In sequential games of traditional game theory, backward induction guarantees existence of Nash equilibrium by yielding a sub-game perfect equilibrium. But if payoffs range over a partially ordered set instead of the reals, then the backward induction predicate does no longer imply the Nash equilibrium predicate. Non-determinism is a solution: a suitable non-deterministic backward induction fun...

This is a brief review of recently derived relations describing the behaviour of systems far from equilibrium. They include the Fluctuation Theorem, Jarzynski’s and Crooks’ equalities, and an extended form of the Second Principle for general steady states. They are very general and their proofs are, in most cases, disconcertingly simple.

These lecture notes give a basic introduction to the physics of phase transitions under non-equilibrium conditions. The notes start with a general introduction to non-equilibrium statistical mechanics followed by four parts. The first one discusses the universality class of directed percolation, which plays a similar role as the Ising model in equilibrium statistical physics. The second one giv...

We employ the influence functional technique to trace out the photonic contribution from full quantum electrodynamics. The reduced density matrix propagator then is constructed for the electron field. We discuss the role of time-dependent renormalization in the propagator and focus our attention to the possibility of obtaining a dynamically induced superselection rule. As a final application of...

Statistical mechanics provides a well-established link between microscopic equilibrium states and thermodynamics. If one considers systems out of equilibrium, the link between microscopic dynamical properties and nonequilibrium macroscopic states is more difficult to establish [1,2]. For systems lying near equilibrium, linear response theory provides a route to derive linear macroscopic laws an...

The mathematical physics of mechanical systems in thermal equilibrium is a well studied, and relatively easy, subject, because the Gibbs distribution is in general an adequate guess for the equilibrium state. On the other hand, the mathematical physics of non-equilibrium systems, such as that of a chain of masses connected with springs to two (infinite) heat reservoirs is more difficult, precis...

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By designating a system as “near equilibrium”, we mean that the system is perturbed from its equilibrium state by some time-dependent external force f(t). The external force is deterministic, not random; typical examples include mechanical forces and forces due to an applied electric or magnetic field. This force drives the expectation values of some of the system’s observables away from their ...

Local Shannon entropy lies at the heart of modern thermodynamics, with much discussion of trajectory-dependent entropy production. When taken at both boundaries of a process in phase space, it reproduces the second law of thermodynamics over a finite time interval for small scale systems. However, given that entropy is an ensemble property, it has never been clear how one can assign such a quan...

The soil environment immediately around a root frequently has a larger number of microorganisms compared to soil just a few millimeters away from a root. This zone of influence is called the rhizosphere (Rovira, 1991), which is composed of many groups of organisms that are capable of affecting plant health beneficially and deleteriously (Schippers et al., 1987). Putting greens are artificially ...