494 research outputs found
A Rigorous Derivation of the Entropy Bound and the Nature of Entropy Variation for Non-equilibrium Systems during Cooling
We use rigorous non-equilibrium thermodynamic arguments to prove (i) the
residual entropy of any system is bounded below by the experimentally
(calorimetrically) determined absolute temperature entropy, which itself is
bounded below by the entropy of the corresponding equilibrium (metastable
supercooled liquid) state, and (ii) the instantaneous entropy cannot drop below
that of the equilibrium state. The theorems follow from the second law and the
existence of internal equilibrium and refer to the thermodynamic entropy. They
go beyond the calorimetric observations by Johari and Khouri [J. Chem. Phys.
134, 034515 (2011)] and others by extending them to all non-equilibrium systems
regardless of how far they are from their equilibrium states. We also discuss
the statistical interpretation of the thermodynamic entropy and show that the
conventional Gibbs or Boltzmann interpretation gives the correct thermodynamic
entropy even for a single sample regardless of the duration of measurements.Comment: 25 pages; 1 figure; new result
Complexity Thermodynamics, Equiprobability Principle, Percolation, and Goldstein's Conjectures
The configurational states as introduced by Goldstein represent the system's
basins and are characterized by their free energies as we show
here. We find that the energies of some of the special points (termed basin
identifiers here) like the basin minima, maxima, lowest energy barriers, etc.
cannot be used to characterize the configurational states of the system in all
cases due to their possible non-monotonic behavior as we explain. The
complexity represents the configurational
state entropy. We prove that , where
and are the basin entropy and free energy,
respectively. We further prove that all basins at equilibrium have the same
equilibrium basin energy and entropy S_{\text{b}% }(T,V). Here,
\ and are measured with respect to the zero of the potential
energy. The Boltzmann equiprobability principle is shown to apply to the basins
in that each equilibrium basin has an equal probability
to be explored. This principle allow us to
draw some useful conclusions about the time-dependence in the system. We
discuss the percolation due to basin connectivity and its relevance for the
dynamic transition. Our analysis validates modified Goldstein's conjectures.
All the above results are shown to be valid at all temperatures, and not just
low temperatures as originally propsed by Goldstein.Comment: 14 pages; no figur
Consequences of the Detailed Balance for the Crooks Fluctuation Theorem
We show that the assumptions of the detailed balance and of the initial
equilibrium macrostate, which are central to the Crooks fluctuation theorem
(CFT), lead to all microstates along a trajectory to have equilibrium
probabilities. We also point out that the Crooks's definition of the backward
trajectory does not return the system back to its initial microstate. Once
corrected, the detailed balance assumption makes the CFT a theorem only about
reversible processes involving reversible trajectories that satisfy
Kolmogorov's criterion. As there is no dissipation, the CFT cannot cover
irreversible processes, which is contrary to the common belief. This is
consistent with our recent result that the JE is also a result only for
reversible processes.Comment: 15 page
Nonequilibrium Thermodynamics. Symmetric and Unique Formulation of the First Law, Statistical Definition of Heat and Work, Adiabatic Theorem and the Fate of the Clausius Inequality: A Microscopic View
The status of heat and work in nonequilibrium thermodynamics is quite
confusing and non-unique at present with conflicting interpretations even after
a long history of the first law in terms of exchange heat and work, and is far
from settled. Moreover, the exchange quantities lack certain symmetry. By
generalizing the traditional concept to also include their time-dependent
irreversible components allows us to express the first law in a symmetric form
dE(t)= dQ(t)-dW(t) in which dQ(t) and work dW(t) appear on an equal footing and
possess the symmetry. We prove that irreversible work turns into irreversible
heat. Statistical analysis in terms of microstate probabilities p_{i}(t)
uniquely identifies dW(t) as isentropic and dQ(t) as isometric (see text)
change in dE(t); such a clear separation does not occur for exchange
quantities. Hence, our new formulation of the first law provides tremendous
advantages and results in an extremely useful formulation of non-equilibrium
thermodynamics, as we have shown recently. We prove that an adiabatic process
does not alter p_{i}. All these results remain valid no matter how far the
system is out of equilibrium. When the system is in internal equilibrium,
dQ(t)\equivT(t)dS(t) in terms of the instantaneous temperature T(t) of the
system, which is reminiscent of equilibrium. We demonstrate that p_{i}(t) has a
form very different from that in equilibrium. The first and second laws are no
longer independent so that we need only one law, which is again reminiscent of
equilibrium. The traditional formulas like the Clausius inequality
{\oint}d_{e}Q(t)/T_{0}<0, etc. become equalities {\oint}dQ(t)/T(t)\equiv0, etc,
a quite remarkable but unexpected result in view of irreversibility. We
determine the irreversible components in two simple cases to show the
usefulness of our approach; here, the traditional formulation is of no use.Comment: 39 pages, 1 figur
Correcting the Mistaken Identification of Nonequilibrium Microscopic Work
The energy change dE_k for the kth microstate is erroneously equated with the
external work done on the microstate. It ignores the ubiquitous internal energy
change d_iW_k due to force imbalance between the internal and external forces.
We show that this contribution is present even in a reversible process, which
is a surprise. We show that the correct identification is dE_k=-dW_k, where
dW_k is the generalized work done by the microstate. We prove that the
thermodynamic average of the internal work gives dissipation and is not
captured by the external work. The latter effectively sets d_iW_k =0 and
results in no dissipation. Using dW_k to account for irreversibility, we obtain
a new work relation that works even for free expansion, where the Jarzynski
equality fails. In the new work relation, dW_k depends only on the energies of
the initial and final states and not on the actual process. This makes the new
relation very different from the Jarzynski equality. The correction has
far-reaching consequences and requires reassessment of current applications of
external work in theoretical physics.Comment: 20 pages, 4 Figures. Some overlap with arXiv:1702.0045
Nonequilibrium Entropy
We consider an isolated system in an arbitrary state and provide a general
formulation using first principles for an additive and non-negative statistical
quantity that is shown to reproduce the equilibrium thermodynamic entropy of
the isolated system. We further show that the statistical quantity represents
the nonequilibrium thermodynamic entropy when the latter is a state function of
nonequilibrium state variables; see text. We consider an isolated 1-d ideal gas
and determine its non-equilibrium statistical entropy as a function of the box
size as the gas expands freely isoenergetically, and compare it with the
equilibrium thermodynamic entropy S_{0eq}. We find that the statistical entropy
is less than S_{0eq} in accordance with the second law, as expected. To
understand how the statistical entropy is different from thermodynamic entropy
of classical continuum models that is known to become negative under certain
conditions, we calculate it for a 1-d lattice model and discover that it can be
related to the thermodynamic entropy of the continuum 1-d Tonks gas by taking
the lattice spacing {\delta} go to zero, but only if the latter is
state-independent. We discuss the semi-classical approximation of our entropy
and show that the standard quantity S_{f}(t) in the Boltzmann's H-theorem does
not directly correspond to the statistical entropy.Comment: 13 pages, 2 figure
Stationary Metastability in an Exact Non-Mean Field Calculation for a Model without Long-Range Interactions
We introduce the concept of stationary metastable states (SMS's) in the
presence of another more stable state. The stationary nature allows us to study
SMS's by using a restricted partition function formalism as advocated by
Penrose and Lebowitz and requires continuing the free energy. The formalism
ensures that SMS free energy satisfies the requirement of thermodynamic
stability everywhere including T=0, but need not represent a pysically
observable metastable state over the range where the entropy under continuation
becomes negative. We consider a 1-dimensional m-component axis-spin model
involving only nearest-neighbor interactions, which is solved exactly. The
high-temperature expansion of the model representys a polymer problem in which
m acts as the activity of a loop formation. We follow deGennes and trerat m as
a real variable. A thermodynamic phase transition occurs in the model for m<1.
The analytic continuation of the high-temperature disordered phase free energy
below the transition represents the free energy of the metastable state. The
calculation shows that the notion of SMS is not necessaily a consequence of
only mean-field analysis or requires long-range interactions.Comment: 9 pages, 2 figure
Comment on "Comment on: On the reality of residual entropies of glasses and disordered crystals" [J. Chem. Phys. 129, 067101 (2008)]
By using very general arguments, we show that the entropy loss conjecture at
the glass transition violates the second law of thermodynamics and must be
rejected.Comment: 6 pages, 2 figure
Entropy Crisis, Defects and the Role of Competition in Monatomic Glass Formers
We establish the existence of an entropy crisis in monatomic glass formers.
The work finally shows that the entropy crisis is ubiqutous in all supercooled
liquids. We also study the roles of defects and energetic competition on the
ideal glass.Comment: 4 pages, 3 figure
The Role of the Communal Entropy and Free Volume for the Viscosity Divergence near the Glass Transition: A New Conceptual Approach
The conventional approach to study glasses either requires considering the
rapid drop in the excess entropy {\Delta}S_ex or the free volume V_f. As the
two quantities are not directly related to each other, the viscosity in the two
approaches do not diverge at the same temperature, which casts doubt on the
physical significance of the divergence and of the ideal glass transition (IG).
By invoking a recently developed nonequilibrium thermodynamics, we identify the
instantaneous temperature, pressure, entropy, etc. and discover the way they
relax. We show that by replacing {\Delta}S_ex by a properly defined communal
entropy S^comm (not to be confused with the configurational entropy) and V_f
vanish simultaneously at IG, where the glass is jammed with no free volume and
communal entropy. By exploiting the fact that there are no thermodynamic
singularities in the entropy of the supercooled liquid at IG, we show that
various currently existing phenomenologies become unified.Comment: 18 pages, 6 figures. A condensed version of this paper is to appear
as a chapter in "Glass Encyclopedia" ed. P. Richet, VCH (2018
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