Abstract
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.
Highlights
Dissipation and heat transfer are universal phenomena in Physics, appearing whenever a small system is coupled to the much larger environment
The formalism can be naturally extended beyond the linear regime, as it was first observed by Schnakenberg [4] and subsequently in more recent works on stochastic thermodynamics [5,6,7]
We shall adopt the formalism of stochastic thermodynamics (ST) [5] applied to the dynamics of complex-valued
Summary
Dissipation and heat transfer are universal phenomena in Physics, appearing whenever a small system is coupled to the much larger environment. In the presence of several environments (thermal baths or reservoirs) at different temperatures, the system reaches a non-equilibrium steady state where thermodynamical currents (such as heat, energy, spin or electrical) may flow through the system from one reservoir to the other. Most importantly, to give a general recipe to calculate currents, dissipated heat and work in a large class of out-of-equilibrium systems To this end, we shall adopt the formalism of stochastic thermodynamics (ST) [5] applied to the dynamics of complex-valued. We shall describe in particular the dynamics of a one dimensional continuum ferromagnet, of a network of classical magnetic spins and of the Frenkel-Kontorova model [29] for nano-friction
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