Path-integral analysis of fluctuation theorems for general Langevin processes

Chernyak, Vladimir; Chertkov, Michael; Jarzynski, Christopher

doi:10.1088/1742-5468/2006/08/p08001

Cited by 206 publications

(292 citation statements)

References 57 publications

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“…We explain the apparent differences with the path integrals used in Ref. [12], and why we do not agree with the claims in Refs. [13,14].…”

Section: Contents 1 Introductioncontrasting

confidence: 89%

“…It differs from the one in Ref. [12] since the authors used a post-point prescription in the stochastic equation (i.e. α = 1) while using a mid-point Stratonovitch prescription in the construction of the path integral formalism.…”

Section: The Path-integral Formulationmentioning

confidence: 97%

“…Contrary to previous works for which the steady states were governed by non-equilibrium potentials, see e.g. [12], [13,14] and [27,28], here the approach to a Gibbs-Boltzmann equilibrium is ensured by the presence of a drift term, see also [29].…”

Section: Contents 1 Introductionmentioning

confidence: 92%

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Dynamical symmetries of Markov processes with multiplicative white noise

Aron¹,

Barci²,

Cugliandolo³

et al. 2016

J. Stat. Mech.

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We analyse various properties of stochastic Markov processes with multiplicative white noise. We take a single-variable problem as a simple example, and we later extend the analysis to the LandauLifshitz-Gilbert equation for the stochastic dynamics of a magnetic moment. In particular, we focus on the non-equilibrium transfer of angular momentum to the magnetization from a spin-polarised current of electrons, a technique which is widely used in the context of spintronics to manipulate magnetic moments. We unveil two hidden dynamical symmetries of the generating functionals of these Markovian multiplicative white-noise processes. One symmetry only holds in equilibrium and we use it to prove generic relations such as the fluctuation-dissipation theorems. Out of equilibrium, we take profit of the symmetry-breaking terms to prove fluctuation theorems. The other symmetry yields strong dynamical relations between correlation and response functions which can notably simplify the numerical analysis of these problems. Our construction allows us to clarify some misconceptions on multiplicative white-noise stochastic processes that can be found in the literature. In particular, we show that a first-order differential equation with multiplicative white noise can be transformed into an additive-noise equation, but that the latter keeps a non-trivial memory of the discretisation prescription used to define the former.

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“…We explain the apparent differences with the path integrals used in Ref. [12], and why we do not agree with the claims in Refs. [13,14].…”

Section: Contents 1 Introductioncontrasting

confidence: 89%

Section: The Path-integral Formulationmentioning

confidence: 97%

See 1 more Smart Citation

Dynamical symmetries of Markov processes with multiplicative white noise

Aron¹,

Barci²,

Cugliandolo³

et al. 2016

J. Stat. Mech.

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“…4) is a genuine nonequilibrium relation: it is valid for arbitrary initial conditions P(x, t 0 ) and arbitrary time-dependent selections. It belongs to a set of relations known as fluctuation theorems, which have played an important role in the nonequilibrium statistical physics of mesoscopic systems over the past decade (31)(32)(33)(34). As an immediate consequence of Eq.…”

Section: Theory Of Fitness Fluxmentioning

confidence: 99%

Fitness flux and ubiquity of adaptive evolution

Mustonen

Lässig

2010

Proc. Natl. Acad. Sci. U.S.A.

173

247

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Natural selection favors fitter variants in a population, but actual evolutionary processes may decrease fitness by mutations and genetic drift. How is the stochastic evolution of molecular biological systems shaped by natural selection? Here, we derive a theorem on the fitness flux in a population, defined as the selective effect of its genotype frequency changes. The fitnessflux theorem generalizes Fisher's fundamental theorem of natural selection to evolutionary processes including mutations, genetic drift, and time-dependent selection. It shows that a generic state of populations is adaptive evolution: there is a positive fitness flux resulting from a surplus of beneficial over deleterious changes. In particular, stationary nonequilibrium evolution processes are predicted to be adaptive. Under specific nonstationary conditions, notably during a decrease in population size, the average fitness flux can become negative. We show that these predictions are in accordance with experiments in bacteria and bacteriophages and with genomic data in Drosophila. Our analysis establishes fitness flux as a universal measure of adaptation in molecular evolution. A daptive processes have taken center stage in molecular evolutionary biology. Deep sequencing of populations opens unprecedented opportunities to trace the genomic basis of adaptation in population-genetic studies within and across species as well as in time series of evolution experiments. Various methods are used to infer natural selection from such data; however, their results lack a common gauge and are sometimes difficult to compare. This paper develops the concept of fitness flux in a population as a generic measure of adaptation applicable to molecular data. Whereas fitness characterizes the state of a population at a given point in time, fitness flux can be accumulated in a population's history over a period (a precise definition of this quantity will be given below). Fitness flux, not fitness, turns out to be the right variable to show that adaptive evolution is a generic state of natural populations. The notion of fitness flux is already implicitly contained in Fisher's fundamental theorem of natural selection (1), which states that any fitness difference within a population leads to adaptation in an evolution process governed by natural selection alone. The fitness flux of this deterministic process equals the (additive) fitness variance in the population. Hence, the flux is positive when adaptation occurs and zero otherwise.Generalizing this picture to realistic processes of molecular evolution has been a long-standing problem (2-8). The solution presented here involves a number of important conceptual steps. First, molecular processes are always stochastic because of genetic drift and mutations, and we include these forces into a stochastic theory of fitness flux. Second, we extend the observation of this dynamics to the time scales of genomic data, describing populations by histories of genotype composition and demography that may extend beyond their ...

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“…On the contrary if f nc is odd, for instance if the coarse-graining has delivered a force which is proportional to odd powers of the velocity of external bodies [14,26], or if magnetic fields are involved [25], the relation (10) does not hold anymore. In such cases, things seem to improve when the so-called conjugated dynamics is considered, by changing the sign of odd external non-conservative forces when computing the probability of inverse paths appearing in the denominator of Equation (6) [18,24,[26][27][28][29]: basically this amounts to change the parity of the force and get back the result in Equation (10). The problem of such an artificial prescription, however, is that the conjugated dynamics cannot be realized in experiments and therefore an empirical evaluation (i.e., without a detailed knowledge of the equation of motions) of the conjugated probability is not available, neither it is possible to experimentally observe the associated fluctuation relation.…”

Section: Mesoscopic Levelmentioning

confidence: 99%

Clausius Relation for Active Particles: What Can We Learn from Fluctuations

Puglisi

Marconi

2017

Entropy

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Many kinds of active particles, such as bacteria or active colloids, move in a thermostatted fluid by means of self-propulsion. Energy injected by such a non-equilibrium force is eventually dissipated as heat in the thermostat. Since thermal fluctuations are much faster and weaker than self-propulsion forces, they are often neglected, blurring the identification of dissipated heat in theoretical models. For the same reason, some freedom-or arbitrariness-appears when defining entropy production. Recently three different recipes to define heat and entropy production have been proposed for the same model where the role of self-propulsion is played by a Gaussian coloured noise. Here we compare and discuss the relation between such proposals and their physical meaning. One of these proposals takes into account the heat exchanged with a non-equilibrium active bath: such an "active heat" satisfies the original Clausius relation and can be experimentally verified.

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Path-integral analysis of fluctuation theorems for general Langevin processes

Cited by 206 publications

References 57 publications

Dynamical symmetries of Markov processes with multiplicative white noise

Dynamical symmetries of Markov processes with multiplicative white noise

Fitness flux and ubiquity of adaptive evolution

Clausius Relation for Active Particles: What Can We Learn from Fluctuations

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