6 research outputs found
A mathematical theorem as the basis for the second law: Thomson's formulation applied to equilibrium
There are several formulations of the second law, and they may, in principle,
have different domains of validity. Here a simple mathematical theorem is
proven which serves as the most general basis for the second law, namely the
Thomson formulation (`cyclic changes cost energy'), applied to equilibrium.
This formulation of the second law is a property akin to particle conservation
(normalization of the wavefunction). It has been stricktly proven for a
canonical ensemble, and made plausible for a micro-canonical ensemble.
As the derivation does not assume time-inversion-invariance, it is applicable
to situations where persistent current occur. This clear-cut derivation allows
to revive the ``no perpetuum mobile in equilibrium'' formulation of the second
law and to criticize some assumptions which are widespread in literature.
The result puts recent results devoted to foundations and limitations of the
second law in proper perspective, and structurizes this relatively new field of
research.Comment: Revised version. Redundant assumption omitted. Microcanonical
ensemble included. Reference added. 7 pages revte
Second law of thermodynamics for macroscopic mechanics coupled to thermodynamic degrees of freedom
Based only on classical Hamiltonian dynamics, we prove the maximum work
principle in a system where macroscopic dynamical degrees of freedom are
intrinsically coupled to microscopic degrees of freedom. Unlike recent
identities between irreversible work and free energy, such as in the Jarzynski
relation, the macroscopic dynamics is not governed by an external action but
undergoes the back reaction of the microscopic degrees of freedom. Our theorems
cover such physical situations as impact between macroscopic bodies,
thermodynamic machines, and molecular motors.Comment: 4 pages, RevTe
Information and entropy in quantum Brownian motion: Thermodynamic entropy versus von Neumann entropy
We compare the thermodynamic entropy of a quantum Brownian oscillator derived
from the partition function of the subsystem with the von Neumann entropy of
its reduced density matrix. At low temperatures we find deviations between
these two entropies which are due to the fact that the Brownian particle and
its environment are entangled. We give an explanation for these findings and
point out that these deviations become important in cases where statements
about the information capacity of the subsystem are associated with
thermodynamic properties, as it is the case for the Landauer principle.Comment: 8 pages, 7 figure