Title: A Statistical Physics Model of Technology Transfer
1A Statistical Physics Model of Technology
Transfer
- Ken Dozier
- USC Viterbi School of Engineering Technology
Transfer Center - Technology Transfer Society (T2S) 26th Annual
Conference - Albany, NY
- October 1, 2004
2Presentation
- Problem (7 slides)
- Approach (9 slides)
- Results (5 slides)
- Conclusions (1 slide)
- Future (1 slide)
3A System of Forces in Organization
Direction
Cooperation
Efficiency
Proficiency
Competition
Concentration
Innovation
Source The Effective Organization Forces and
Form, Sloan Management Review, Henry Mintzberg,
McGill University 1991
4Make Sell vs Sense Respond
Chart SourceCorporate Information Systems and
Management, Applegate, 2000
5Supply Chain (Firm)
Source Gus Koehler, University of Southern
California Department of Policy and Planning,
2002
6Supply Chain (Government)
Source Gus Koehler, University of Southern
California Department of Policy and Planning,
2002
7Supply Chain (Framework)
Source Gus Koehler, University of Southern
California Department of Policy and Planning,
2002
8Supply Chain (Interactions)
Source Gus Koehler, University of Southern
California Department of Policy and Planning,
2002
9Theoretical Environment
Seven Organizational Change Propositions
Framework, Framing the Domains of IT
Management Zmud 2002
10Framework Assumptions
- U.S. Manufacturing Industry Sectors can be
Stratified using Average Company Size and
Assigned to Layers of the Change Propositions - Layers with Large Average Firm Size Will Have
High B and Lowest T(1/B) - Layers with Small Average Firm Size Will Have Low
B and High T (1/B) - The B and T Values Provide the Entry Point to
Thermodynamics
11 Thermodynamics ?
- Ample Examples of Support
- Long Term Association with Economics
- Krugman, 2004
- Systems Far from Equilibrium can be Treated by
(open systems) Thermodynamics - Thorne, Fernando, Lenden, Silva, 2000
- Thermodynamics and Biology Drove New Growth
Economics - Costanza, Perrings, and Cleveland, 1997
- Economics and Thermodynamics are Constrained
Optimization Problems - Smith and Foley, 2002
12Thermodynamics ?
- Mathematical Complexity Could Discourage
Practitioners - Requires an Extension of Traditional Energy
Abstractions - Expansion May Require Knowledge to be Considered
Pseudo Form of Energy?! - Knowledge Potential and Kinetic States?!
- Patent potential
- Technology Transfer Kinetic
- Tacit versus Explicit
13Constrained Optimization Approach
- Thermodynamics
- A systematic mathematical technique for
determining what can be inferred from a minimum
amount of data - Key Many microstates possible to give an
observed macrostate - Basic principle Most likely situation given by
maximization of the number of microstates
consistent with an observed macrostate - Why pseudo?
- Conventional thermodynamics energy rules
supreme - Thermodynamics of economics phenomena energy
shown by statistical physics analysis to be
replaced by quantities related to productivity,
i.e. output per employee
14Pseudo-Thermodynamic Approach
- Macrostate givens N and E, and census-reported
sector productivities p(i) - Total manufacturing output of a metropolitan area
N - Total number of manufacturing employees in
metropolitan area E - Productivities p(i), where p(i) is the
output/employee of manufacturing sector I -
- Convenient to work with a dimensionless
productivity - p(i) p(i)/ltPgt (Chang Simplification)
- where ltPgt is the average value for the
manufacturing sectors of the output/employee for
the metropolitan area. - Thermodynamic problem with the foregoing
givens - What is the most likely distribution of employees
e(i) over the sectors that comprise the
metropolitan manufacturing activity ? - What is the most likely distribution of output
n(i) over the sectors?
15Pseudo-Thermodynamic Approach
- Relations between total metropolitan employee
number E and output N and sector employee numbers
e(i) and outputs n(i) - E S e(i)
- N S n(i)
-
- Relation between sector outputs, employee
numbers, and productivities -
- n(i) e(i) p(i)
-
- n(i) e(i)ltPgtp(i)
-
- Accordingly,
- N S n(i) S e(i) ltPgt p(i)
16Pseudo-Thermodynamic Approach
- Look for the (microstate) distribution e(i) that
will give the maximum number of ways W in which a
known (macrostate) N and E can be achieved. - Number of ways (distinguishable permutations) in
which N and E can be achieved - W N! / ? n(i)!E! / ? e(i)!
- Maximization of W subject to constraint
equations of previous slide - Introduce Lagrange multipliers ? and ß to take
into account constraint equations - Deal with lnW rather than W in order to use
Stirling approximation for natural logarithm of
factorials for large numbers - lnn! gt n lnn- n when n gtgt1
17Optimization
- Maximization of lnW with Lagrange multipliers
- ? / ? e(i) lnW ?N-Sn(i) ßE-Se(i)
0 - Use of relation between n(i) and e(i) and p(i)
- ?/ ? e(i) lnW ?N-S e(i)ltPgtp(i)
ßE-Se(i) 0 - where, using Stirlings approximation
- lnW N(lnN-1) E(lnE-1) - S e(i)p(i)ltPgtlne(i)
p(i)ltPgt-1 -
- - S e(i)lne(i)-1
18Resulting Distributions
- Employee distribution over manufacturing sectors
e(i) - e(i) D p(i)-p(i)/p(i)1 Exp -
ßp(i)/1p(i) - where the constants D and ß are expressible
in terms of the Lagrange multipliers that allow
for the constraint relations -
- Output distribution over manufacturing sectors
n(i) - n(i) DltPgt p(i) 1/p(i)1 Exp -
ßp(i)/1p(i) - Two interesting features
- NonMaxwellian i.e. Not a simple exponential
- An inverse temperature factor (or bureacratic
factor) ß that gives the disperion of the
distribution
19Figure 1 Predicted shape of output n(i) vs.
productivity p(i) for a sector bureaucratic
factor ß 0.1 lower curve and ß1 upper
curve.
Output
n(i)
p(i)
20Figure 2. Predicted shape of employee number
e(i) vs. productivity p(i) for a sector
bureaucratic factor ß 0.1 lower curve and ß1
upper curve.
Employment
e(i)
p(i)
21Figure 3. Data Employment vs productivity for
the 140 manufacturing sectors in the Los Angeles
consolidated metropolitan statistical area in 1997
Data
22Productivity Paradox
Figure 4. Productivities in Los Angeles
consolidated metropolitan statistical area.
(Ignore Industry Sector Average Company Size)
1.8
1.6
1.4
1.2
1
Ratio of 1997 productivity to 1992 productivity
0.8
0.6
0.4
0.2
0
0
15
30
45
60
75
90
105
120
135
Average rank of per capita information technology
expenditure
23Stratified
Figure 5. Productivities in Los Angeles
consolidated metropolitan statistical area. (3
Industry sector sizes)
1.8
1.6
26 largest company size sectors
1.4
1.2
26 intermediate company size sectors
24 smallest company size sectors
1
Ratio of 1997 productivity to 1992 productivity
0.8
0.6
0.4
0.2
0
0
15
30
45
60
75
90
105
120
135
Average rank of per capita information technology
expenditure
24Conclusions
- Agreement with industry sector behavior to
thermodynamic model. - Consistent across multiple definitions of
productivity. - Interaction between average per capita
expenditure on information technology,
organizational size and the average increase in
productivity - IT investment alters B
- High IT (electronics) Investor changed their B,
Low IT Investor (heavy springs) did not
25Future Work
- Examine NAICS consistent 2002 and 1997 U.S.
manufacturing economic census data - Use seven organizational change proposition
strata to further explore the linkage between
organizational size and productivity. - Compare results across the strata and within each
stratum - Check for compliance to thermodynamic model
- Expand to technology transfer
26Comparison of Statistical Formalism in Physics
and in Economics
Variable Physics Economics State
(i) Hamiltonian eigenfunction Production
site Energy Hamiltonian eigenvalue Ei
Unit production cost Ci Occupation number
Number in state Ni Production output
Ni Partition function Z ?exp-(1/kBT)Ei ?
exp-ßCi Free energy F kBT lnZ (1/ß)
lnZ Generalized force f?
?F/?? ?F/?? Example Pressure Technology Ex
ample Electric field x charge Knowledge Entropy
(randomness) - ?F / ?T kBß2?F/??
27Maxwell-Boltzmann distributions for different
effective industry sector temperatures and
productivities
Output
High temperature flatter curves
High productivity
Low productivity
Unit cost
28Example Maxwell-Boltzmann dependence of output
on unit costs
Ln Output
High productivity, High temperature
High productivity, Low temperature
Low productivity, High temperature
Low productivity, Low temperature
Unit costs
29Conservation law for Technology Transfer
Total cost of production C ? C(i) exp
-ß(C(i) F)
Effect of a change d? in a parameter ? in the
system and a change d ß In bureaucratic factor
dC - ltf? gt d? ß ?2F/ ?ß?? d? ?2ßF/
?ß2 dß
which can be rewritten
dC - ltf? gt d? TdS
Significance First term on the RHS
describes lowering of unit cost of production.
Second term on RHS describes increase in
entropy (temperature)
30Effects of Technology Transfer
Ln Output
High productivity, High temperature
Costs down
High productivity, Low temperature
Low productivity, High temperature
Entropy up
Low productivity, Low temperature
Unit costs
31Very preliminary examples
(1) Semiconductor and (2) Heavy spring
manufacturing in consolidated LA metropolitan
area US Economic census data for 1992 and 1997
- LA consolidated metropolitan statistical area
(CMSA) comprised of 4 primary metropolitan
statistical areas (PMSAs) - Los Angeles-Long Beach PMSA
- Orange County PMSA
- Riverside-San Bernardino County PMSA
- Ventura County PMSA
- Semiconductor and heavy spring production spread
over all 4 PMSAs - Semiconductor manufacturing sector investment in
information technology high while heavy spring
manufacturing sector investment in information is
low
32Example 1. Semiconductor production in
consolidated LA metropolitan area in 1992 and 1987
- Observations on a sector with large investment in
information - Correlation between PMSAs with highest
production and lowest unit costs - Qualitatively consistent with a Boltzmann
distribution - Large decrease in temperature (increase in
bureaucratic factor) between 1992 and 1997 - slope 7 x larger in 1997 than in 1992
- Large increase in employee productivity between
1992 and 1997 - Value of shipments per employee 1.8 x larger in
1997 230K/employee than in 1992
33Semiconductor example Movement between 1992 and
1997 on Maxwell Boltzmann plot
Ln Output
High productivity, High temperature
High productivity, Low temperature
Low productivity, High temperature
Low productivity, Low temperature
Unit costs
34Example 2. Heavy springs production in
consolidated LA metropolitan area in 1992 and 1987
- Observations on a sector with small investment in
information - A lower sector temperature in 1992 than
semiconductor sector slope of -5.5 compared to
-1.2 for semiconductor sector - Possibly higher sector temperature in 1997
- Clustering of PMSAs around (MC)/S 0.5
- Virtually no increase in productivity per
employee between 1992 and 1997 - Close to 120K/employee both years
35Heavy spring example Movement between 1992 and
1997 on Maxwell Boltzmann plot
Ln Output
High productivity, High temperature
High productivity, Low temperature
Low productivity, High temperature
Low productivity, Low temperature
Unit costs