986 research outputs found
Entropy Production in Open Systems: The Predominant Role of Intra-Environment Correlations
We show that the entropy production in small open systems coupled to
environments made of extended baths is predominantly caused by the displacement
of the environment from equilibrium rather than, as often assumed, the mutual
information between the system and the environment. The latter contribution is
strongly bounded from above by the Araki-Lieb inequality, and therefore is not
time-extensive, in contrast to the entropy production itself. We confirm our
results with exact numerical calculations of the system-environment dynamics.Comment: 6 pages, 2 figures, with the Supplemental Materia
Conservation Laws shape Dissipation
Starting from the most general formulation of stochastic
thermodynamics---i.e. a thermodynamically consistent nonautonomous stochastic
dynamics describing systems in contact with several reservoirs---, we define a
procedure to identify the conservative and the minimal set of nonconservative
contributions in the entropy production. The former is expressed as the
difference between changes caused by time-dependent drivings and a generalized
potential difference. The latter is a sum over the minimal set of flux--force
contributions controlling the dissipative flows across the system. When the
system is initially prepared at equilibrium (e.g. by turning off drivings and
forces), a finite-time detailed fluctuation theorem holds for the different
contributions. Our approach relies on identifying the complete set of conserved
quantities and can be viewed as the extension of the theory of generalized
Gibbs ensembles to nonequilibrium situations.Comment: 24 pages, 11 figures, 3 tables. Published version in double column
forma
Mutual Entropy-Production and Sensing in Bipartite Systems
We introduce and analyze the notion of mutual entropy-production (MEP) in
autonomous systems. Evaluating MEP rates is in general a difficult task due to
non-Markovian effects. For bipartite systems, we provide closed expressions in
various limiting regimes which we verify using numerical simulations. Based on
the study of a biochemical and an electronic sensing model, we suggest that the
MEP rates provide a relevant measure of the accuracy of sensing.Comment: 9 pages, 6 figure
Pseudo-differential operators with nonlinear quantizing functions
In this paper we develop the calculus of pseudo-differential operators
corresponding to the quantizations of the form where is a general function. In
particular, for the linear choices , , and
this covers the well-known Kohn-Nirenberg,
anti-Kohn-Nirenberg, and Weyl quantizations, respectively. Quantizations of
such type appear naturally in the analysis on nilpotent Lie groups for
polynomial functions and here we investigate the corresponding calculus
in the model case of . We also give examples of nonlinear
appearing on the polarised and non-polarised Heisenberg groups, inspired by the
recent joint work with Marius Mantoiu.Comment: 26 page
Fluctuation theorems for quantum master equations
A quantum fluctuation theorem for a driven quantum subsystem interacting with
its environment is derived based solely on the assumption that its reduced
density matrix obeys a closed evolution equation i.e. a quantum master equation
(QME). Quantum trajectories and their associated entropy, heat and work appear
naturally by transforming the QME to a time dependent Liouville space basis
that diagonalizes the instantaneous reduced density matrix of the subsystem. A
quantum integral fluctuation theorem, a steady state fluctuation theorem and
the Jarzynski relation are derived in a similar way as for classical stochastic
dynamics.Comment: Submitted to Phys. Rev.
Stochastic thermodynamics for "Maxwell demon" feedbacks
We propose a way to incorporate the effect of a specific class of feedback
processes into stochastic thermodynamics. These "Maxwell demon" feedbacks do
not affect the system energetics but only the energy barriers between the
system states (in a way which depends on the system states). They are thus of a
purely informational nature. We show that the resulting formalism can be
applied to study the thermodynamic effect of a feedback process acting on
electron transfers through a junction.Comment: 3 figures, v2:accepted in EP
Effective thermodynamics for a marginal observer
Thermodynamics is usually formulated on the presumption that the observer has
complete information about the system he/she deals with: no parasitic current,
exact evaluation of the forces that drive the system. For example, the
acclaimed Fluctuation Relation (FR), relating the probability of time-forward
and time-reversed trajectories, assumes that the measurable transitions suffice
to characterize the process as Markovian (in our case, a continuous-time jump
process). However, most often the observer only measures a marginal current. We
show that he/she will nonetheless produce an effective description that does
not dispense with the fundamentals of thermodynamics, including the FR and the
2nd law. Our results stand on the mathematical construction of a hidden time
reversal of the dynamics, and on the physical requirement that the observed
current only accounts for a single transition in the configuration space of the
system. We employ a simple abstract example to illustrate our results and to
discuss the feasibility of generalizations.Comment: 8 pages, 1 figur
Transient fluctuation theorems for the currents and initial equilibrium ensembles
We prove a transient fluctuation theorem for the currents for continuous-time
Markov jump processes with stationary rates, generalizing an asymptotic result
by Andrieux and Gaspard [J. Stat. Phys. 127, 107 (2007)] to finite times. The
result is based on a graph theoretical decomposition in cycle currents and an
additional set of tidal currents that characterize the transient relaxation
regime. The tidal term can then be removed by a preferred choice of a suitable
initial equilibrium ensemble, a result that provides the general theory for the
fluctuation theorem without ensemble quantities recently addressed in [Phys.
Rev. E 89, 052119 (2014)]. As an example we study the reaction network of a
simple stochastic chemical engine, and finally we digress on general properties
of fluctuation relations for more complex chemical reaction networks.Comment: 19 pages, 2 figures. Sign error corrected in Eq.(50) and followin
Quantum master equation for the microcanonical ensemble
By using projection superoperators, we present a new derivation of the
quantum master equation first obtained by the Authors in Phys. Rev. E {\bf 68},
066112 (2003). We show that this equation describes the dynamics of a subsystem
weakly interacting with an environment of finite heat capacity and initially
described by a microcanonical distribution. After applying the rotating wave
approximation to the equation, we show that the subsystem dynamics preserves
the energy of the total system (subsystem plus environment) and tends towards
an equilibrium state which corresponds to equipartition inside the energy shell
of the total system. For infinite heat capacity environments, this equation
reduces to the Redfield master equation for a subsystem interacting with a
thermostat. These results should be of particular interest to describe
relaxation and decoherence in nanosystems where the environment can have a
finite number of degrees of freedom and the equivalence between the
microcanonical and the canonical ensembles is thus not always guaranteed.Comment: 8 pages, 0 figures; v2: typos in eq 42 and 43 corrected; v3:
submitted to Phys.Rev.E; v4: accepted in Phys.Rev.
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