    costs)

10
Minimal dissipation processes in thermodynamics
For ? a( p )g( p, u ) We get
11
Minimal dissipation processes in thermodynamics
Heat transfer p T1, u T2
12
Minimal dissipation processes in thermodynamics
13
Minimal dissipation processes in thermodynamics
If
14
Stationary state of open macro system
  • Thermodynamics
  • n power, p1iTi
  • q heat,
  • g mass,
  • p intensive variables

for
å
å


g
p
p
g
q
p
p
q
,
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,
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,
)
,
(
i
j
i
ij
i
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i
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å

g
,
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i
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é
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i
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.
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ij



m
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1
0
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i
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15
If 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).
16
Stationary states of open macro systems
  • Microeconomics
  • ui prices,
  • p estimates

17
If 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.
18
Optimal 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

19
If
exergy
20
Separation systems
21
Microeconomics. Profitability ?
  • E? analogous of exergy .
  • t given
  • c(t) obeys conditions of minimal dissipation
    during all contacts
  • ?
  • obeys the conditions

22
Realizability area
Thermodynamics (heat engine)
23
Realizability area
Microeconomics (intermediary)
24
Optimal processes in macro systems
(thermodynamics and economics)
  • e-mail tsirlin_at_sarc.botik.ru
  • vladimir.kazakov_at_uts.edu.au
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