89 research outputs found

### Nonequilibrium steady state thermodynamics and fluctuations for stochastic systems

We use the work done on and the heat removed from a system to maintain it in
a nonequilibrium steady state for a thermodynamic-like description of such a
system as well as of its fluctuations. Based on a generalized Onsager-Machlup
theory for nonequilibrium steady states we indicate two ambiguities, not
present in an equilibrium state, in defining such work and heat: one due to a
non-uniqueness of time-reversal procedures and another due to multiple
possibilities to separate heat into work and an energy difference in
nonequilibrium steady states. As a consequence, for such systems, the work and
heat satisfy multiple versions of the first and second laws of thermodynamics
as well as of their fluctuation theorems. Unique laws and relations appear only
to be obtainable for concretely defined systems, using physical arguments to
choose the relevant physical quantities. This is illustrated on a number of
systems, including a Brownian particle in an electric field, a driven torsion
pendulum, electric circuits and an energy transfer driven by a temperature
difference.Comment: 39 pages, 3 figur

### Extended Clausius Relation and Entropy for Nonequilibrium Steady States in Heat Conducting Quantum Systems

Recently, in their attempt to construct steady state thermodynamics (SST),
Komatsu, Nakagwa, Sasa, and Tasaki found an extension of the Clausius relation
to nonequilibrium steady states in classical stochastic processes. Here we
derive a quantum mechanical version of the extended Clausius relation. We
consider a small system of interest attached to large systems which play the
role of heat baths. By only using the genuine quantum dynamics, we realize a
heat conducting nonequilibrium steady state in the small system. We study the
response of the steady state when the parameters of the system are changed
abruptly, and show that the extended Clausius relation, in which "heat" is
replaced by the "excess heat", is valid when the temperature difference is
small. Moreover we show that the entropy that appears in the relation is
similar to von Neumann entropy but has an extra symmetrization with respect to
time-reversal. We believe that the present work opens a new possibility in the
study of nonequilibrium phenomena in quantum systems, and also confirms the
robustness of the approach by Komtatsu et al.Comment: 19 pages, 2 figure

### A quantum version of free energy - irreversible work relations

We give a quantum version of the Jarzynski relation between the distribution
of work done over a certain time-interval on a system and the difference of
equilibrium free energies. The main new ingredient is the identification of
work depending on the quantum history of the system and the proper definition
of various quantum ensembles over which the averages should be made. We also
discuss a number of different regimes that have been considered by other
authors and which are unified in the present set-up. In all cases, and quantum
or classical, it is a general relation between heat and time-reversal that
makes the Jarzynski relation so universally valid

### Glassy behavior of a homopolymer from molecular dynamics simulations

We study at- and out-of-equilibrium dynamics of a single homopolymer chain at
low temperature using molecular dynamics simulations. The main quantities of
interest are the average root mean square displacement of the monomers below
the theta point, and the structure factor, as a function of time. The
observation of these quantities show a close resemblance to those measured in
structural glasses and suggest that the polymer chain in its low temperature
phase is in a glassy phase, with its dynamics dominated by traps. In
equilibrium, at low temperature, we observe the trapping of the monomers and a
slowing down of the overall motion of the polymer as well as non-exponential
relaxation of the structure factor. In out-of-equilibrium, at low temperatures,
we compute the two-time quantities and observe breaking of ergodicity in a
range of waiting times, with the onset of aging.Comment: 11 pages, 4 figure

### Quantum Jarzynski-Sagawa-Ueda relations

We consider a (small) quantum mechanical system which is operated by an
external agent, who changes the Hamiltonian of the system according to a fixed
scenario. In particular we assume that the agent (who may be called a demon)
performs measurement followed by feedback, i.e., it makes a measurement of the
system and changes the protocol according to the outcome. We extend to this
setting the generalized Jarzynski relations, recently derived by Sagawa and
Ueda for classical systems with feedback. One of the two relations by Sagawa
and Ueda is derived here in error-free quantum processes, while the other is
derived only when the measurement process involves classical errors. The first
relation leads to a second law which takes into account the efficiency of the
feedback.Comment: 11 pages. a major revision in v.2. Minor revision in v.3. The present
version will appear in J. Stat. Phy

### Representation of nonequilibrium steady states in large mechanical systems

Recently a novel concise representation of the probability distribution of
heat conducting nonequilibrium steady states was derived. The representation is
valid to the second order in the ``degree of nonequilibrium'', and has a very
suggestive form where the effective Hamiltonian is determined by the excess
entropy production. Here we extend the representation to a wide class of
nonequilibrium steady states realized in classical mechanical systems where
baths (reservoirs) are also defined in terms of deterministic mechanics. The
present extension covers such nonequilibrium steady states with a heat
conduction, with particle flow (maintained either by external field or by
particle reservoirs), and under an oscillating external field. We also simplify
the derivation and discuss the corresponding representation to the full order.Comment: 27 pages, 3 figure

### Onsager-Machlup theory and work fluctuation theorem for a harmonically driven Brownian particle

We extend Tooru-Cohen analysis for nonequilirium steady state(NSS) of a
Brownian particle to nonequilibrium oscillatory state (NOS) of Brownian
particle by considering time dependent external drive protocol. We consider an
unbounded charged Brownian particle in the presence of an oscillating electric
field and prove work fluctuation theorem, which is valid for any initial
distribution and at all times. For harmonically bounded and constantly dragged
Brownian particle considered by Tooru and Cohen, work fluctuation theorem is
valid for any initial condition(also NSS), but only in large time limit. We use
Onsager-Machlup Lagrangian with a constraint to obtain frequency dependent work
distribution function, and describe entropy production rate and properties of
dissipation functions for the present system using Onsager-Machlup functional.Comment: 6 pages, 1 figur

### Model of a fluid at small and large length scales and the hydrophobic effect

We present a statistical field theory to describe large length scale effects
induced by solutes in a cold and otherwise placid liquid. The theory divides
space into a cubic grid of cells. The side length of each cell is of the order
of the bulk correlation length of the bulk liquid. Large length scale states of
the cells are specified with an Ising variable. Finer length scale effects are
described with a Gaussian field, with mean and variance affected by both the
large length scale field and by the constraints imposed by solutes. In the
absence of solutes and corresponding constraints, integration over the Gaussian
field yields an effective lattice gas Hamiltonian for the large length scale
field. In the presence of solutes, the integration adds additional terms to
this Hamiltonian. We identify these terms analytically. They can provoke large
length scale effects, such as the formation of interfaces and depletion layers.
We apply our theory to compute the reversible work to form a bubble in liquid
water, as a function of the bubble radius. Comparison with molecular simulation
results for the same function indicates that the theory is reasonably accurate.
Importantly, simulating the large length scale field involves binary arithmetic
only. It thus provides a computationally convenient scheme to incorporate
explicit solvent dynamics and structure in simulation studies of large
molecular assemblies

### Quantum Fluctuation Relations for the Lindblad Master Equation

An open quantum system interacting with its environment can be modeled under
suitable assumptions as a Markov process, described by a Lindblad master
equation. In this work, we derive a general set of fluctuation relations for
systems governed by a Lindblad equation. These identities provide quantum
versions of Jarzynski-Hatano-Sasa and Crooks relations. In the linear response
regime, these fluctuation relations yield a fluctuation-dissipation theorem
(FDT) valid for a stationary state arbitrarily far from equilibrium. For a
closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula

### On the validity of entropy production principles for linear electrical circuits

We discuss the validity of close-to-equilibrium entropy production principles
in the context of linear electrical circuits. Both the minimum and the maximum
entropy production principle are understood within dynamical fluctuation
theory. The starting point are Langevin equations obtained by combining
Kirchoff's laws with a Johnson-Nyquist noise at each dissipative element in the
circuit. The main observation is that the fluctuation functional for time
averages, that can be read off from the path-space action, is in first order
around equilibrium given by an entropy production rate. That allows to
understand beyond the schemes of irreversible thermodynamics (1) the validity
of the least dissipation, the minimum entropy production, and the maximum
entropy production principles close to equilibrium; (2) the role of the
observables' parity under time-reversal and, in particular, the origin of
Landauer's counterexample (1975) from the fact that the fluctuating observable
there is odd under time-reversal; (3) the critical remark of Jaynes (1980)
concerning the apparent inappropriateness of entropy production principles in
temperature-inhomogeneous circuits.Comment: 19 pages, 1 fi

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