Total entropy production fluctuation theorems in a nonequilibrium time-periodic steady state

Lahiri, Sourabh; Jayannavar, A. M.

doi:10.1140/epjb/e2009-00017-7

Cited by 12 publications

(14 citation statements)

References 61 publications

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“…Therefore, variational principles relevant to the Brownian scheme, must go beyond entropy production considerations, and include among others, free energies, efficiency factors and power output as well [69,70] and connected to nonequilibrium fluctuation and work relations [176][177][178][179][180][181][182][183][184][185].…”

Section: Discussionmentioning

confidence: 99%

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

Lagos

Simões

2011

Physica A: Statistical Mechanics and its Applications

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a b s t r a c tWe consider a charged Brownian gas under the influence of external and non-uniform electric, magnetic and mechanical fields, immersed in a non-uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To the first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle density, a Smoluchowski-reactive like equation; for the particle's momentum density, a generalized Ohm's-like equation; and for the particle's energy density, a Maxwell-Cattaneo-like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann's entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non-linear reactive kinetics and a mean field approach to interacting Brownian particles.

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Section: Discussionmentioning

confidence: 99%

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

Lagos

Simões

2011

Physica A: Statistical Mechanics and its Applications

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“…Stochastic resonance For a colloidal particle in a double well potential that is additionally subject to a modulated linear potential to generate conditions of stochastic resonance [138], distributions for work, heat and entropy were measured and calculated in [139,140]. Other numerical work using the concepts of stochastic thermodynamics to investigate stochastic resonance includes [141,142,143]. 5.2.6.…”

Section: 25mentioning

confidence: 99%

Stochastic thermodynamics, fluctuation theorems and molecular machines

2012

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Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.

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“…which represents a mathematical generalization of the Clausius inequality [149,158,[163][164][165][166].…”

Section: Stochastic Thermodynamics and Entropy Productionmentioning

confidence: 99%

“…Several fluctuation relations have been demonstrated experimentally, mainly for colloidal particles trapped by an optical device, some examples are given in references [121,140,152,163,164,[168][169][170][171].…”

Section: Stochastic Thermodynamics and Entropy Productionmentioning

confidence: 99%

Entropy Production: Its Role in Non-Equilibrium Thermodynamics

Velasco

García‐Colín

Uribe

2011

Entropy

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It is unquestionable that the concept of entropy has played an essential role both in the physical and biological sciences. However, the entropy production, crucial to the second law, has also other features not clearly conceived. We all know that the main difficulty is concerned with its quantification in non-equilibrium processes and consequently its value for some specific cases is limited. In this work we will review the ideas behind the entropy production concept and we will give some insights about its relevance.

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Total entropy production fluctuation theorems in a nonequilibrium time-periodic steady state

Cited by 12 publications

References 61 publications

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

Stochastic thermodynamics, fluctuation theorems and molecular machines

Entropy Production: Its Role in Non-Equilibrium Thermodynamics

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