Derivation of the Local-Mean Stochastic Quantum Force

We regard the non-relativistic Schrodinger equation as an ensemble mean representation of the stochastic motion of a single particle in a vacuum, subject to an undefined stochastic quantum force. The local mean of the quantum force is found to be proportional to the third spatial derivative of the probability density function, while its associated pressure is proportional to the second spatial derivative. The latter arises from the single particle diluted gas pressure, and this observation allows to interpret the quantum Bohm potential as the energy required to put a particle in a bath of fluctuating vacuum at constant entropy and volume. The stochastic force expectation value is zero and is uncorrelated with the particle location, thus does not perform work on average. Nonetheless it is anti-correlated with volume and this anti-correlation leads to an uncertainty relation. We analyze the dynamic Gaussian solution to the Schrodinger equation as a simple example for exploring the mean properties of this quantum force. We conclude with a few possible interpretations as to the origins of quantum stochasticity.Comment: Accepted to Fluctuation and Noise Letters. This manuscript supersedes arXiv:1607.0284

On entropy production in the Madelung fluid and the role of Bohm's potential in classical diffusion

The Madelung equations map the non-relativistic time-dependent Schrodinger equation into hydrodynamic equations of a virtual fluid. Here we show that an increase of the Boltzmann entropy of this Madelung fluid is proportional to the expectation value of its velocity divergence. Hence, entropy growth is accompanied by expansion resulting from the ability of the Madelung fluid to be compressible. The compressibility itself reflects superposition of solutions of the Schrodinger equation. Thus, in unitary processes where the Madelung fluid expands and then shrinks, the Boltzmann entropy may, correspondingly, grow and then decrease. The notion of entropy growth due to expansion is common in diffusive processes, however in the latter the process is irreversible. Much unlike the Boltzmann entropy, the von Neumann entropy, does not vary with time. To elucidate the physical underpinning of the Boltzmann entropy, we examine several specific examples. We demonstrate that, for classical diffusive processes, the "force" accelerating diffusion has the form of the positive gradient of the quantum Bohm potential. In the Madelung fluid, the advective and the diffusive velocities correspond respectively to the the real and imaginary parts of the complex momentum. We find that the diffusion coefficient provides a lower bound of Heisenberg uncertainty type product between the gas mean free path and the Brownian momentum.Comment: 9 pages. The second version contains more examples and explanation

Unintended Legislative Inertia

Institutional and political forces create strong inertial pressures that make updating legislation a difficult task. As a result, laws often stagnate, leading to the continued existence of obsolete rules and policies that serve long-forgotten purposes. Recognizing this inertial power, legislatures over the last few decades have increasingly relied on a perceived solution -- temporary legislation. In theory, this measure avoids inertia by requiring legislators to choose to extend a law deliberately. This Article argues that temporary legislation is a double-edged sword. While some temporary laws ultimately expire, many perpetuate through cycles of extension and reauthorization. Temporary legislation often creates its own inertial force, leading to the unintended permanence of what was originally believed to be provisional. Using a case study from a large public subsidy adopted as a localized fix to a temporary problem, this Article demonstrates how the subsidy has inadvertently grown in scope and in size, creating its own inertial pathways that made its repeal exceedingly difficult. Path-dependent dynamics of temporary legislation affect not only present-day policies, but also the ability of legislatures to resist status quo bias and bring about legal change. This Article concludes with normative insights on ways to utilize flexible rulemaking whilst circumventing legislative inaction. Careful design of expiring provisions that is aware of the inertial power of temporary legislation can effectively ensure that laws are kept or discarded given their merits, not by force of the past

Innovation Agents

The standard narrative of entrepreneurship is one of self-employed creative individuals working out of their garage or independently owned start-up companies. Intrapreneurship— where employees are responsible for being alert to new opportunities inside firms—is another model for developing innovations. Relatively little is known, however, about the latter process through which large, complex firms engage in groundbreaking corporate entrepreneurship. This Article’s focus is on these types of innovation agents. It provides a thorough account of the positive and negative spillovers of intrapreneurial firms while making the following key points: First, intrapreneurial companies utilize their economies of scale, scope, and age to deliver innovations to the masses. They transform ideas, labor, and raw materials into tangible assets that can be traded in the market. Second, in doing so they offer individual entrepreneurs opportunities to capitalize their knowledge. Sustaining entrepreneurs’ prospects for supra-competitive profits is the main engine that motivates the latter to invest in discoveries in the first place. Lastly, intrapreneurial firms also serve asgreenhouses for entrepreneurship through the migration of their own talented labor in the market. While these spillovers have tremendous societal benefits, they can also introduce harms. First, the race for the next breakthrough might result in anticompetitive behavior by rivals who conspire with employees-intrapreneurs to leave their firms and take with them confidential information. Second, intrapreneurs often aspire to undertake their own independent journey. In so doing, they leave secure positions and high salaries while carrying valuable knowledge and expertise. This, in return, often prompts intrapreneurial firms to act opportunistically and lock-in or lock-out intrapreneurs in restrictive and wasteful arrangements. As a solution, this Article proposes ways law can balance the positive and negative spillovers of intrapreneurship and ways the tax system can help achieve such result

Through the Lens of Innovation

The legal system constantly follows the footsteps of innovation and attempts to discourage its migration overseas. Yet, present legal rules that inform and explain entrepreneurial circumstances lack a core understanding of the concept of entrepreneurship. By its nature, law imposes order. It provides rules, remedies, and classifications that direct behavior in a consistent manner. Entrepreneurship turns on the contrary. It entails making creative judgments about the unknown. It involves adapting to disarray. It thrives on deviation as opposed to traditional causation. This Article argues that these differences matter. It demonstrates that current laws lock entrepreneurs into inefficient legal routes. Through specific legal classifications, it points to significant distortionary effects. It theorizes that a legal culture that wishes to entice entrepreneurship is one that requires legal agents to think like entrepreneurs. Thereafter, it offers a bridge between law and entrepreneurship by providing policymakers with tools to recognize its distinctive modus operandi

Innovation Agents

The standard narrative of entrepreneurship is one of self-employed creative individuals working out of their garage or independently owned start-up companies. Intrapreneurship--where employees are responsible for being alert to new opportunities inside firms--is another model for developing innovations. Relatively little is known, however, about the latter process through which large, complex firms engage in groundbreaking corporate entrepreneurship. This Article\u27s focus is on these types of innovation agents. It provides a thorough account of the positive and negative spillovers of intrapreneurial firms while making the following key points: First, intrapreneurial companies utilize their economies of scale, scope, and age to deliver innovations to the masses. They transform ideas, labor, and raw materials into tangible assets that can be traded in the market. Second, in doing so they offer individual entrepreneurs opportunities to capitalize their knowledge. Sustaining entrepreneurs\u27 prospects for supra-competitive profits is the main engine that motivates the latter to invest in discoveries in the first place. Lastly, intrapreneurial firms also serve as greenhouses for entrepreneurship through the migration of their own talented labor in the market. While these spillovers have tremendous societal benefits, they can also introduce harms. First, the race for the next breakthrough might result in anticompetitive behavior by rivals who conspire with employees-intrapreneurs to leave their firms and take with them confidential information. Second, intrapreneurs often aspire to undertake their own independent journey. In so doing, they leave secure positions and high salaries while carrying valuable knowledge and expertise. This, in return, often prompts intrapreneurial firms to act opportunistically and lock-in or lock-out intrapreneurs in restrictive and wasteful arrangements. As a solution, this Article proposes ways law can balance the positive and negative spillovers of intrapreneurship and ways the tax system can help achieve such result