Related papers: How and why does statistical mechanics work
At the core of equilibrium statistical mechanics lies the notion of statistical ensembles: a collection of microstates, each occurring with a given a priori probability that depends only on a few macroscopic parameters such as temperature,…
The methods of statistical mechanics are applied to two-dimensional foams under macroscopic agitation. A new variable -- the total cell curvature -- is introduced, which plays the role of energy in conventional statistical thermodynamics.…
When modelling driven steady states of matter, it is common practice either to choose transition rates arbitrarily, or to assume that the principle of detailed balance remains valid away from equilibrium. Neither of those practices is…
We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…
Within the abstract framework of dynamical system theory we describe a general approach to the Transient (or Evans-Searles) and Steady State (or Gallavotti-Cohen) Fluctuation Theorems of non-equilibrium statistical mechanics. Our main…
We derive the first two moments of generic positive stochastic functionals in terms of the one- and two-time probability density functions of the underlying random walk, and we prove ergodicity of observables in stationary random walks.…
Using generating functional and replica techniques, respectively, we study the dynamics and statics of a spherical Minority Game (MG), which in contrast with a spherical MG previously presented in J.Phys A: Math. Gen. 36 11159 (2003)…
Recent results obtained in quantum measurements indicate that the fundamental relations between three physical properties of a system can be represented by complex conditional probabilities. Here, it is shown that these relations provide a…
In this paper we develop a general formalism of a path approach for non-equilibrium statistical mechanics. Firstly, we consider the classical Gibbs approach for states and find that this formalism is ineffective for non-equilibrium…
Turbulence exhibits significant velocity fluctuations even if the scale is much larger than the scale of the energy supply. Since any spatial correlation is negligible, these large-scale fluctuations have many degrees of freedom and are…
Statistical equilibrium configurations are important in the physics of macroscopic systems with a large number of constituent degrees of freedom. They are expected to be crucial also in discrete quantum gravity, where dynamical spacetime…
Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system…
In a classically chaotic system that is ergodic, any trajectory will be arbitrarily close to any point of the available phase space after a long time, filling it uniformly. Using Born's rules to connect quantum states with probabilities,…
Statistical physics provides a useful perspective for the analysis of many complex systems; it allows us to relate microscopic fluctuations to macroscopic observations. Developmental biology, but also cell biology more generally, are…
Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic…
Quantum mechanics postulates the existence of states determined by a particle position at a single time. This very concept, in conjunction with superposition, induces much of the quantum-mechanical structure. In particular, it implies the…
Classical, Quantum and Relativistic mechanics elect time and space as fundamentals, extracting the measure of motion -velocity- from this static space-time platform. Conversely, the timelessness of Statistical mechanics computes the…
Numerical simulations have shown that certain driven nonlinear systems can be characterized by mean-field statistical properties often associated with ergodic dynamics [C.D. Ferguson, W. Klein, and J.B. Rundle, Phys. Rev. E 60, 1359 (1999);…
Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new…
The Birkhoff Ergodic Theorem asserts under mild conditions that Birkhoff averages (i.e. time averages computed along a trajectory) converge to the space average. For sufficiently smooth systems, our small modification of numerical Birkhoff…