11 research outputs found
Tsallis Ensemble as an Exact Orthode
We show that Tsallis ensemble of power-law distributions provides a
mechanical model of nonextensive equilibrium thermodynamics for small
interacting Hamiltonian systems, i.e., using Boltzmann's original nomenclature,
we prove that it is an exact orthode. This means that the heat differential
admits the inverse average kinetic energy as an integrating factor. One
immediate consequence is that the logarithm of the normalization function can
be identified with the entropy, instead of the q-deformed logarithm. It has
been noted that such entropy coincides with Renyi entropy rather than Tsallis
entropy, it is non-additive, tends to the standard canonical entropy as the
power index tends to infinity and is consistent with the free energy formula
proposed in [S. Abe et. al. Phys. Lett. A 281, 126 (2001)]. It is also shown
that the heat differential admits the Lagrange multiplier used in non-extensive
thermodynamics as an integrating factor too, and that the associated entropy is
given by ordinary nonextensive entropy. The mechanical approach proposed in
this work is fully consistent with an information-theoretic approach based on
the maximization of Renyi entropy.Comment: 5 pages. Added connection with Renyi entrop
Nonextensive Reaction Rate
The Kramers' survival probability has been generalized by using nonextensive
formalism. This nonextensive survival probability is studied in detail and
associated Kramers' rate has been calculated in the high and low viscosity
limit. It has been showed that the proportionality of nonextensive Kramers'
rate to the nonextensive friction term in the high viscosity limit changes to
inverse proportionality in the low viscosity limit. It has also been observed
that friction constant of nonextensive processes is of rescaled form of the
ordinary frictional term. Since the relation between the ordinary rate and
nonextensive rate is found out to be linear, the Arrhenius nature of the
Kramers' rate is preserved. By using experimental results related to CO
rebinding to myoglobin after photodissociation, we conclude that nonextensivity
plays an important role in protein reactions.Comment: 6 pages, 1 Figur
Non-Boltzmann stationary distributions and nonequilibrium relations in active baths
Most natural and engineered processes, such as biomolecular reactions, protein folding, and population dynamics, occur far from equilibrium and therefore cannot be treated within the framework of classical equilibrium thermodynamics. Here we experimentally study how some fundamental thermodynamic quantities and relations are affected by the presence of the nonequilibrium fluctuations associated with an active bath. We show in particular that, as the confinement of the particle increases, the stationary probability distribution of a Brownian particle confined within a harmonic potential becomes non-Boltzmann, featuring a transition from a Gaussian distribution to a heavy-tailed distribution. Because of this, nonequilibrium relations (e.g., the Jarzynski equality and Crooks fluctuation theorem) cannot be applied. We show that these relations can be restored by using the effective potential associated with the stationary probability distribution. We corroborate our experimental findings with theoretical arguments. © 2016 American Physical Society
Bistability in Apoptosis: Roles of Bax, Bcl-2, and Mitochondrial Permeability Transition Pores
We propose a mathematical model for mitochondria-dependent apoptosis, in which kinetic cooperativity in formation of the apoptosome is a key element ensuring bistability. We examine the role of Bax and Bcl-2 synthesis and degradation rates, as well as the number of mitochondrial permeability transition pores (MPTPs), on the cell response to apoptotic stimuli. Our analysis suggests that cooperative apoptosome formation is a mechanism for inducing bistability, much more robust than that induced by other mechanisms, such as inhibition of caspase-3 by the inhibitor of apoptosis (IAP). Simulations predict a pathological state in which cells will exhibit a monostable cell survival if Bax degradation rate is above a threshold value, or if Bax expression rate is below a threshold value. Otherwise, cell death or survival occur depending on initial caspase-3 levels. We show that high expression rates of Bcl-2 can counteract the effects of Bax. Our simulations also demonstrate a monostable (pathological) apoptotic response if the number of MPTPs exceeds a threshold value. This study supports our contention, based on mathematical modeling, that cooperativity in apoptosome formation is critically important for determining the healthy responses to apoptotic stimuli, and helps define the roles of Bax, Bcl-2, and MPTP vis-Ã -vis apoptosome formation