scholarly journals Stochastic Thermodynamics of Oscillators' Networks

2018 ◽  
Author(s):  
Simone Borlenghi ◽  
Anna Delin
Keyword(s):  
Entropy Production ◽  
Time Reversal ◽  
Detailed Balance ◽  
Nonlinear Oscillators ◽  
Time Reversal Symmetry ◽  
Equilibrium Thermodynamics ◽  
Stochastic Thermodynamics ◽  
Far From Equilibrium ◽  
Fokker Planck Equations ◽  
Kontorova Model

We apply the stochastic thermodynamics formalism to describe the dynamics of systems of complex Langevin and Fokker-Planck equations. We provide in particular a simple and general recipe to calculate thermodynamical currents, dissipated and propagating heat for networks of nonlinear oscillators. By using the Hodge decomposition of thermodynamical forces and fluxes, we derive a formula for entropy production that generalises the notion of non-potential forces and makes transparent the breaking of detailed balance and of time reversal symmetry for states arbitrarily far from equilibrium. Our formalism is then applied to describe the off-equilibrium thermodynamics of a few examples, notably a continuum ferromagnet, a network of classical spin-oscillators and the Frenkel-Kontorova model of nano friction.

scholarly journals Stochastic Thermodynamics of Oscillators’ Networks

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 992
Author(s):  
Simone Borlenghi ◽  
Anna Delin
Keyword(s):  
Entropy Production ◽  
Time Reversal ◽  
Detailed Balance ◽  
Nonlinear Oscillators ◽  
Time Reversal Symmetry ◽  
Equilibrium Thermodynamics ◽  
Stochastic Thermodynamics ◽  
Far From Equilibrium ◽  
Fokker Planck Equations ◽  
Kontorova Model

We apply the stochastic thermodynamics formalism to describe the dynamics of systems of complex Langevin and Fokker-Planck equations. We provide in particular a simple and general recipe to calculate thermodynamical currents, dissipated and propagating heat for networks of nonlinear oscillators. By using the Hodge decomposition of thermodynamical forces and fluxes, we derive a formula for entropy production that generalises the notion of non-potential forces and makes transparent the breaking of detailed balance and of time reversal symmetry for states arbitrarily far from equilibrium. Our formalism is then applied to describe the off-equilibrium thermodynamics of a few examples, notably a continuum ferromagnet, a network of classical spin-oscillators and the Frenkel-Kontorova model of nano friction.

scholarly journals Energy dissipation and fluctuations in a driven liquid

2018 ◽  
Vol 115 (14) ◽  
pp. 3569-3574 ◽  
Author(s):  
Clara del Junco ◽  
Laura Tociu ◽  
Suriyanarayanan Vaikuntanathan
Keyword(s):  
Phase Transition ◽  
Steady State ◽  
Time Reversal ◽  
Time Dependent ◽  
Time Reversal Symmetry ◽  
Nonequilibrium Systems ◽  
Minimal Models ◽  
Stochastic Thermodynamics ◽  
Periodic Steady State ◽  
Time Periodic

Minimal models of active and driven particles have recently been used to elucidate many properties of nonequilibrium systems. However, the relation between energy consumption and changes in the structure and transport properties of these nonequilibrium materials remains to be explored. We explore this relation in a minimal model of a driven liquid that settles into a time periodic steady state. Using concepts from stochastic thermodynamics and liquid state theories, we show how the work performed on the system by various nonconservative, time-dependent forces—this quantifies a violation of time reversal symmetry—modifies the structural, transport, and phase transition properties of the driven liquid.

scholarly journals Heat, temperature and Clausius inequality in a model for active Brownian particles

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Umberto Marini Bettolo Marconi ◽  
Andrea Puglisi ◽  
Claudio Maggi
Keyword(s):  
Entropy Production ◽  
Detailed Balance ◽  
Constructive Method ◽  
Kinetic Temperature ◽  
Uniform Temperature ◽  
Local Pressure ◽  
Stochastic Thermodynamics ◽  
Hydrodynamic Description ◽  
Coloured Noise ◽  
Clausius Inequality

Abstract Methods of stochastic thermodynamics and hydrodynamics are applied to a recently introduced model of active particles. The model consists of an overdamped particle subject to Gaussian coloured noise. Inspired by stochastic thermodynamics, we derive from the system’s Fokker-Planck equation the average exchanges of heat and work with the active bath and the associated entropy production. We show that a Clausius inequality holds, with the local (non-uniform) temperature of the active bath replacing the uniform temperature usually encountered in equilibrium systems. Furthermore, by restricting the dynamical space to the first velocity moments of the local distribution function we derive a hydrodynamic description where local pressure, kinetic temperature and internal heat fluxes appear and are consistent with the previous thermodynamic analysis. The procedure also shows under which conditions one obtains the unified coloured noise approximation (UCNA): such an approximation neglects the fast relaxation to the active bath and therefore yields detailed balance and zero entropy production. In the last part, by using multiple time-scale analysis, we provide a constructive method (alternative to UCNA) to determine the solution of the Kramers equation and go beyond the detailed balance condition determining negative entropy production.

A note on time-reversal symmetry

1985 ◽  
Vol 63 (8) ◽  
pp. 1128-1131
Author(s):  
Ralph Girard ◽  
Helmut Kröger
Keyword(s):  
Perturbation Theory ◽  
Cross Sections ◽  
Time Reversal ◽  
Detailed Balance ◽  
Time Reversal Symmetry ◽  
Sensitive Test ◽  
Polarization Asymmetry ◽  
First Order ◽  
Model Independent ◽  
First Order Perturbation

Model-independent results on time-reversal symmetry are presented. It is shown that, for any Hermitian, time-reversal noninvariant Hamiltonian, one can find invariant cross sections. The sensitivity of polarization–asymmetry and detailed balance is studied. In first-order perturbation theory, only polarization–asymmetry is found to be a sensitive test.

scholarly journals Entropy Production in Field Theories without Time-Reversal Symmetry: Quantifying the Non-Equilibrium Character of Active Matter

2017 ◽  
Vol 7 (2) ◽  
Author(s):  
Cesare Nardini ◽  
Étienne Fodor ◽  
Elsen Tjhung ◽  
Frédéric van Wijland ◽  
Julien Tailleur ◽  
...  
Keyword(s):  
Entropy Production ◽  
Time Reversal ◽  
Field Theories ◽  
Time Reversal Symmetry ◽  
Active Matter ◽  
Non Equilibrium

scholarly journals Entropy Production in Exactly Solvable Systems

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1252
Author(s):  
Luca Cocconi ◽  
Rosalba Garcia-Millan ◽  
Zigan Zhen ◽  
Bianca Buturca ◽  
Gunnar Pruessner
Keyword(s):  
Entropy Production ◽  
Time Reversal ◽  
First Principles ◽  
Detailed Balance ◽  
Particle Systems ◽  
Stochastic Particle Systems ◽  
Continuous State ◽  
Exactly Solvable ◽  
Multiple Particle ◽  
Stochastic Particle

The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which global detailed balance and time-reversal symmetry are broken. Despite abundant references to entropy production in the literature and its many applications in the study of non-equilibrium stochastic particle systems, a comprehensive list of typical examples illustrating the fundamentals of entropy production is lacking. Here, we present a brief, self-contained review of entropy production and calculate it from first principles in a catalogue of exactly solvable setups, encompassing both discrete- and continuous-state Markov processes, as well as single- and multiple-particle systems. The examples covered in this work provide a stepping stone for further studies on entropy production of more complex systems, such as many-particle active matter, as well as a benchmark for the development of alternative mathematical formalisms.

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