1,351 research outputs found
Collisional invariants for the phonon Boltzmann equation
For the phonon Boltzmann equation with only pair collisions we characterize
the set of all collisional invariants under some mild conditions on the
dispersion relation
Approach to equilibrium for the phonon Boltzmann equation
We study the asymptotics of solutions of the Boltzmann equation describing
the kinetic limit of a lattice of classical interacting anharmonic oscillators.
We prove that, if the initial condition is a small perturbation of an
equilibrium state, and vanishes at infinity, the dynamics tends diffusively to
equilibrium. The solution is the sum of a local equilibrium state, associated
to conserved quantities that diffuse to zero, and fast variables that are
slaved to the slow ones. This slaving implies the Fourier law, which relates
the induced currents to the gradients of the conserved quantities.Comment: 23 page
Complementarity relation for irreversible process derived from stochastic energetics
When the process of a system in contact with a heat bath is described by
classical Langevin equation, the method of stochastic energetics [K. Sekimoto,
J. Phys. Soc. Jpn. vol. 66 (1997) p.1234] enables to derive the form of
Helmholtz free energy and the dissipation function of the system. We prove that
the irreversible heat Q_irr and the time lapse $Delta t} of an isothermal
process obey the complementarity relation, Q_irr {Delta t} >= k_B T S_min,
where S_min depends on the initial and the final values of the control
parameters, but it does not depend on the pathway between these values.Comment: 3 pages. LaTeX with 6 style macro
Clausius inequality and optimality of quasi static transformations for nonequilibrium stationary states
Nonequilibrium stationary states of thermodynamic systems dissipate a
positive amount of energy per unit of time. If we consider transformations of
such states that are realized by letting the driving depend on time, the amount
of energy dissipated in an unbounded time window becomes then infinite.
Following the general proposal by Oono and Paniconi and using results of the
macroscopic fluctuation theory, we give a natural definition of a renormalized
work performed along any given transformation. We then show that the
renormalized work satisfies a Clausius inequality and prove that equality is
achieved for very slow transformations, that is in the quasi static limit. We
finally connect the renormalized work to the quasi potential of the macroscopic
fluctuation theory, that gives the probability of fluctuations in the
stationary nonequilibrium ensemble
Ground States in the Spin Boson Model
We prove that the Hamiltonian of the model describing a spin which is
linearly coupled to a field of relativistic and massless bosons, also known as
the spin-boson model, admits a ground state for small values of the coupling
constant lambda. We show that the ground state energy is an analytic function
of lambda and that the corresponding ground state can also be chosen to be an
analytic function of lambda. No infrared regularization is imposed. Our proof
is based on a modified version of the BFS operator theoretic renormalization
analysis. Moreover, using a positivity argument we prove that the ground state
of the spin-boson model is unique. We show that the expansion coefficients of
the ground state and the ground state energy can be calculated using regular
analytic perturbation theory
Recently fixed carbon fuels microbial activity several meters below the soil surface
This data file (Scheibe_2022.xlsx) contains radiocarbon data of bulk soil carbon and CO2 respired in incubations from soil profiles in three climate zones (arid, mediterranean, and humid) of the Costal Cordillera of Chile down to a depth of six meters. Variable descriptions are provided in Template Info File. The data are part of a study, which investigates how soil microbial carbon cycling affects soil formation especially in the critical zone by understanding the carbon source of microbial activity in deep soil. The study was conducted within the framework of the Deep EarthShape priority program funded by the German Science Foundation (DFG-SPP 1803)
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