Nonequilibrium Thermodynamics of Stochastic Systems with Odd and Even Variables

Time-integrated quantities such as work and heat increase incessantly in time during nonequilibrium processes near steady states. In the long-time limit, the average values of work and heat become asymptotically equivalent to each other, since they only differ by a finite energy change in average. However, the fluctuation theorem (FT) for the heat is found not to hold with the equilibrium initial ensemble, while the FT for the work holds. This reveals an intriguing effect of everlasting initial memory stored in rare events. We revisit the problem of a Brownian particle in a harmonic potential dragged with a constant velocity, which is in contact with a thermal reservoir. The heat and work fluctuations are investigated with initial Boltzmann ensembles at temperatures generally different from the reservoir temperature. We find that, in the infinite-time limit, the FT for the work is fully recovered for arbitrary initial temperatures, while the heat fluctuations significantly deviate from the FT characteristics except for the infinite initial-temperature limit (a uniform initial ensemble). Furthermore, we succeed in calculating finite-time corrections to the heat and work distributions analytically, using the modified saddle point integral method recently developed by us. Interestingly, we find noncommutativity between the infinite-time limit and the infinite-initial-temperature limit for the probability distribution function (PDF) of the heat.

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“…We present f τ (p) defined in Eq. (37) such that f τ (p) = −h τ (p) + h τ (−p). All the results in this subsection are summarized into…”

Section: Ft Violationsmentioning

confidence: 98%

Heat fluctuations and initial ensembles

2014

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“…Although the Maes-Netocny scheme is based on microscopic (or mesoscopic) dynamics, it does not apply to models with inertia (momenta) as it is. As for the Hatano-Sasa scheme it has been pointed out [31] that a consistent thermodynamic interpretation is impossible once the momentum degrees of freedom is introduced. See also [14].…”

Section: Extended Clausius Relationmentioning

confidence: 99%

Exact Equalities and Thermodynamic Relations for Nonequilibrium Steady States

et al. 2015

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We study thermodynamic operations which bring a nonequilibrium steady state (NESS) to another NESS in physical systems under nonequilibrium conditions. We model the system by a suitable Markov jump process, and treat thermodynamic operations as protocols according to which the external agent varies parameters of the Markov process. Then we prove, among other relations, a NESS version of the Jarzynski equality and the extended Clausius relation. The latter can be a starting point of thermodynamics for NESS. We also find that the corresponding nonequilibrium entropy has a microscopic representation in terms of symmetrized Shannon entropy in systems where the microscopic description of states involves "momenta". All the results in the present paper are mathematically rigorous.

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“…This work extends the previous theoretical framework in at least two aspects. One aspect is the inclusion of odd variable under time reversal (the velocity field) [32,33,42,43,44], which was not considered in the previous framework and has to be dealt with in fluid systems. This leads to the distinction of reversible and irreversible driving forces and probability fluxes that require explicit consideration of their time reversal properties, which was not necessary in the previous framework that deals with only even variables.…”

Section: Introductionmentioning

confidence: 99%

Potential landscape and flux field theory for turbulence and nonequilibrium fluid systems

Zhang

Wang

2018

Annals of Physics

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Turbulence is a paradigm for far-from-equilibrium systems without time reversal symmetry. To capture the nonequilibrium irreversible nature of turbulence and investigate its implications, we develop a potential landscape and flux field theory for turbulent flow and more general nonequilibrium fluid systems governed by stochastic Navier-Stokes equations. We find that equilibrium fluid systems with time reversibility are characterized by a detailed balance constraint that quantifies the detailed balance condition. In nonequilibrium fluid systems with nonequilibrium steady states, detailed balance breaking leads directly to a pair of interconnected consequences, namely, the non-Gaussian potential landscape and the irreversible probability flux, forming a 'nonequilibrium trinity'. The nonequilibrium trinity characterizes the nonequilibrium irreversible essence of fluid systems with intrinsic time irreversibility and is manifested in various aspects of these systems. The nonequilibrium stochastic dynamics of fluid systems including turbulence with detailed balance breaking is shown to be driven by both the nonGaussian potential landscape gradient and the irreversible probability flux, together with the reversible convective force and the stochastic stirring force. We reveal an underlying connection of the energy flux essential for turbulence energy cascade to the irreversible probability flux and the non-Gaussian potential landscape generated by detailed balance breaking. Using the energy flux as a center of connection, we demonstrate that the four-fifths law in fully developed turbulence is a consequence and reflection of the nonequilibrium trinity. We also show how the nonequilibrium trinity can affect the scaling laws in turbulence.

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Nonequilibrium Thermodynamics of Stochastic Systems with Odd and Even Variables

Cited by 90 publications

References 27 publications

Heat fluctuations and initial ensembles

Heat fluctuations and initial ensembles

Exact Equalities and Thermodynamic Relations for Nonequilibrium Steady States

Potential landscape and flux field theory for turbulence and nonequilibrium fluid systems

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