On the relaxation to nonequilibrium steady states

The issue of relaxation has been addressed in terms of ergodic theory in the past. However, the application of that theory to models of physical interest is problematic, especially when dealing with relaxation to nonequilibrium steady states. Here, we consider the relaxation of classical, thermostatted particle systems to equilibrium as well as to nonequilibrium steady states, using dynamical notions including decay of correlations. We show that the condition known as {\Omega}T-mixing is necessary and sufficient to prove relaxation of ensemble averages to steady state values. We then observe that the condition known as weak T-mixing applied to smooth observables is sufficient for relaxation to be independent of the initial ensemble. Lastly, weak T-mixing for integrable functions makes relaxation independent of the ensemble member, apart from a negligible set of members enabling the result to be applied to observations from a single physical experiment. The results also allow us to give a microscopic derivation of Prigogine's principle of minimum entropy production in the linear response regime. The key to deriving these results lies in shifting the discussion from characteristics of dynamical systems, such as those related to metric transitivity, to physical measurements and to the behaviour of observables. This naturally leads to the notion of physical ergodicity.Comment: 44 pages, 1 figur

Fluctuation Theorems

Fluctuation theorems, which have been developed over the past 15 years, have resulted in fundamental breakthroughs in our understanding of how irreversibility emerges from reversible dynamics, and have provided new statistical mechanical relationships for free energy changes. They describe the statistical fluctuations in time-averaged properties of many-particle systems such as fluids driven to nonequilibrium states, and provide some of the very few analytical expressions that describe nonequilibrium states. Quantitative predictions on fluctuations in small systems that are monitored over short periods can also be made, and therefore the fluctuation theorems allow thermodynamic concepts to be extended to apply to finite systems. For this reason, fluctuation theorems are anticipated to play an important role in the design of nanotechnological devices and in understanding biological processes. These theorems, their physical significance and results for experimental and model systems are discussed.Comment: A review, submitted to Annual Reviews in Physical Chemistry, July 2007 Acknowledgements corrected in revisio

The Glass Transition and the Jarzynski Equality

A simple model featuring a double well potential is used to represent a liquid that is quenched from an ergodic state into a history dependent glassy state. Issues surrounding the application of the Jarzynski Equality to glass formation are investigated. We demonstrate that the Jarzynski Equality gives the free energy difference between the initial state and the state we would obtain if the glass relaxed to true thermodynamic equilibrium. We derive new variations of the Jarzynski Equality which are relevant to the history dependent glassy state rather than the underlying equilibrium state. It is shown how to compute the free energy differences for the nonequilibrium history dependent glassy state such that it remains consistent with the standard expression for the entropy and with the second law inequality.Comment: 16 pages, 5 figure

Independence of the transient fluctuation theorem to thermostatting details

The dependence of fluctuation theorem on the precise mathematical details of thermostatting mechanism for an infinite class of fictious time reversible deterministic thermostats was analyzed. Theoretical and numerical analysis were carried out for a class of time reversible deterministic thermostats that fix various moments of the momentum distribution. In this large thermostat the transient fluctuation theorem (TFT) was found dependent of the precise moment that the thermostat fixes. The study shows that in a non-equilibrium system in contact with a thermostat and having large degrees of freedom, the transient fluctuation relation is insensitive to the details of thermostatting mechanisms

On the relationship between dissipation and the rate of spontaneous entropy production from linear irreversible thermodynamics

When systems are far from equilibrium, the temperature, the entropy and the thermodynamic entropy production are not defined and the Gibbs entropy does not provide useful information about the physical properties of a system. Furthermore, far from equilibrium, or if the dissipative field changes in time, the spontaneous entropy production of linear irreversible thermodynamics becomes irrelevant. In 2000 we introduced a definition for the dissipation function and showed that for systems of arbitrary size, arbitrarily near or far from equilibrium, the time integral of the ensemble average of this quantity can never decrease. In the low-field limit, its ensemble average becomes equal to the spontaneous entropy production of linear irreversible thermodynamics. We discuss how these quantities are related and why one should use dissipation rather than entropy or entropy production for non-equilibrium systems

IRE1α and IGF signaling predict resistance to an endoplasmic reticulum stress-inducing drug in glioblastoma cells.

To date current therapies of glioblastoma multiforme (GBM) are largely ineffective. The induction of apoptosis by an unresolvable unfolded protein response (UPR) represents a potential new therapeutic strategy. Here we tested 12ADT, a sarcoendoplasmic reticulum Ca2+ ATPase (SERCA) inhibitor, on a panel of unselected patient-derived neurosphere-forming cells and found that GBM cells can be distinguished into "responder" and "non-responder". By RNASeq analysis we found that the non-responder phenotype is significantly linked with the expression of UPR genes, and in particular ERN1 (IRE1) and ATF4. We also identified two additional genes selectively overexpressed among non-responders, IGFBP3 and IGFBP5. CRISPR-mediated deletion of the ERN1, IGFBP3, IGFBP5 signature genes in the U251 human GBM cell line increased responsiveness to 12ADT. Remarkably, >65% of GBM cases in The Cancer Genome Atlas express the non-responder (ERN1, IGFBP3, IGFBP5) gene signature. Thus, elevated levels of IRE1α and IGFBPs predict a poor response to drugs inducing unresolvable UPR and possibly other forms of chemotherapy helping in a better stratification GBM patients

The Ursinus Weekly, October 9, 1975

\u2779 elects Delli-Bovi; Jill Leauber fills vacancy • Ursinus hosts family fete • Danforth Foundation offers fellowships • Dept. addition • From the cluttered desk of the U.S.G.A. President • Correction • Editorial: The Fact, after or before • Focus: Dr. Parsons • Overview: Intro. Philosophy • Lions in another Bowl? • The Throwaway children • U.S.G.A. Carnival • Phila. singers open season • Aerosmith: Bedlam • Opportunity for women • Reflections: A letter home • AFC forecast • George McGinnis: $3 million man • Field hockey report • Lebanon Valley crushes Ursinushttps://digitalcommons.ursinus.edu/weekly/1042/thumbnail.jp

Dissipation and the Relaxation to Equilibrium

Using the recently derived Dissipation Theorem and a corollary of the Transient Fluctuation Theorem (TFT), namely the Second Law Inequality, we derive the unique time independent, equilibrium phase space distribution function for an ergodic Hamiltonian system in contact with a remote heat bath. We prove under very general conditions that any deviation from this equilibrium distribution breaks the time independence of the distribution. Provided temporal correlations decay, and the system is ergodic, we show that any nonequilibrium distribution that is an even function of the momenta, eventually relaxes (not necessarily monotonically) to the equilibrium distribution. Finally we prove that the negative logarithm of the microscopic partition function is equal to the thermodynamic Helmholtz free energy divided by the thermodynamic temperature and Boltzmann's constant. Our results complement and extend the findings of modern ergodic theory and show the importance of dissipation in the process of relaxation towards equilibrium.Comment: 18 pages, no figure