A rigourous demonstration of the validity of Boltzmann's scenario for the spatial homogenization of a freely expanding gas and the equilibration of the Kac ring

Boltzmann provided a scenario to explain why individual macroscopic systems composed of a large number $N$ of microscopic constituents are inevitably (i.e., with overwhelming probability) observed to approach a unique macroscopic state of thermodynamic equilibrium, and why after having done so, they are then observed to remain in that state, apparently forever. We provide here rigourous new results that mathematically prove the basic features of Boltzmann's scenario for two classical models: a simple boundary-free model for the spatial homogenization of a non-interacting gas of point particles, and the well-known Kac ring model. Our results, based on concentration inequalities that go back to Hoeffding, and which focus on the typical behavior of individual macroscopic systems, improve upon previous results by providing estimates, exponential in $N$, of probabilities and time scales involved

The dS/dS Correspondence

We present a holographic duality for the de Sitter static patch which consolidates basic features of its geometry and the behavior of gravity and brane probes, valid on timescales short compared to the decay or Poincare recurrence times. Namely de Sitter spacetime $dS_d(R)$ in $d$ dimensions with curvature radius $R$ is holographically dual to two conformal field theories on $dS_{d-1}(R)$, cut off at an energy scale 1/R where they couple to each other and to $d-1$ dimensional gravity. As part of our analysis, we study brane probes in de Sitter and thermal Anti de Sitter spaces, and interpret the terms in the corresponding DBI action via strongly coupled thermal field theory. This provides a dual field theoretic interpretation of the fact that probes take forever to reach a horizon in general relativity.Comment: 29 pages, harvmac big; 3 figures; v2: references added, minor typo fixe

Visions of a Martian Future

As we look beyond our terrestrial boundary to a multi-planetary future for humankind, it becomes paramount to anticipate the challenges of various human factors on the most likely scenario for this future: permanent human settlement of Mars. Even if technical hurdles are circumvented to provide adequate resources for basic physiological and psychological needs, Homo sapiens will not survive on an alien planet if a dysfunctional psyche prohibits the utilization of these resources. No matter how far we soar into the stars, our psychologies for future generations will be forever tethered to the totality of our surroundings. By shaping our environment toward survival and welfare during the voyage to Mars and in a Martian colony, we indirectly shape our psyches and prepare them for a mission of unprecedented alienation and duration. Once on Mars, human factors such as leadership structure, social organization and code of conduct, group size, gender balance, developmental cycle, mobility, length of stay and the ecological settings and type and manner of subsistence, will create a novel Martian culture. The degree that settlers are severed from the Earth will affect how radically foreign this culture will be when compared with cultures on Earth

Healing Waters

When Ryan Jones graduated from Gardner-Webb University in May of last year, he made plans to tour the country with a friend before starting life in the ‘real world.’ He never imagined that a car accident would change his plans and perspective forever. A year later, he is fully recovered, but is now motivated to make life better for those without access to the basic necessity of clean water.https://digitalcommons.gardner-webb.edu/gardner-webb-newscenter-archive/2786/thumbnail.jp

Termination Criteria for Solving Concurrent Safety and Reachability Games

We consider concurrent games played on graphs. At every round of a game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety objective to stay forever in a given set of states, and its dual, the reachability objective to reach a given set of states. We present in this paper a strategy improvement algorithm for computing the value of a concurrent safety game, that is, the maximal probability with which player~1 can enforce the safety objective. The algorithm yields a sequence of player-1 strategies which ensure probabilities of winning that converge monotonically to the value of the safety game. Our result is significant because the strategy improvement algorithm provides, for the first time, a way to approximate the value of a concurrent safety game from below. Since a value iteration algorithm, or a strategy improvement algorithm for reachability games, can be used to approximate the same value from above, the combination of both algorithms yields a method for computing a converging sequence of upper and lower bounds for the values of concurrent reachability and safety games. Previous methods could approximate the values of these games only from one direction, and as no rates of convergence are known, they did not provide a practical way to solve these games

Care Work in Massachusetts: A Call for Racial and Economic Justice for a Neglected Sector

Care work has forever been critical to the health and basic functioning of our society. With the steady aging of our population, care jobs are also among the fastest growing in our economy. These jobs are staffed predominantly by immigrant women and women of color, so despite their societal importance, racial prejudice and gender discrimination have led to a systematic devaluation of this sort of labor. In this paper, Boston Indicators and SkillWorks provide a demographic profile of care workers in Massachusetts and pairs that with a job quality analysis for a few key subsectors

Resurrecting Keynes to Revamp the International Monetary System

There is a broad consensus that the current, large U.S. current-account deficits financed with foreign capital inflows at low interest rates cannot continue forever; there is much less consensus on when the system is likely to end and how badly it will end. The paper resurrects the basic principles of the plan Keynes wrote for the Bretton Woods Conference to propose an alternative to the current international monetary system. We argue for the creation of a supranational bank money that would coexist along side national currencies and for the establishment of a new international clearing union. The new international money would be created against domestic earning assets of the Fed and the ECB. In addition to recording credit and debit entries of the supranational bank money, the new agency would determine the size of quotas, the size and time length of overdrafts, and the coordination of monetary policies. The substitution of supranational bank money for dollars would harden the external constraint of the United States and resolve the n-1 redundancy problem.Keynes Plan, external imbalances, exchange rates, international monetary system, key currency, supranational bank money