7,518 research outputs found
Temperature in and out of equilibrium: a review of concepts, tools and attempts
We review the general aspects of the concept of temperature in equilibrium
and non-equilibrium statistical mechanics. Although temperature is an old and
well-established notion, it still presents controversial facets. After a short
historical survey of the key role of temperature in thermodynamics and
statistical mechanics, we tackle a series of issues which have been recently
reconsidered. In particular, we discuss different definitions and their
relevance for energy fluctuations. The interest in such a topic has been
triggered by the recent observation of negative temperatures in condensed
matter experiments. Moreover, the ability to manipulate systems at the micro
and nano-scale urges to understand and clarify some aspects related to the
statistical properties of small systems (as the issue of temperature's
"fluctuations"). We also discuss the notion of temperature in a dynamical
context, within the theory of linear response for Hamiltonian systems at
equilibrium and stochastic models with detailed balance, and the generalised
fluctuation-response relations, which provide a hint for an extension of the
definition of temperature in far-from-equilibrium systems. To conclude we
consider non-Hamiltonian systems, such as granular materials, turbulence and
active matter, where a general theoretical framework is still lacking.Comment: Review article, 137 pages, 12 figure
Multi-parameter generalization of nonextensive statistical mechanics
We show that the stochastic interpretation of Tsallis' thermostatistics given
recently by Beck [Phys. Rev. Lett {\bf 87}, 180601 (2001)] leads naturally to a
multi-parameter generalization. The resulting class of distributions is able to
fit experimental results which cannot be reproduced within the Boltzmann's or
Tsallis' formalism.Comment: ReVTex 4.0, 4 eps figure
Synchronicity From Synchronized Chaos
The synchronization of loosely coupled chaotic oscillators, a phenomenon
investigated intensively for the last two decades, may realize the
philosophical notion of synchronicity. Effectively unpredictable chaotic
systems, coupled through only a few variables, commonly exhibit a predictable
relationship that can be highly intermittent. We argue that the phenomenon
closely resembles the notion of meaningful synchronicity put forward by Jung
and Pauli if one identifies "meaningfulness" with internal synchronization,
since the latter seems necessary for synchronizability with an external system.
Jungian synchronization of mind and matter is realized if mind is analogized to
a computer model, synchronizing with a sporadically observed system as in
meteorological data assimilation. Internal synchronization provides a recipe
for combining different models of the same objective process, a configuration
that may also describe the functioning of conscious brains. In contrast to
Pauli's view, recent developments suggest a materialist picture of
semi-autonomous mind, existing alongside the observed world, with both
exhibiting a synchronistic order. Basic physical synchronicity is manifest in
the non-local quantum connections implied by Bell's theorem. The quantum world
resides on a generalized synchronization "manifold", a view that provides a
bridge between nonlocal realist interpretations and local realist
interpretations that constrain observer choice .Comment: 1) clarification regarding the connection with philosophical
synchronicity in Section 2 and in the concluding section 2) reference to
Maldacena-Susskind "ER=EPR" relation in discussion of role of wormholes in
entanglement and nonlocality 3) length reduction and stylistic changes
throughou
Stress Propagation through Frictionless Granular Material
We examine the network of forces to be expected in a static assembly of hard,
frictionless spherical beads of random sizes, such as a colloidal glass. Such
an assembly is minimally connected: the ratio of constraint equations to
contact forces approaches unity for a large assembly. However, the bead
positions in a finite subregion of the assembly are underdetermined. Thus to
maintain equilibrium, half of the exterior contact forces are determined by the
other half. We argue that the transmission of force may be regarded as
unidirectional, in contrast to the transmission of force in an elastic
material. Specializing to sequentially deposited beads, we show that forces on
a given buried bead can be uniquely specified in terms of forces involving more
recently added beads. We derive equations for the transmission of stress
averaged over scales much larger than a single bead. This derivation requires
the Ansatz that statistical fluctuations of the forces are independent of
fluctuations of the contact geometry. Under this Ansatz, the
-component stress field can be expressed in terms of a d-component
vector field. The procedure may be generalized to non-sequential packings. In
two dimensions, the stress propagates according to a wave equation, as
postulated in recent work elsewhere. We demonstrate similar wave-like
propagation in higher dimensions, assuming that the packing geometry has
uniaxial symmetry. In macroscopic granular materials we argue that our approach
may be useful even though grains have friction and are not packed
sequentially.=17Comment: 15 pages, 4 figures, revised vertion for Phys. Rev.
The effective temperature
This review presents the effective temperature notion as defined from the
deviations from the equilibrium fluctuation-dissipation theorem in out of
equilibrium systems with slow dynamics. The thermodynamic meaning of this
quantity is discussed in detail. Analytic, numeric and experimental
measurements are surveyed. Open issues are mentioned.Comment: 58 page
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