The crucial condition in the derivation of the Jarzynski equality （JE） from the fluctuation theorem is that the time integral of the phase space contraction factor can be exactly expressed as the entropy production ...The crucial condition in the derivation of the Jarzynski equality （JE） from the fluctuation theorem is that the time integral of the phase space contraction factor can be exactly expressed as the entropy production resulting from the heat absorbed by the system from the thermal bath. For the system violating this condition, a more general form of JE may exist. This existence is verified by three Gedanken experiments and numerical simulations, and may be confirmed by the real experiment in the nanoscale.展开更多
The crystal structure of Ig81 domain confirms that the domain folds into a compactβ-sandwich,but with an evanescent BC-loop at the N-terminus.It is not clear whether the divergent BC-loop has an effect on the stabili...The crystal structure of Ig81 domain confirms that the domain folds into a compactβ-sandwich,but with an evanescent BC-loop at the N-terminus.It is not clear whether the divergent BC-loop has an effect on the stability of the shear topology formed by two of parallel A and Gβ-strands.In this paper,two Cαatoms in A and Gβ-strands were selected as two stress points,and the domains were stretched in opposite directions as a speed of 2.5×10-4 nm·ps-1.Under the same stretching conditions,100 steered molecular dynamics(SMD)runs were performed.The free energy of Ig81 was constructed as a function of the increasing distance between the two stress points using the Jarzynski's equality.For comparison,the free energy profile of the Ig27 domain was reconstructed with same method.The results show that the work done to unfold Ig81 is greater than the work done to unfold Ig27,and that the folding barrier of Ig81 is lower than that of Ig27.This suggests that the presence of the distinctive long BC-loop increases the sta-bility of the shear topology,thereby improving the mechanical strength of the protein.展开更多
Ted Jacobson discovered that gravity was related to thermodynamics. However, the calculated temperature using the Boltzmann area entropy is still not reasonable. We searched and discovered an empirical equation for th...Ted Jacobson discovered that gravity was related to thermodynamics. However, the calculated temperature using the Boltzmann area entropy is still not reasonable. We searched and discovered an empirical equation for the gravitational constant with a reasonable temperature. The calculated value was 3.20 K, which is similar to the temperature of the cosmic microwave background of 2.73 K. Then, we examined Yasuo Katayama’s theory. For this purpose, we introduced the modified Wagner’s equation, which is compatible with Jarzynski equality. Finally, using Ted Jacobson’s theory, we proposed our theory of gravity with the Gibbs volume entropy.展开更多
Previously, we proposed several empirical equations to describe the relationship between an electromagnetic force and the temperature of the cosmic microwave background (CMB).We attempted to justify why our empirical ...Previously, we proposed several empirical equations to describe the relationship between an electromagnetic force and the temperature of the cosmic microwave background (CMB).We attempted to justify why our empirical equations cannot be coincidental from the mathematical connections between our three equations. However, there are small errors in our empirical equations, which may lead to “indeed or not” arguments. After evaluating our equations, we discovered a method to improve the accuracy of the numerical calculations. For the value of the CMB, we used 2.72642 K instead of 2.72548 K. Regarding the factor of 9/2, we used 4.48870 instead of 4.5. Regarding the factor of <span style="white-space:nowrap;">π</span>, we used 3.13189 instead of 3.14159. Then, the error becomes less than 10<sup>-5</sup>. This means that our equations cannot be coincidental. Furthermore, we attempt to provide hints on how to construct the background theory.展开更多
基金We are grateful to the useful comments from Profs. C. Jarzynski, U. Seifert, M. Bier, and Dr. Gomez-Marin.
文摘The crucial condition in the derivation of the Jarzynski equality （JE） from the fluctuation theorem is that the time integral of the phase space contraction factor can be exactly expressed as the entropy production resulting from the heat absorbed by the system from the thermal bath. For the system violating this condition, a more general form of JE may exist. This existence is verified by three Gedanken experiments and numerical simulations, and may be confirmed by the real experiment in the nanoscale.
基金supported by Natural Science Foundation of Shandong Province(ZR2021QD126)。
文摘The crystal structure of Ig81 domain confirms that the domain folds into a compactβ-sandwich,but with an evanescent BC-loop at the N-terminus.It is not clear whether the divergent BC-loop has an effect on the stability of the shear topology formed by two of parallel A and Gβ-strands.In this paper,two Cαatoms in A and Gβ-strands were selected as two stress points,and the domains were stretched in opposite directions as a speed of 2.5×10-4 nm·ps-1.Under the same stretching conditions,100 steered molecular dynamics(SMD)runs were performed.The free energy of Ig81 was constructed as a function of the increasing distance between the two stress points using the Jarzynski's equality.For comparison,the free energy profile of the Ig27 domain was reconstructed with same method.The results show that the work done to unfold Ig81 is greater than the work done to unfold Ig27,and that the folding barrier of Ig81 is lower than that of Ig27.This suggests that the presence of the distinctive long BC-loop increases the sta-bility of the shear topology,thereby improving the mechanical strength of the protein.
文摘Ted Jacobson discovered that gravity was related to thermodynamics. However, the calculated temperature using the Boltzmann area entropy is still not reasonable. We searched and discovered an empirical equation for the gravitational constant with a reasonable temperature. The calculated value was 3.20 K, which is similar to the temperature of the cosmic microwave background of 2.73 K. Then, we examined Yasuo Katayama’s theory. For this purpose, we introduced the modified Wagner’s equation, which is compatible with Jarzynski equality. Finally, using Ted Jacobson’s theory, we proposed our theory of gravity with the Gibbs volume entropy.
文摘Previously, we proposed several empirical equations to describe the relationship between an electromagnetic force and the temperature of the cosmic microwave background (CMB).We attempted to justify why our empirical equations cannot be coincidental from the mathematical connections between our three equations. However, there are small errors in our empirical equations, which may lead to “indeed or not” arguments. After evaluating our equations, we discovered a method to improve the accuracy of the numerical calculations. For the value of the CMB, we used 2.72642 K instead of 2.72548 K. Regarding the factor of 9/2, we used 4.48870 instead of 4.5. Regarding the factor of <span style="white-space:nowrap;">π</span>, we used 3.13189 instead of 3.14159. Then, the error becomes less than 10<sup>-5</sup>. This means that our equations cannot be coincidental. Furthermore, we attempt to provide hints on how to construct the background theory.
