17 research outputs found
Model study on steady heat capacity in driven stochastic systems
We explore two- and three-state Markov models driven out of thermal
equilibrium by non-potential forces to demonstrate basic properties of the
steady heat capacity based on the concept of quasistatic excess heat. It is
shown that large enough driving forces can make the steady heat capacity
negative. For both the low- and high-temperature regimes we propose an
approximative thermodynamic scheme in terms of "dynamically renormalized"
effective energy levels.Comment: 10 pages, 7 figures, 1 tabl
Fluctuation Relation for Heat Engines
We derive the exact equality, referred to as the fluctuation relation for
heat engines (FRHE), that relates statistics of heat extracted from one of the
two heat baths and the work per one cycle of a heat engine operation. Carnot's
inequality of classical thermodynamics follows as a direct consequence of the
FRHE.Comment: 3 pages, 1 figur
A nonequilibrium extension of the Clausius heat theorem
We generalize the Clausius (in)equality to overdamped mesoscopic and
macroscopic diffusions in the presence of nonconservative forces. In contrast
to previous frameworks, we use a decomposition scheme for heat which is based
on an exact variant of the Minimum Entropy Production Principle as obtained
from dynamical fluctuation theory. This new extended heat theorem holds true
for arbitrary driving and does not require assumptions of local or close to
equilibrium. The argument remains exactly intact for diffusing fields where the
fields correspond to macroscopic profiles of interacting particles under
hydrodynamic fluctuations. We also show that the change of Shannon entropy is
related to the antisymmetric part under a modified time-reversal of the
time-integrated entropy flux.Comment: 23 pages; v2: manuscript significantly extende
Nonequilibrium Linear Response for Markov Dynamics, II: Inertial Dynamics
We continue our study of the linear response of a nonequilibrium system. This
Part II concentrates on models of open and driven inertial dynamics but the
structure and the interpretation of the result remain unchanged: the response
can be expressed as a sum of two temporal correlations in the unperturbed
system, one entropic, the other frenetic. The decomposition arises from the
(anti)symmetry under time-reversal on the level of the nonequilibrium action.
The response formula involves a statistical averaging over explicitly known
observables but, in contrast with the equilibrium situation, they depend on the
model dynamics in terms of an excess in dynamical activity. As an example, the
Einstein relation between mobility and diffusion constant is modified by a
correlation term between the position and the momentum of the particle
An update on nonequilibrium linear response
The unique fluctuation-dissipation theorem for equilibrium stands in contrast
with the wide variety of nonequilibrium linear response formulae. Their most
traditional approach is "analytic", which, in the absence of detailed balance,
introduces the logarithm of the stationary probability density as observable.
The theory of dynamical systems offers an alternative with a formula that
continues to work when the stationary distribution is not smooth. We show that
this method works equally well for stochastic dynamics, and we illustrate it
with a numerical example for the perturbation of circadian cycles. A second
"probabilistic" approach starts from dynamical ensembles and expands the
probability weights on path space. This line suggests new physical questions,
as we meet the frenetic contribution to linear response, and the relevance of
the change in dynamical activity in the relaxation to a (new) nonequilibrium
condition.Comment: v2: removed typos, updated ref