Theoretische Physik IV: Statistische Mechanik, Exercise 6
... (b) Using the result from (a) show that absolute zero cannot be reached by an
In the following we gain intuition whether absolute zero can be reached at all. We
consider the fact that cooling processes always take place between two curves with
X = const., e.g. X1 = P1 , X2 = P2 ...
Does the Third Law of Thermodynamics Hold
... where H is the Hamiltonian for the whole system (quantum particle plus heat
bath plus interaction). The question is how to calculate the entropy S from this
expression. In Ref. 4, three different results for the entropy are obtained based on
use of the free energy (S p given in (3.59) of Ref. 4), th ...
Entanglement Entropies in the Ground States of Helium
... We also computed the entanglement entropies for the ground states of the two-electron atoms with different
values of Z . Our results for the linear entropy and the vN entropy are listed in the table 6, where a comparison
with the literature [16,17] is also made. It is worth stressing that in each ca ...
An equal area law for holographic entanglement entropy of the AdS
... Motivated by the themes above, in this paper we track entanglement entropy across
a family of van der Waals-like phase transitions of charged black holes in AdS. The first
phase transition under study is the one of AdS-RN in the canonical ensemble in 4 and 5
dimensions. This transition was first di ...
Modeling and Analysis of Entropy Generation in Light
... Each of the three components (lattice, electrons and holes) is locally in thermodynamic equilibrium;
(c) They are able to interchange energy with each other by various scattering mechanisms; (d) The
three components are in thermal equilibrium; (e) The admissible states of electrons and holes are
Maximum Entropy Closure of Balance Equations for Miniband
... solution of the kinetic equations, or by comparison with the results of a systematic perturbation
procedure that has been positively contrasted with the numerical solution of the kinetic equations.
For linear kinetic equations, the related minimum entropy production principle [10–12], has been used
Entropy (arrow of time)
Entropy is the only quantity in the physical sciences (apart from certain rare interactions in particle physics; see below) that requires a particular direction for time, sometimes called an arrow of time. As one goes ""forward"" in time, the second law of thermodynamics says, the entropy of an isolated system can increase, but not decrease. Hence, from one perspective, entropy measurement is a way of distinguishing the past from the future. However in thermodynamic systems that are not closed, entropy can decrease with time: many systems, including living systems, reduce local entropy at the expense of an environmental increase, resulting in a net increase in entropy. Examples of such systems and phenomena include the formation of typical crystals, the workings of a refrigerator and living organisms.Entropy, like temperature, is an abstract concept, yet, like temperature, everyone has an intuitive sense of the effects of entropy. Watching a movie, it is usually easy to determine whether it is being run forward or in reverse. When run in reverse, broken glasses spontaneously reassemble, smoke goes down a chimney, wood ""unburns"", cooling the environment and ice ""unmelts"" warming the environment. No physical laws are broken in the reverse movie except the second law of thermodynamics, which reflects the time-asymmetry of entropy. An intuitive understanding of the irreversibility of certain physical phenomena (and subsequent creation of entropy) allows one to make this determination.By contrast, all physical processes occurring at the microscopic level, such as mechanics, do not pick out an arrow of time. Going forward in time, an atom might move to the left, whereas going backward in time the same atom might move to the right; the behavior of the atom is not qualitatively different in either case. It would, however, be an astronomically improbable event if a macroscopic amount of gas that originally filled a container evenly spontaneously shrunk to occupy only half the container.Certain subatomic interactions involving the weak nuclear force violate the conservation of parity, but only very rarely. According to the CPT theorem, this means they should also be time irreversible, and so establish an arrow of time. This, however, is neither linked to the thermodynamic arrow of time, nor has anything to do with our daily experience of time irreversibility.