Considering that thermodynarmic irreversibility and hydrodynamic equations can not be derived rigorously and unifiedly from the Liouville equations, the anomalous Langevin equation in the Liouville space is proposed a...Considering that thermodynarmic irreversibility and hydrodynamic equations can not be derived rigorously and unifiedly from the Liouville equations, the anomalous Langevin equation in the Liouville space is proposed as a fundamental equation of statistical physics. This equation reflects that the law of motion of particles obeying reversible, deterministic laws in dynamics becomes irreversible and stochastic in thermodynamics. From this the fundamental equations of nonequilibrium thermodynamics, the principle of entropy increase and the theorem of minimum entropy production have been derived. The hydrodynamic equations, such as the generalized Navier-Stokes equation and the mass drift-diffusion equation etc. have been derived rigorously from the kinetic kinetic equation which is reduced from the anomalous Langevin equation in Liouville space. All these are unified and self consistent. But it is difficult to prove that entropy production density σ can never be negative everywhere for all the isolated inhomogeneous systems far from equilibrium.展开更多
A Brownian microscopic heat engine with a particle hopping on a one-dimensional lattice driven by adiscrete and periodic temperature field in a periodic sawtooth potential is investigated.In order to clarify the under...A Brownian microscopic heat engine with a particle hopping on a one-dimensional lattice driven by adiscrete and periodic temperature field in a periodic sawtooth potential is investigated.In order to clarify the underlyingphysical pictures of the heat engine, the heat flow via the potential energy and the kinetic energy of the particles areconsidered simultaneously.Based on describing the jumps among the three states, the expressions of the efficiency andpower output of the heat engine are derived analytically.The general performance characteristic curves are plotted bynumerical calculation.It is found that the power output-efficiency curve is a loop-shaped one, which is similar to onefor a real irreversible heat engine.The influence of the ratio of the temperature of the hot and cold reservoirs and thesawtooth potential on the maximum efficiency and power output is analyzed for some given parameters.When the heatflows via the kinetic energy is neglected, the power output-efficiency curve is an open-shaped one, which is similar to onefor an endroeversible heat engine.展开更多
Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determin...Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.展开更多
The Carnot-like heat engines are classified into three types （normal-, sub- and, super-dissipative） accord- ing to relations between the minimum irreversible entropy production in the ＂isothermal＂ processes and th...The Carnot-like heat engines are classified into three types （normal-, sub- and, super-dissipative） accord- ing to relations between the minimum irreversible entropy production in the ＂isothermal＂ processes and the time for completing those processes. The efficiencies at maximum power of normal-, sub- and super-dissipative Carnot-like heat engines are proved to be bounded between ηc/2 and ηc/ （2 - ηc ）, ηc /2 and ηc, 0 and ηc/ （2 - ηc ）, respectively. These bounds are also shared by linear, sub- and super-linear irreversible Carnot-like engines [Tu and Wang, Europhys. Left. 98 （2012） 40001] although the dissipative engines and the irreversible ones are inequivalent to each other.展开更多
Atmospheric oxygen （02） is the most crucial element on earth for the aerobic organisms that depend on it to release energy from carbon-based macromolecules. This is the first study to systematically analyze the glob...Atmospheric oxygen （02） is the most crucial element on earth for the aerobic organisms that depend on it to release energy from carbon-based macromolecules. This is the first study to systematically analyze the global O2 budget and its changes over the past 100 years. It is found that anthropogenic fossil fuel combustion is the largest contributor to the current O2 deficit, which consumed 2.0 Gt/a in 1900 and has increased to 38.2 Gt/a by 2015. Under the Representative Concentration Pathways （RCPs） RCP8,5 scenario, approximately 100Gt （gigatonnes） of O2 would be removed from the atmosphere per year until 2100, and the O2 concentration will decrease from its current level of 20.946% to 20.825%. Human activities have caused irreversible decline of atmospheric O2. It is time to take actions to promote O2 production and reduce O2 consumption.展开更多
A model of the irreversible regenerative Brayton refrigeration cycle working with paramagnetic materials is established,in which the regeneration problem in two constant-magnetic field processes and the irreversibilit...A model of the irreversible regenerative Brayton refrigeration cycle working with paramagnetic materials is established,in which the regeneration problem in two constant-magnetic field processes and the irreversibility in two adiabatic processes are considered synthetically.Expressions for the COP,cooling rate,power input,theminimum ratio of the two magnetic fields,etc.,are derived.It is found that the influence of the irreversibility and the regeneration on the main performance parameters of the magnetic Brayton refrigerator is remarkable.It is important that we have obtained several optimal criteria,which may provide some theoretical basis for the optimal design and operation of the Brayton refrigerator.The results obtained in the paper can provide some new theoretical information for the optimal design and performance improvement of real Brayton refrigerators.展开更多
文摘Considering that thermodynarmic irreversibility and hydrodynamic equations can not be derived rigorously and unifiedly from the Liouville equations, the anomalous Langevin equation in the Liouville space is proposed as a fundamental equation of statistical physics. This equation reflects that the law of motion of particles obeying reversible, deterministic laws in dynamics becomes irreversible and stochastic in thermodynamics. From this the fundamental equations of nonequilibrium thermodynamics, the principle of entropy increase and the theorem of minimum entropy production have been derived. The hydrodynamic equations, such as the generalized Navier-Stokes equation and the mass drift-diffusion equation etc. have been derived rigorously from the kinetic kinetic equation which is reduced from the anomalous Langevin equation in Liouville space. All these are unified and self consistent. But it is difficult to prove that entropy production density σ can never be negative everywhere for all the isolated inhomogeneous systems far from equilibrium.
基金Supported by the National Natural Science Foundation of China under Grant No.10765004
文摘A Brownian microscopic heat engine with a particle hopping on a one-dimensional lattice driven by adiscrete and periodic temperature field in a periodic sawtooth potential is investigated.In order to clarify the underlyingphysical pictures of the heat engine, the heat flow via the potential energy and the kinetic energy of the particles areconsidered simultaneously.Based on describing the jumps among the three states, the expressions of the efficiency andpower output of the heat engine are derived analytically.The general performance characteristic curves are plotted bynumerical calculation.It is found that the power output-efficiency curve is a loop-shaped one, which is similar to onefor a real irreversible heat engine.The influence of the ratio of the temperature of the hot and cold reservoirs and thesawtooth potential on the maximum efficiency and power output is analyzed for some given parameters.When the heatflows via the kinetic energy is neglected, the power output-efficiency curve is an open-shaped one, which is similar to onefor an endroeversible heat engine.
基金the Shanghai Science and Technology Commission, No. 01ZA14003.
文摘Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.
基金Supported by the National Natural Science Foundation of China under Grant No. 11075015the Fundamental Research Funds for the Central Universities
文摘The Carnot-like heat engines are classified into three types （normal-, sub- and, super-dissipative） accord- ing to relations between the minimum irreversible entropy production in the ＂isothermal＂ processes and the time for completing those processes. The efficiencies at maximum power of normal-, sub- and super-dissipative Carnot-like heat engines are proved to be bounded between ηc/2 and ηc/ （2 - ηc ）, ηc /2 and ηc, 0 and ηc/ （2 - ηc ）, respectively. These bounds are also shared by linear, sub- and super-linear irreversible Carnot-like engines [Tu and Wang, Europhys. Left. 98 （2012） 40001] although the dissipative engines and the irreversible ones are inequivalent to each other.
基金supported by the National Natural Science Foundation of China (41521004)the China University Research Talents Recruitment Program (111 project, B13045)
文摘Atmospheric oxygen （02） is the most crucial element on earth for the aerobic organisms that depend on it to release energy from carbon-based macromolecules. This is the first study to systematically analyze the global O2 budget and its changes over the past 100 years. It is found that anthropogenic fossil fuel combustion is the largest contributor to the current O2 deficit, which consumed 2.0 Gt/a in 1900 and has increased to 38.2 Gt/a by 2015. Under the Representative Concentration Pathways （RCPs） RCP8,5 scenario, approximately 100Gt （gigatonnes） of O2 would be removed from the atmosphere per year until 2100, and the O2 concentration will decrease from its current level of 20.946% to 20.825%. Human activities have caused irreversible decline of atmospheric O2. It is time to take actions to promote O2 production and reduce O2 consumption.
基金supported by the Program for Excellent Young Teachers of Shanghai,China (Grant No.thc-20100036)
文摘A model of the irreversible regenerative Brayton refrigeration cycle working with paramagnetic materials is established,in which the regeneration problem in two constant-magnetic field processes and the irreversibility in two adiabatic processes are considered synthetically.Expressions for the COP,cooling rate,power input,theminimum ratio of the two magnetic fields,etc.,are derived.It is found that the influence of the irreversibility and the regeneration on the main performance parameters of the magnetic Brayton refrigerator is remarkable.It is important that we have obtained several optimal criteria,which may provide some theoretical basis for the optimal design and operation of the Brayton refrigerator.The results obtained in the paper can provide some new theoretical information for the optimal design and performance improvement of real Brayton refrigerators.
