In this paper, we first investigate the thermodynamic features of the black hole with a coulomb-like field. Moreover, we obtain the geometric description of the black hole thermodynamics. We find that for the black ho...In this paper, we first investigate the thermodynamic features of the black hole with a coulomb-like field. Moreover, we obtain the geometric description of the black hole thermodynamics. We find that for the black hole with a coulomb-like field the Weinhold geometry is fiat, whereas its Ruppeiner geometry is curved. For the heat capacity and curvature calculation shows the Ruppeiner geometry has a transition point.展开更多
It is a challenge to recover lithium from the leaching solution of spent lithium-ion batteries,and crown ethers are potential extractants due to their selectivity to alkali metal ions.The theoretical calculations for ...It is a challenge to recover lithium from the leaching solution of spent lithium-ion batteries,and crown ethers are potential extractants due to their selectivity to alkali metal ions.The theoretical calculations for the selectivity of crown ethers with different structures to Li ions in aqueous solutions were carried out based on the density functional theory.The calculated results of geometries,binding energies,and thermodynamic parameters show that 15C5 has the strongest selectivity to Li ions in the three crown ethers of 12C4,15C5,and 18C6.B15C5 has a smaller binding energy but more negative free energy than 15C5 when combined with Li^+,leading to that the lithium ions in aqueous solutions will combine with B15C5 rather than 15C5.The exchange reactions between B15C5 and hydrated Li^+,Co^2+,and Ni^2+were analyzed and the results show that B15C5 is more likely to capture Li^+from the hydrated ions in an aqueous solution containing Li^+,Co^2+,and Ni^2+.This study indicates that it is feasible to extract Li ions selectively using B15C5 as an extractant from the leaching solution of spent lithium-ion batteries.展开更多
The recent thermodynamical interpretation of the field equations of gravity is revisited and extended to the killing horizons linked to the rotation （Kerr black holes）. An entropic force can be defined also for thes...The recent thermodynamical interpretation of the field equations of gravity is revisited and extended to the killing horizons linked to the rotation （Kerr black holes）. An entropic force can be defined also for these horizons which are not event horizons but show thermodynamical features that in previous works were used to explain the rotational properties of Kerr solutions. Such entropic force is needed to describe the energetic processes, which do not change the usual thermal entropy of the rotating black hole （reversible transformations, superradiance）.展开更多
The paper addresses the formulation of rate equations, via objective time derivatives, within continuum physics. The concept of objectivity is reviewed and distinction is made with material frame-indifference whose me...The paper addresses the formulation of rate equations, via objective time derivatives, within continuum physics. The concept of objectivity is reviewed and distinction is made with material frame-indifference whose meaning is restricted to the invariance of the balance equations relative to Galilean frames. Objective time derivatives are defined to leave the tensor character of the appropriate field invariant within the set of Euclidean frames. Rate equations are required to involve objective time derivatives and to be consistent with the second law of thermodynamics. Here the general structure of objective time derivatives is established and the known derivatives of the physical literature are shown to be particular cases. Next, to fix ideas, a rate equation is considered for the model of heat conduction via a generalization of the Maxwell-Cattaneo equation with higher-order gradients as in the Guyer-Krumhansl equation. The thermodynamic restrictions are investigated and the expected effects, of the selected derivative of the heat flux, on the stress tensor are derived.展开更多
In this paper, we study the thermodynamic geometry for the charged Ad S black hole surrounded by quintessence. Three different kinds of the geometries are constructed, and the corresponding curvatures are obtained. It...In this paper, we study the thermodynamic geometry for the charged Ad S black hole surrounded by quintessence. Three different kinds of the geometries are constructed, and the corresponding curvatures are obtained. It is found that there are different divergence behaviors of these curvatures, which is general thought to closely link to the phase transition of the black hole.展开更多
The heat capacity and the electric capacitance of the black p-branes(BPB) are generally defined,then they are calculated for some special processes.It is found that the Ruppeiner thermodynamic geometry of BPB is flat....The heat capacity and the electric capacitance of the black p-branes(BPB) are generally defined,then they are calculated for some special processes.It is found that the Ruppeiner thermodynamic geometry of BPB is flat.Finally,we give some discussions for the flatness of the Ruppeiner thermodynamic geometry of BPB and some black holes.展开更多
The thermodynamic behavior of field equations for the generalized f(R) gravity with arbitrary coupling between matter and geometry is studied in the two kinds of spacetime,i.e.,the both spatially homogenous,isotropic ...The thermodynamic behavior of field equations for the generalized f(R) gravity with arbitrary coupling between matter and geometry is studied in the two kinds of spacetime,i.e.,the both spatially homogenous,isotropic FRW universe and static,spherically symmetric black hole spacetime.The field equations of the generalized f(R) gravity with arbitrary coupling between matter and geometry can be cast to the form of the first law of thermodynamics with the reputed entropy production terms dS,which are quite general and can degenerate to the cases of Einstein's general relativity and pure f(R) gravity with non-coupling and nonminimal coupling as special cases.The appearance of the entropy production term dS illustrates that the horizon thermodynamics is non-equilibrium one for the generalized f(R) gravity with arbitrary coupling between matter and geometry.展开更多
基金Supported by the Scientific and Technological Foundation of Chongqing Municipal Education Commission under Grant N0.KJ100706
文摘In this paper, we first investigate the thermodynamic features of the black hole with a coulomb-like field. Moreover, we obtain the geometric description of the black hole thermodynamics. We find that for the black hole with a coulomb-like field the Weinhold geometry is fiat, whereas its Ruppeiner geometry is curved. For the heat capacity and curvature calculation shows the Ruppeiner geometry has a transition point.
基金supported by the National Natural Science Foundation of China(No.51604005,No.U1703130,and No.51574003)
文摘It is a challenge to recover lithium from the leaching solution of spent lithium-ion batteries,and crown ethers are potential extractants due to their selectivity to alkali metal ions.The theoretical calculations for the selectivity of crown ethers with different structures to Li ions in aqueous solutions were carried out based on the density functional theory.The calculated results of geometries,binding energies,and thermodynamic parameters show that 15C5 has the strongest selectivity to Li ions in the three crown ethers of 12C4,15C5,and 18C6.B15C5 has a smaller binding energy but more negative free energy than 15C5 when combined with Li^+,leading to that the lithium ions in aqueous solutions will combine with B15C5 rather than 15C5.The exchange reactions between B15C5 and hydrated Li^+,Co^2+,and Ni^2+were analyzed and the results show that B15C5 is more likely to capture Li^+from the hydrated ions in an aqueous solution containing Li^+,Co^2+,and Ni^2+.This study indicates that it is feasible to extract Li ions selectively using B15C5 as an extractant from the leaching solution of spent lithium-ion batteries.
文摘The recent thermodynamical interpretation of the field equations of gravity is revisited and extended to the killing horizons linked to the rotation （Kerr black holes）. An entropic force can be defined also for these horizons which are not event horizons but show thermodynamical features that in previous works were used to explain the rotational properties of Kerr solutions. Such entropic force is needed to describe the energetic processes, which do not change the usual thermal entropy of the rotating black hole （reversible transformations, superradiance）.
文摘The paper addresses the formulation of rate equations, via objective time derivatives, within continuum physics. The concept of objectivity is reviewed and distinction is made with material frame-indifference whose meaning is restricted to the invariance of the balance equations relative to Galilean frames. Objective time derivatives are defined to leave the tensor character of the appropriate field invariant within the set of Euclidean frames. Rate equations are required to involve objective time derivatives and to be consistent with the second law of thermodynamics. Here the general structure of objective time derivatives is established and the known derivatives of the physical literature are shown to be particular cases. Next, to fix ideas, a rate equation is considered for the model of heat conduction via a generalization of the Maxwell-Cattaneo equation with higher-order gradients as in the Guyer-Krumhansl equation. The thermodynamic restrictions are investigated and the expected effects, of the selected derivative of the heat flux, on the stress tensor are derived.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11675064,11205074the Fundamental Research Funds for the Central Universities under Grant No.lzujbky-2016-121
文摘In this paper, we study the thermodynamic geometry for the charged Ad S black hole surrounded by quintessence. Three different kinds of the geometries are constructed, and the corresponding curvatures are obtained. It is found that there are different divergence behaviors of these curvatures, which is general thought to closely link to the phase transition of the black hole.
基金Supported by National Natural Science Foundation of China under Grant No.201210782
文摘The heat capacity and the electric capacitance of the black p-branes(BPB) are generally defined,then they are calculated for some special processes.It is found that the Ruppeiner thermodynamic geometry of BPB is flat.Finally,we give some discussions for the flatness of the Ruppeiner thermodynamic geometry of BPB and some black holes.
基金supported by the National Natural Science Foundation of China(Grant Nos.11175077 and 11147150)the Natural Science Foundation of Liaoning Province(Grant Nos.20102124 and L2011189)
文摘The thermodynamic behavior of field equations for the generalized f(R) gravity with arbitrary coupling between matter and geometry is studied in the two kinds of spacetime,i.e.,the both spatially homogenous,isotropic FRW universe and static,spherically symmetric black hole spacetime.The field equations of the generalized f(R) gravity with arbitrary coupling between matter and geometry can be cast to the form of the first law of thermodynamics with the reputed entropy production terms dS,which are quite general and can degenerate to the cases of Einstein's general relativity and pure f(R) gravity with non-coupling and nonminimal coupling as special cases.The appearance of the entropy production term dS illustrates that the horizon thermodynamics is non-equilibrium one for the generalized f(R) gravity with arbitrary coupling between matter and geometry.
