Entropic force between biomembranes

Undulation force, an entropic force, stems from thermally excited fluctuations, and plays a key role in the essential interactions between neighboring surfaces of objects. Although the characteristics of the undulation force have been widely studied theoretically and experimentally,the distance dependence of the force, which constitutes its most fundamental characteristic, remains poorly understood.In this paper, first, we obtain a novel expression for the undulation force by employing elasticity and statistical mechanics and prove it to be in good agreement with existing experimental results. Second, we clearly demonstrate that the two representative forms of the undulation force proposed by Helfrich and Freund were respectively the upper and lower bounds of the present expression when the separation between membranes is sufficiently small, which was intrinsically different from the existing results where Helfrich＇s and Freund＇s forms of the undulation force were only suitable for the intermediate and small separations. The investigations show that only in a sufficiently small separation does Helfrich＇s result stand for the undulation force with a large wave number and Freund＇s result express the force with a small wave number. Finally, a critical acting distance of the undulation force, beyond which the entropic force will rapidly decay approaching zero, is presented.

A Note on Friedmann Equation of FRW Universe in Deformed Hoava-Lifshitz Gravity from Entropic Force

With entropic interpretation of gravity proposed by Verlinde, we obtain the Friedmann equation of the Friedmann Robertson-Walker universe for the deformed Hofava-Lifshitz gravity. It is shown that, when the parameter of Hofava-Lifshitz gravity ω →∞, the modified Friedmann equation will go back to the one in Einstein gravity. This results may imply that the entropic interpretation of gravity is effective for the deformed Hofava-Lifshitz gravity.

Debye Entropic Force and Modified Newtonian Dynamics

Verlinde has suggested that the gravity has an entropic origin, and a gravitational system could be regarded as a thermodynarnical system. It is well-known that the equipartition law of energy is invalid at very low temperature. Therefore, entropic force should be modified while the temperature of the holographic screen is very low. It is shown that the modified entropic force is proportional to the square of the acceleration, while the temperature of the holographic screen is much lower than the Debye temperature TD. The modified entropic force returns to the Newton＇s law of gravitation while the temperature of the holographic screen is much higher than the Debye temperature. The modified entropic force is connected with modified Newtonian dynamics （MOND）. The constant ao involved in MOND is linear in the Debye frequency WD, which can be regarded as the largest frequency of the bits in screen. We find that there do have a strong connection between MOND and cosmology in the framework of Verlinde＇s entropic force, if the holographic screen is taken to be bound of the Universe. The Debye frequency is linear in the Hubble constant Ho.

Spherical Confinement Generates Entropic Force to Accelerate Polymer Chain Detachment

To understand the dynamic process of polymer detachment, it is necessary to determine the mean detachment time of a single breakable link, which is modeled as a spring. Normally, this time can be viewed as the escape of a Brownian particle from the potential well of the spring. However, as the free dangling length of the polymer chain increases, the conformational entropy of the chain is affected by geometric confinement. It means that the wall exerts a repulsive force on the chain, resulting in accelerated link detachment from a macroscopic perspective. In this work, we investigate the effect of entropy on the detachment rate in the case where the substrate is spherical. We demonstrate that spherical confinement accelerates chain detachment both inside and outside the sphere. An analytical expression for the mean detachment time of breakable links is given, which includes an additional pre-factor that is related to the partition function. Additionally, we analyze the expressions for entropic forces inside the sphere, outside the sphere, and on a flat wall, comparing their magnitudes to explain the difference in mean detachment time.

Unruh-Verlinde temperature and energy of (2+1)-dimensional matter coupled black hole via entropic force

Verlinde＇s recent work, which shows that gravity may be explained as an entropic force caused by the changes in information associated with the positions of material bodies, is extended to study the Unruh-Verlinde temperature and energy of a static spherically symmetric charged black hole. The results indicate that the Unruh-Verlinde temperature is equal to the Hawking temperature at the event horizon. The energy is dependent on the radius of the screen, which is Mso a consequence of the Gauss＇ laws of gravity and electrostatics.

Entropic force between two horizons of dilaton black holes with a power-Maxwell field

In this paper,we consider(n+1)-dimensional topological dilaton de Sitter black holes with a powerMaxwell field as thermodynamic systems.The thermodynamic quantities corresponding to the black hole horizon and the cosmological horizon are interrelated.Therefore,the total entropy of the space-time should be the sum of the entropies of the black hole horizon and the cosmological horizon plus a correction term which is produced by the association of the two horizons.We analyze the entropic force produced by the correction term at given temperatures,which is affected by the parameters and dimensions of the space-time.It is shown that the change of entropic force with the position ratio of the two horizons in some regions is similar to that of the variation of the Lennard-Jones force with the position of particles.If the effect of entropic force is similar to that of the Lennard-Jones force,and other forces are absent,the motion of the cosmological horizon relative to the black hole horizon should have an oscillating process.The entropic force between the two horizons is probably one of the participants in driving the evolution of the universe.

Entropic destruction of heavy quarkonium with hyperscaling violation

We study the entropic destruction of heavy quarkonium in strongly coupled theories with an anisotropic scaling symmetry in time and a spatial direction.We consider Lifshitz and hyperscaling violation theories,which are covariant under a generalized Lifshitz scaling symmetry with the dynamical exponent z and hyperscaling violation exponentθ.It is shown that the entropic force depends on the parameters of these theories.In particular,increasing z decreases the entropic force,thus reducing the quarkonium dissociation,while increasingθhas the opposite effect.

A new explanation for statistical entropy of charged black hole

Using the Unruh-Verlinde temperature obtained by the idea of entropy force,we directly calculated the partition functions of Boson field in Reissner-Nordstro¨m spacetime with quantum statistical method.We obtain the expression of the black hole quantum statistical entropy.We find that the term is proportional to the area of black hole horizon and the logarithmic correction term appears.Our result is valid for flat spacetime.