1,272 research outputs found
Irreversible thermodynamics of open chemical networks I: Emergent cycles and broken conservation laws
In this and a companion paper we outline a general framework for the
thermodynamic description of open chemical reaction networks, with special
regard to metabolic networks regulating cellular physiology and biochemical
functions. We first introduce closed networks "in a box", whose thermodynamics
is subjected to strict physical constraints: the mass-action law, elementarity
of processes, and detailed balance. We further digress on the role of solvents
and on the seemingly unacknowledged property of network independence of free
energy landscapes. We then open the system by assuming that the concentrations
of certain substrate species (the chemostats) are fixed, whether because
promptly regulated by the environment via contact with reservoirs, or because
nearly constant in a time window. As a result, the system is driven out of
equilibrium. A rich algebraic and topological structure ensues in the network
of internal species: Emergent irreversible cycles are associated to
nonvanishing affinities, whose symmetries are dictated by the breakage of
conservation laws. These central results are resumed in the relation between the number of fundamental affinities , that of broken
conservation laws and the number of chemostats . We decompose the
steady state entropy production rate in terms of fundamental fluxes and
affinities in the spirit of Schnakenberg's theory of network thermodynamics,
paving the way for the forthcoming treatment of the linear regime, of
efficiency and tight coupling, of free energy transduction and of thermodynamic
constraints for network reconstruction.Comment: 18 page
Entropic fluctuations in thermally driven harmonic networks
We consider a general network of harmonic oscillators driven out of thermal
equilibrium by coupling to several heat reservoirs at different temperatures.
The action of the reservoirs is implemented by Langevin forces. Assuming the
existence and uniqueness of the steady state of the resulting process, we
construct a canonical entropy production functional which satisfies the
Gallavotti--Cohen fluctuation theorem, i.e., a global large deviation principle
with a rate function I(s) obeying the Gallavotti--Cohen fluctuation relation
I(-s)-I(s)=s for all s. We also consider perturbations of our functional by
quadratic boundary terms and prove that they satisfy extended fluctuation
relations, i.e., a global large deviation principle with a rate function that
typically differs from I(s) outside a finite interval. This applies to various
physically relevant functionals and, in particular, to the heat dissipation
rate of the network. Our approach relies on the properties of the maximal
solution of a one-parameter family of algebraic matrix Riccati equations. It
turns out that the limiting cumulant generating functions of our functional and
its perturbations can be computed in terms of spectral data of a Hamiltonian
matrix depending on the harmonic potential of the network and the parameters of
the Langevin reservoirs. This approach is well adapted to both analytical and
numerical investigations
Nonequilibrium phase transition in a non integrable zero-range process
The present work is an endeavour to determine analytically features of the
stationary measure of a non-integrable zero-range process, and to investigate
the possible existence of phase transitions for such a nonequilibrium model.
The rates defining the model do not satisfy the constraints necessary for the
stationary measure to be a product measure. Even in the absence of a drive,
detailed balance with respect to this measure is violated. Analytical and
numerical investigations on the complete graph demonstrate the existence of a
first-order phase transition between a fluid phase and a condensed phase, where
a single site has macroscopic occupation. The transition is sudden from an
imbalanced fluid where both species have densities larger than the critical
density, to a critical neutral fluid and an imbalanced condensate
Level 2.5 large deviations for continuous time Markov chains with time periodic rates
We consider an irreducible continuous time Markov chain on a finite state
space and with time periodic jump rates and prove the joint large deviation
principle for the empirical measure and flow and the joint large deviation
principle for the empirical measure and current. By contraction we get the
large deviation principle of three types of entropy production flow. We derive
some Gallavotti-Cohen duality relations and discuss some applications.Comment: 37 pages. corrected versio
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