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
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.
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.
