要旨
This thesis investigates irreversible dynamics. It is shown analytically that the recent Fluctuation
Theorem extends to relativistic
dynamics. In the analytic consideration of non-relativistic granular gases with broken time-reversal symmetry we find violations of the Fluctuation Theorem
for large fluctuations. This is
confirmed by simulations of wet granular matter in driven
stationary states. It is shown that the theorem persists to hold for small fluctuations, which
explains earlier reports of
confirmation in literature as a
consequence of their measurement
range. The particle interaction in wet granular matter is experimentally shown to be hysteretic with the formation and rupture of capillary bridges. The measured dissipation is quantified
by the rupture length and energy of the bridges. For a kinematic description of wet granular
matter based on these experimental findings, the Enskog factor is generalized analytically to
a set of six fa
tors, which acount for the hysteretic
interaction in a statistical description.
Such a statistical and, moreover,
continuum description is made possible by the analytical
and numerical
computations of the Kolmogorov-Sinai entropy, which demonstrates the substantial
increase of dynamical chaos due to the
capillary interaction in wet granular matter.
On this basis, the equation of state of wet granular matter is derived analytically. A van-der-Waals-like
mechanical instability is predicted, and verified in simulations and experiments.
In the simulations, the instability leads to the breakup of capillary bridges. This nonequilibrium
dynamics is described analytically by a mean-field theory in quantitative agreement
with the simulations. The experimentally determined
critical point of this instability agrees
quantitatively with the theory. A novel method, which allows to measure the velocity distribution
in nonequilibrium steady states of granular matter based on the Mössbauer effect,
is suggested. In a first measurement, an exponential velocity distribution is observed for the fluid-like state. It is demonstrated that the global instantaneous state of the dynamical
capillary
network in wet granular matter is observable by electrical
conductivity, when an ionic
liquid is added. This allows to detect the transition of wet granular matter from the solid to
the fluid state in the bulk, excluding surface effects, and to demonstrate experimentally with
unprecedented precision that this transition is discontinuous and hysteretic
with respect to
the external driving. Simulations and experiments show that this nonequilibrium transition
sets in at a
critical acceleration of the external driving. Furthermore, the transition from the
fluid-like to the gaseous state of wet granular matter is demonstrated experimentally and by
simulations. In both approaches it is shown quantitatively that this transition is determined
by a
critical velocity of the driving, which is directly related to the
capillary energy. States of
fluid/gas
coexistence, which emerge in experiments and simulations are explained analytically
as subcritical instabilities in the balance of power. Applying the derived equation of state, the
spatial distributions of temperature, density and dissipation are computed. Order parameters
are measured, and the global phase diagram of the nonequilibrium states and transitions of
wet granular matter is presented.
