Teaching the third law of thermodynamics

This work gives a brief summary of major formulations of the third law of thermodynamics and their implications, including the impossibility of perpetual motion of the third kind. The last sections of this work review more advanced applications of the third law to systems with negative temperatures and negative heat capacities. The relevance of the third law to protecting the arrow of time in general relativity is also discussed. Additional information, which may useful in analysis of the third law, is given in the Appendices. This short review is written to assist lecturers in selecting a strategy for teaching the third law of thermodynamics to engineering and science students. The paper provides a good summary of the various issues associated with the third law, which are typically scattered over numerous research publications and not discussed in standard textbooks.Comment: 22 pages, 5 figure

Intransitivity in Theory and in the Real World

This work considers reasons for and implications of discarding the assumption of transitivity, which (transitivity) is the fundamental postulate in the utility theory of Von Neumann and Morgenstern, the adiabatic accessibility principle of Caratheodory and most other theories related to preferences or competition. The examples of intransitivity are drawn from different fields, such as law, biology, game theory, economics and competitive evolutionary dynamic. This work is intended as a common platform that allows us to discuss intransitivity in the context of different disciplines. The basic concepts and terms that are needed for consistent treatment of intransitivity in various applications are presented and analysed in a unified manner. The analysis points out conditions that necessitate appearance of intransitivity, such as multiplicity of preference criteria and imperfect (i.e. approximate) discrimination of different cases. The present work observes that with increasing presence and strength of intransitivity, thermodynamics gradually fades away leaving space for more general kinetic considerations. Intransitivity in competitive systems is linked to complex phenomena that would be difficult or impossible to explain on the basis of transitive assumptions. Human preferences that seem irrational from the perspective of the conventional utility theory, become perfectly logical in the intransitive and relativistic framework suggested here. The example of competitive simulations for the risk/benefit dilemma demonstrates the significance of intransitivity in cyclic behaviour and abrupt changes in the system. The evolutionary intransitivity parameter, which is introduced in the Appendix, is a general measure of intransitivity, which is particularly useful in evolving competitive systems. Quantum preferences are also considered in the Appendix.Comment: 44 pages, 14 figures, 47 references, 6 appendice

Symmetric and antisymmetric forms of the Pauli master equation (for interaction of matter and antimatter quantum states)

When applied to matter and antimatter states, the Pauli master equation (PME) may have two forms: time-symmetric, which is conventional, and time-antisymmetric, which is suggested in the present work. The symmetric and antisymmetric forms correspond to symmetric and antisymmetric extensions of thermodynamics from matter to antimatter --- this is demonstrated by proving the corresponding H-theorem. The two forms are based on the thermodynamic similarity of matter and antimatter and differ only in the directions of thermodynamic time for matter and antimatter (the same in the time-symmetric case and the opposite in the time-antisymmetric case). We demonstrate that, while the symmetric form of PME predicts an equi-balance between matter and antimatter, the antisymmetric form of PME favours full conversion of antimatter into matter. At this stage, it is impossible to make an experimentally justified choice in favour of the symmetric or antisymmetric versions of thermodynamics since we have no experience of thermodynamic properties of macroscopic objects made of antimatter, but experiments of this kind may become possible in the future.Comment: 12 pages, 2 figure

Duration and Term Structure of Trade Agreements

Why are some trade agreements concluded for a limited period of time while others have the form of evergreen contracts supplemented with an advance termination notice clause? We use a dynamic incomplete contracting model to demonstrate that the time structure of the trade agreement is related to the nature of the underlying trade-related investments (or other types of irreversible resource adjustments). If these investments are lumpy and specialized to trade in a particular homogeneous good, the agreements with the \u85xed term of duration are more likely. The xed-term agreement provides incentives for the initial investment but leaves the parties the exibility to revisit the need for future investment by resorting to renegotiation. If the agreement covers trade in goods or services requiring incremental investments with spillovers of the investment bene\u85ts across industries, there is a lower risk of overinvestment. Therefore, the parties are more likely to choose an evergreen agreement (with an advance termination notice or an escape clause). We show that these predictions are consistent with the econometric evidence on the trade agreements to which the U.S. is a party. We are grateful to Arnaud Costinot, Petros Mavroidis, Marc Melitz and the participants of the Midwest In

Asymptotic properties of Arnold tongues and Josephson effect

A three-parametrical family of ODEs on a torus arises from a model of Josephson effect in a resistive case when a Josephson junction is biased by a sinusoidal microwave current. We study asymptotics of Arnold tongues of this family on the parametric plane (the third parameter is fixed) and prove that the boundaries of the tongues are asymptotically close to Bessel functions.Comment: 21 pages, 1 figur

Change of the *congruence canonical form of 2-by-2 matrices under perturbations

We study how small perturbations of a 2-by-2 complex matrix can change its canonical form for *congruence. We construct the Hasse diagram for the closure ordering on the set of *congruence classes of 2-by-2 matrices.Comment: 8 pages. arXiv admin note: substantial text overlap with arXiv:1105.216