Spacetime Thermodynamics And Entropy

Gravity, being one of the four fundamental interactions, has not yet been unit-ed with other united interactions. This conundrum has puzzled innumerable scientif-ic researchers. Superstring theory and loop quantum theory, as the prevalent theoriesof quantization of gravity, give different descriptions of this problem. However, theythemselves still have various troubles and have not been verified.The research on Hawking radiation, black hole entropy and thermodynamics havebrought great inspiration since the 1970s. A considerable amount of theoretic physi-cist believe that the gravity is rather emergent than fundamental. Jacobson assumedthe proportionality of entropy and area of horizon, and the Clausius relation, to derivethe Einstein equations and then the field equation of the f(R) gravity. Verlinde alsoobtained the Einstein equations with hypothesis of entropy force.The meaning and function of entropy production term is not definite. Some fol-lowing papers truncate this term to analyze generalized gravity. We noticed that theambiguity term of approximate Killing vector field may be the origin of entropy pro-duction term. Our approach is to reverse the logic of Jacobson by assuming the validityof field equations, and then derive and analyze the form of entropy. We then find thedynamics related entropy and the unrelated entropy production term separately. Thequantity constructing the entropy production term is boost variant, which has ambigui-ty. After comparison, We find the entropy production term has direct relation with theambiguity term of approximate Killing vector field.In 2010, our group found a new entropy force scenario and holographic thermo-dynamics based on the work of Jacobson and Verlinde, by introducing Brown-Yorkquasi-local energy and a stress tensor on holographic screen. In chapter 3, we apply t-wo ideal systems to calculate the thermodynamics of screen. The first model is a sparseand constant density ball. Let a holographic screen sweep a short distance in the ballradially, and then derive the first law of thermodynamics on screen. The second modelis sweeping the screen in vacuum at infinity from a ball with constant mass. Since bothof these are of extreme condition, the entropy we obtain is the entropy bound which iscoincident with Bekenstein entropy bound.