O ne manifestation of the sec­ ond law of thermodynamics is that such devices as refrigera­ tors, which create inequalities of tem­ perature, require energy in order to operate. Conversely, an existing in­ equality of temperature can be ex­ ploited to do useful work-for exam­ ple by a steam engine, which exploits the temperature difference between its hot boiler and its cold condenser. Yet in 1...

The Second Law of Thermodynamics governs the average direction of all non-equilibrium dissipative processes. However it tells us nothing about their actual rates, or the probability of fluctuations about the average behaviour. The last few decades have seen significant advances, both theoretical and applied, in understanding and predicting the behaviour of non-equilibrium systems beyond what th...

An apparent violation of the second law of thermodynamics occurs when an atom coupled to a zero-temperature bath, being necessarily in an excited state, is used to extract work from the bath. Here the fallacy is that it takes work to couple the atom to the bath and this work must exceed that obtained from the atom. For the example of an oscillator coupled to a bath described by the single relax...

The geometric entropy in quantum field theory is not a Lorentz scalar and has no invariant meaning, while the black hole entropy is invariant. Renormalization of entropy and energy for reduced density matrices may lead to the negative free energy even if no boundary conditions are imposed. The presence of particles outside the horizon of a uniformly accelerated observer prevents the description...

Dubovsky and Sibiryakov recently proposed a scenario in which particles of different species propagate with different speeds due to their direct couplings to ghost condensate. It was argued that this extended version of ghost condensate allows a gedanken experiment leading to violation of the generalized second law. However, in the original ghost condensate scenario, difference in propagation s...

The probability distribution function for an out of equilibrium system may sometimes be approximated by a physically motivated "trial" distribution. A particularly interesting case is when a driven system (e.g., active matter) is approximated by a thermodynamic one. We show here that every set of trial distributions yields an inequality playing the role of a generalization of the second law. Th...

A few years ago I gave a method, mainly based on the second law of thermodynamics, for calculating the maximum efficiency with which light energy can be converted into so-called high grade energy such as work or Gibbs free energy (1) [cf. also (2)]. This efficiency approached zero with decreasing light intensity and with increasing temperature of the system for conversion of light energy. An es...

The development of U.S. corporate law has traditionally been explained through a race model: jurisdictions compete for corporate franchise taxes and thus corporate law converges towards efficiency. Recent critiques have undermined this argument without presenting a new model in its place. This paper develops theoretically and tests empirically two alternative theories of corporate law developme...

Discussion in this Essay is designed to explore recently introduced efficiency considerations and to compare developing law in the United States and the European Union. The following sections discuss why incorporation of efficiency factors has been controversial, explore efficiency analysis in connection with mergers under U.S. law, explore comparable developments in EU law, and, finally, offer...