3,207 research outputs found
Non-analytic microscopic phase transitions and temperature oscillations in the microcanonical ensemble: An exactly solvable 1d-model for evaporation
We calculate exactly both the microcanonical and canonical thermodynamic
functions (TDFs) for a one-dimensional model system with piecewise constant
Lennard-Jones type pair interactions. In the case of an isolated -particle
system, the microcanonical TDFs exhibit (N-1) singular (non-analytic)
microscopic phase transitions of the formal order N/2, separating N
energetically different evaporation (dissociation) states. In a suitably
designed evaporation experiment, these types of phase transitions should
manifest themselves in the form of pressure and temperature oscillations,
indicating cooling by evaporation. In the presence of a heat bath (thermostat),
such oscillations are absent, but the canonical heat capacity shows a
characteristic peak, indicating the temperature-induced dissociation of the
one-dimensional chain. The distribution of complex zeros (DOZ) of the canonical
partition may be used to identify different degrees of dissociation in the
canonical ensemble.Comment: version accepted for publication in PRE, minor additions in the text,
references adde
Adiabatic invariance with first integrals of motion
The construction of a microthermodynamic formalism for isolated systems based
on the concept of adiabatic invariance is an old but seldom appreciated effort
in the literature, dating back at least to P. Hertz [Ann. Phys. (Leipzig) 33,
225 (1910)]. An apparently independent extension of such formalism for systems
bearing additional first integrals of motion was recently proposed by Hans H.
Rugh [Phys. Rev. E 64, 055101 (2001)], establishing the concept of adiabatic
invariance even in such singular cases. After some remarks in connection with
the formalism pioneered by Hertz, it will be suggested that such an extension
can incidentally explain the success of a dynamical method for computing the
entropy of classical interacting fluids, at least in some potential
applications where the presence of additional first integrals cannot be
ignored.Comment: 2 pages, no figures (REVTeX 4
On the work distribution for the adiabatic compression of a dilute classical gas
We consider the adiabatic and quasi-static compression of a dilute classical
gas, confined in a piston and initially equilibrated with a heat bath. We find
that the work performed during this process is described statistically by a
gamma distribution. We use this result to show that the model satisfies the
non-equilibrium work and fluctuation theorems, but not the
flucutation-dissipation relation. We discuss the rare but dominant realizations
that contribute most to the exponential average of the work, and relate our
results to potentially universal work distributions.Comment: 4 page
Effects of Diversity on Multi-agent Systems: Minority Games
We consider a version of large population games whose agents compete for
resources using strategies with adaptable preferences. The games can be used to
model economic markets, ecosystems or distributed control. Diversity of initial
preferences of strategies is introduced by randomly assigning biases to the
strategies of different agents. We find that diversity among the agents reduces
their maladaptive behavior. We find interesting scaling relations with
diversity for the variance and other parameters such as the convergence time,
the fraction of fickle agents, and the variance of wealth, illustrating their
dynamical origin. When diversity increases, the scaling dynamics is modified by
kinetic sampling and waiting effects. Analyses yield excellent agreement with
simulations.Comment: 41 pages, 16 figures; minor improvements in content, added
references; to be published in Physical Review
Higher-order Kerr terms allow ionization-free filamentation in gases
We show that higher-order nonlinear indices (, , , )
provide the main defocusing contribution to self-channeling of ultrashort laser
pulses in air and Argon at 800 nm, in contrast with the previously accepted
mechanism of filamentation where plasma was considered as the dominant
defocusing process. Their consideration allows to reproduce experimentally
observed intensities and plasma densities in self-guided filaments.Comment: 11 pages, 6 figures (11 panels
Minimal Work Principle and its Limits for Classical Systems
The minimal work principle asserts that work done on a thermally isolated
equilibrium system, is minimal for the slowest (adiabatic) realization of a
given process. This principle, one of the formulations of the second law, is
operationally well-defined for any finite (few particle) Hamiltonian system.
Within classical Hamiltonian mechanics, we show that the principle is valid for
a system of which the observable of work is an ergodic function. For
non-ergodic systems the principle may or may not hold, depending on additional
conditions. Examples displaying the limits of the principle are presented and
their direct experimental realizations are discussed.Comment: 4 + epsilon pages, 1 figure, revte
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