A Statistical Physics Model of Technology Transfer

1. A 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

2. Presentation • Problem (7 slides) • Approach (9 slides) • Results (5 slides) • Conclusions (1 slide) • Future (1 slide)

3. A 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

4. Make & Sell vs Sense & Respond Chart Source:“Corporate Information Systems and Management”, Applegate, 2000

5. Supply Chain (Firm) Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002

6. Supply Chain (Government) Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002

7. Supply Chain (Framework) Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002

8. Supply Chain (Interactions) Source: Gus Koehler, University of Southern California Department of Policy and Planning, 2002

9. Market Redefinition Supply-chain Expansion Supply-chain Discovery Business Model Redefinition Business Model Refinement Business Process Redesign Business Process Improvement Theoretical Environment Seven Organizational Change Propositions Framework, “Framing the Domains of IT Management” Zmud 2002

10. Framework 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

12. Thermodynamics ? • 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

13. Constrained 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”

14. Pseudo-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)/<P> (Chang Simplification) where <P> 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?

15. Pseudo-Thermodynamic Approach • Relations between total metropolitan employee number E and output N and sector employee numbers e(i) and outputs n(i) E = Σ e(i) N = Σ n(i) • Relation between sector outputs, employee numbers, and productivities n(i) = e(i) p(i) n(i) = e(i)<P>p(i) • Accordingly, N = Σ n(i) = Σ e(i) <P> p(i)

16. Pseudo-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 β 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 ln{n!} => n ln{n}- n when n >>1

17. Optimization • Maximization of lnW with Lagrange multipliers  /  e(i) [ lnW + {N-Σn(i)} +β{E-Σe(i)}]= 0 • Use of relation between n(i) and e(i) and p(i): /  e(i) [ lnW + {N-Σ e(i)<P>p(i)} +β{E-Σe(i)}]=0 where, using Stirling’s approximation: lnW = N(lnN-1) +E(lnE-1) - Σ e(i)p(i)<P>[ln{e(i)p(i)<P>}-1] - Σ e(i)[ln{e(i)}-1]

18. Resulting Distributions • Employee distribution over manufacturing sectors e(i) e(i) = D p(i)-[p(i)/{p(i)+1}] Exp [- βp(i)/{1+p(i)}] where the constants D and β are expressible in terms of the Lagrange multipliers that allow for the constraint relations • Output distribution over manufacturing sectors n(i) n(i) = D<P> p(i) [1/{p(i)+1}] Exp [- βp(i)/{1+p(i)}] • Two interesting features: • NonMaxwellian – i.e. Not a simple exponential • An inverse temperature factor (or bureacratic factor) β that gives the disperion of the distribution

19. Figure 1: Predicted shape of output n(i) vs. productivity p(i) for a sector bureaucratic factor β = 0.1 [lower curve] and β=1 [upper curve]. Output n(i) p(i)

20. Figure 2. Predicted shape of employee number e(i) vs. productivity p(i) for a sector bureaucratic factor β = 0.1 [lower curve] and β=1 [upper curve]. Employment e(i) p(i)

21. Figure 3. Data Employment vs productivity for the 140 manufacturing sectors in the Los Angeles consolidated metropolitan statistical area in 1997 Data

22. Productivity 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

23. Stratified 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

24. Conclusions • 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

25. Future 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

26. Comparison of Statistical Formalism in Physics and in Economics VariablePhysicsEconomics 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[-βCi] Free energy F kBT lnZ (1/β) lnZ Generalized force fξ ∂F/∂ξ ∂F/∂ξ Example Pressure Technology Example Electric field x charge Knowledge Entropy (randomness) - ∂F / ∂T kBβ2∂F/∂ξ

27. Maxwell-Boltzmann distributions for different effective industry sector “temperatures” and productivities Output High temperature flatter curves High productivity Low productivity Unit cost

28. Example: 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

29. Conservation law for Technology Transfer Total cost of production C = ∑ C(i) exp [-β(C(i) – F)] Effect of a change dξ in a parameter ξ in the system and a change d β In bureaucratic factor dC = - <fξ > dξ + β [2F/ βξ] dξ + [2[βF]/ β2] dβ which can be rewritten dC = - <fξ > dξ + TdS Significance First term on the RHS describes lowering of unit cost of production. Second term on RHS describes increase in entropy (temperature)

30. Effects 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

31. Very 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 (PMSA’s) • 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 PMSA’s • Semiconductor manufacturing sector investment in information technology high while heavy spring manufacturing sector investment in information is low

32. Example 1. Semiconductor production in consolidated LA metropolitan area in 1992 and 1987 • Observations on a sector with large investment in information • Correlation between PMSA’s 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

33. Semiconductor 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

34. Example 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 PMSA’s around (M+C)/S = 0.5 • Virtually no increase in productivity per employee between 1992 and 1997 • Close to $120K/employee both years

35. Heavy 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