Abstract A finite-time thermodynamic (FTT) model of three-heat-reservoir thermal Brownian refrigerator is established in this paper. This model can be equivalent to the coupling of a thermal Brownian engine and a thermal Brownian refrigerator with heat transfer effects. Expressions for cooling load and coefficient of performance (COP) are derived by combining FTT and non-equilibrium thermodynamics (NET). The system performance is studied and compared with those of previous models. For fixed internal parameters, the thermal conductance distributions among three heat exchangers are optimized for maximal cooling load. For fixed inventory allocations, the internal parameters are also optimized for maximal cooling load. Finally, the double-maximum cooling load is obtained by optimizing internal parameters and external thermal conductance distributions simultaneously, and the optimal operating temperatures are also derived. Results show that half of total thermal conductance should be placed in condenser to reject heat to ambient under maximal cooling load regime. The heat transfer determines system performance by controlling the working temperatures and the coupling of two external loads. The system works in reversible state when COP reaches its maximum value. The new performance limits can predict that of three-heat-reservoir thermal Brownian refrigerator more accurately, and also include those of NET model.
{"title":"Heat transfer effect on the performance of three-heat-reservoir thermal Brownian refrigerator","authors":"Congzheng Qi, Lingen Chen, Yanlin Ge, Huijun Feng","doi":"10.1515/jnet-2023-0050","DOIUrl":"https://doi.org/10.1515/jnet-2023-0050","url":null,"abstract":"Abstract A finite-time thermodynamic (FTT) model of three-heat-reservoir thermal Brownian refrigerator is established in this paper. This model can be equivalent to the coupling of a thermal Brownian engine and a thermal Brownian refrigerator with heat transfer effects. Expressions for cooling load and coefficient of performance (COP) are derived by combining FTT and non-equilibrium thermodynamics (NET). The system performance is studied and compared with those of previous models. For fixed internal parameters, the thermal conductance distributions among three heat exchangers are optimized for maximal cooling load. For fixed inventory allocations, the internal parameters are also optimized for maximal cooling load. Finally, the double-maximum cooling load is obtained by optimizing internal parameters and external thermal conductance distributions simultaneously, and the optimal operating temperatures are also derived. Results show that half of total thermal conductance should be placed in condenser to reject heat to ambient under maximal cooling load regime. The heat transfer determines system performance by controlling the working temperatures and the coupling of two external loads. The system works in reversible state when COP reaches its maximum value. The new performance limits can predict that of three-heat-reservoir thermal Brownian refrigerator more accurately, and also include those of NET model.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135044125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-01DOI: 10.1515/jnet-2023-frontmatter4
{"title":"Frontmatter","authors":"","doi":"10.1515/jnet-2023-frontmatter4","DOIUrl":"https://doi.org/10.1515/jnet-2023-frontmatter4","url":null,"abstract":"","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134935280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Noha M. Sayed, Hussien Noby, Kyaw Thu, Ahmed H. El-Shazly
Abstract Some of the previous investigations neglect the mass transfer contribution of the hydrophilic layer for modeling the Janus membrane that is used for direct contact membrane distillation (DCMD). This work studies the impact of adding such resistance on the performance of the DCMD, especially on the temperature polarization coefficient (TPC), thermal efficiency, and permeate flux. The commercial software Ansys 2020 was used to describe the transport behavior through the Janus membrane. The bulk-flow model was employed to evaluate the permeate flow through the hydrophilic layer for the first time. Simulation results were compared with the experimental results from the literature for validating the model, and a satisfactory agreement was found. Results demonstrated that the permeate flux increased by about 61.3 % with changing the porosity of the hydrophilic layer from 0.5 to 0.9 for the membrane with the lowest hydrophilic layer thickness. Moreover, the thermal conductivities of both layers contribute significantly to the DCMD’s overall performance enhancement. Vapour flux might be enhanced by increasing the hydrophilic layer’s thermal conductivity while decreasing the hydrophobic layer’s thermal conductivity. Finally, the DCMD thermal efficiency was investigated, for the first time, in terms of both layer characteristics.
{"title":"Improved modeling of Janus membrane considering the influence of hydrophilic layer characteristics","authors":"Noha M. Sayed, Hussien Noby, Kyaw Thu, Ahmed H. El-Shazly","doi":"10.1515/jnet-2023-0037","DOIUrl":"https://doi.org/10.1515/jnet-2023-0037","url":null,"abstract":"Abstract Some of the previous investigations neglect the mass transfer contribution of the hydrophilic layer for modeling the Janus membrane that is used for direct contact membrane distillation (DCMD). This work studies the impact of adding such resistance on the performance of the DCMD, especially on the temperature polarization coefficient (TPC), thermal efficiency, and permeate flux. The commercial software Ansys 2020 was used to describe the transport behavior through the Janus membrane. The bulk-flow model was employed to evaluate the permeate flow through the hydrophilic layer for the first time. Simulation results were compared with the experimental results from the literature for validating the model, and a satisfactory agreement was found. Results demonstrated that the permeate flux increased by about 61.3 % with changing the porosity of the hydrophilic layer from 0.5 to 0.9 for the membrane with the lowest hydrophilic layer thickness. Moreover, the thermal conductivities of both layers contribute significantly to the DCMD’s overall performance enhancement. Vapour flux might be enhanced by increasing the hydrophilic layer’s thermal conductivity while decreasing the hydrophobic layer’s thermal conductivity. Finally, the DCMD thermal efficiency was investigated, for the first time, in terms of both layer characteristics.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135110266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Based on the irreversible Otto cycle model, applying finite-time-thermodynamic theory, this paper takes power and efficiency as the objective functions, further studies the cycle performance under the condition of non-ideal gas working fluid, analyzes the effects of different loss items and freedom degree (d) of monatomic gas on the cycle performance, and compares performance differences of ideal gas and non-ideal gas under different specific heat models. The results demonstrate that, with the increase of d, the maximum-power-output (Pmax), the maximum-thermal-efficiency (ηmax), the corresponding optimal compression-ratio ( ( γ opt ) p ${({gamma }_{text{opt}})}_{p}$ ) and efficiency (η P ) at the Pmax point, and the corresponding optimal compression ratio ( ( γ opt ) η ${({gamma }_{text{opt}})}_{eta }$ ) and power (P η ) at the ηmax point will all increase; the Pmax, ( γ opt ) p ${({gamma }_{text{opt}})}_{p}$ , ηmax, ( γ opt ) η ${({gamma }_{text{opt}})}_{eta }$ , η p and P η will decrease with the increases of three irreversible losses; the specific heat model has only quantitative effect on cycle performance but no qualitative effect; under condition of non-ideal gas specific heat model, the power and efficiency are the smallest.
{"title":"Effect of non-ideal gas working fluid on power and efficiency performances of an irreversible Otto cycle","authors":"Di Wu, Y. Ge, Lingen Chen, Lei Tian","doi":"10.1515/jnet-2023-0036","DOIUrl":"https://doi.org/10.1515/jnet-2023-0036","url":null,"abstract":"Abstract Based on the irreversible Otto cycle model, applying finite-time-thermodynamic theory, this paper takes power and efficiency as the objective functions, further studies the cycle performance under the condition of non-ideal gas working fluid, analyzes the effects of different loss items and freedom degree (d) of monatomic gas on the cycle performance, and compares performance differences of ideal gas and non-ideal gas under different specific heat models. The results demonstrate that, with the increase of d, the maximum-power-output (Pmax), the maximum-thermal-efficiency (ηmax), the corresponding optimal compression-ratio ( ( γ opt ) p ${({gamma }_{text{opt}})}_{p}$ ) and efficiency (η P ) at the Pmax point, and the corresponding optimal compression ratio ( ( γ opt ) η ${({gamma }_{text{opt}})}_{eta }$ ) and power (P η ) at the ηmax point will all increase; the Pmax, ( γ opt ) p ${({gamma }_{text{opt}})}_{p}$ , ηmax, ( γ opt ) η ${({gamma }_{text{opt}})}_{eta }$ , η p and P η will decrease with the increases of three irreversible losses; the specific heat model has only quantitative effect on cycle performance but no qualitative effect; under condition of non-ideal gas specific heat model, the power and efficiency are the smallest.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":6.6,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44655173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Radiative heat transport involving complex geometries is an important area of investigation. The formulation of the transport phenomenon is more involved and consideration of the proper treatment of the irregular geometry becomes necessary for accurate estimation of heat transfer rates. Therefore, the present study focuses on the modeling and the solution of the radiative transfer equation (RTE) in an absorbing, emitting, and isotropically scattering, participating media for complex geometries using the body-fitted coordinates. The RTE in an orthogonal coordinate system is formulated and is then numerically solved in conjunction with a numerically generated, body-fitted, curvilinear coordinate system. The geometries are considered to be opaque and, in the analysis, both the radiative as well as the non-radiative equilibrium cases are considered. The formulation is validated through the previously published results. Notable agreement is observed between the results and those reported earlier for different complex geometries and various properties of the participating media.
{"title":"Computational radiative transport in complex geometries using orthogonal coordinates","authors":"Md. Ershadul Haque, S. Mansoor, B. Yilbas","doi":"10.1515/jnet-2023-0009","DOIUrl":"https://doi.org/10.1515/jnet-2023-0009","url":null,"abstract":"Abstract Radiative heat transport involving complex geometries is an important area of investigation. The formulation of the transport phenomenon is more involved and consideration of the proper treatment of the irregular geometry becomes necessary for accurate estimation of heat transfer rates. Therefore, the present study focuses on the modeling and the solution of the radiative transfer equation (RTE) in an absorbing, emitting, and isotropically scattering, participating media for complex geometries using the body-fitted coordinates. The RTE in an orthogonal coordinate system is formulated and is then numerically solved in conjunction with a numerically generated, body-fitted, curvilinear coordinate system. The geometries are considered to be opaque and, in the analysis, both the radiative as well as the non-radiative equilibrium cases are considered. The formulation is validated through the previously published results. Notable agreement is observed between the results and those reported earlier for different complex geometries and various properties of the participating media.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":6.6,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48120885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Parsa Movahedi, Ali Jalali Qush Qayeh, Javad Rahbar Shahrouzi
Abstract In order to commercialize aqueous two-phase systems (ATPSs), not only the equilibrium data is essential, but also the knowledge of separation mechanisms, kinetics, settling time, and operational conditions are needed. Mixing duration and settling time are the most critical factors affecting separation and biomolecule partitioning in terms of economic aspects. This research aimed to find the desired conditions for separating cephalexin in an ATPS consisting of acetonitrile, glucose, and water. Firstly, the evolution of the interphase region was observed. Hereafter, to examine the effect of time on the experimental tie-lines and partition coefficient in non-equilibrium states, the settling time was varied from 2 min to 24 h. In addition, centrifugation was applied to help the separation at different time intervals and rotational speeds. The results of tie-lines slope and partitioning coefficients showed that the system approaches equilibrium after 5 h. However, using the centrifuge separation at 4000 rpm improved the separation time to 45 min, reaching 80 % of the actual partition coefficient. It can be concluded that with an acceptable tolerance in the partition coefficient, a remarkably diminished settling time is available for economic productivity in industrial units.
{"title":"Investigation of non-equilibrium separation time on the partitioning of cephalexin in an aqueous two-phase system composed of glucose and acetonitrile","authors":"Parsa Movahedi, Ali Jalali Qush Qayeh, Javad Rahbar Shahrouzi","doi":"10.1515/jnet-2023-0028","DOIUrl":"https://doi.org/10.1515/jnet-2023-0028","url":null,"abstract":"Abstract In order to commercialize aqueous two-phase systems (ATPSs), not only the equilibrium data is essential, but also the knowledge of separation mechanisms, kinetics, settling time, and operational conditions are needed. Mixing duration and settling time are the most critical factors affecting separation and biomolecule partitioning in terms of economic aspects. This research aimed to find the desired conditions for separating cephalexin in an ATPS consisting of acetonitrile, glucose, and water. Firstly, the evolution of the interphase region was observed. Hereafter, to examine the effect of time on the experimental tie-lines and partition coefficient in non-equilibrium states, the settling time was varied from 2 min to 24 h. In addition, centrifugation was applied to help the separation at different time intervals and rotational speeds. The results of tie-lines slope and partitioning coefficients showed that the system approaches equilibrium after 5 h. However, using the centrifuge separation at 4000 rpm improved the separation time to 45 min, reaching 80 % of the actual partition coefficient. It can be concluded that with an acceptable tolerance in the partition coefficient, a remarkably diminished settling time is available for economic productivity in industrial units.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":6.6,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45751585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract While genetic mutations, natural selection and environmental pressures are well-known drivers of enzyme evolution, we show that their structural adaptations are significantly influenced by energy dissipation. Enzymes use chemical energy to do work, which results in a loss of free energy due to the irreversible nature of the process. By assuming that the catalytic process occurs along a potential barrier, we describe the kinetics of the conversion of enzyme-substrate complexes to enzyme-product complexes and calculate the energy dissipation. We show that the behaviour of the dissipated energy is a non-monotonic function of the energy of the intermediate state. This finding supports our main result that enzyme configurations evolve to minimise energy dissipation and simultaneously improve kinetic and thermodynamic efficiencies. Our study provides a novel insight into the complex process of enzyme evolution and highlights the crucial role of energy dissipation in shaping structural adaptations.
{"title":"Uncovering enzymatic structural adaptations from energy dissipation","authors":"A. Arango-Restrepo, D. Barragán, J. Rubí","doi":"10.1515/jnet-2023-0044","DOIUrl":"https://doi.org/10.1515/jnet-2023-0044","url":null,"abstract":"Abstract While genetic mutations, natural selection and environmental pressures are well-known drivers of enzyme evolution, we show that their structural adaptations are significantly influenced by energy dissipation. Enzymes use chemical energy to do work, which results in a loss of free energy due to the irreversible nature of the process. By assuming that the catalytic process occurs along a potential barrier, we describe the kinetics of the conversion of enzyme-substrate complexes to enzyme-product complexes and calculate the energy dissipation. We show that the behaviour of the dissipated energy is a non-monotonic function of the energy of the intermediate state. This finding supports our main result that enzyme configurations evolve to minimise energy dissipation and simultaneously improve kinetic and thermodynamic efficiencies. Our study provides a novel insight into the complex process of enzyme evolution and highlights the crucial role of energy dissipation in shaping structural adaptations.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":6.6,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42499241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-13DOI: 10.1515/jnet-2023-frontmatter3
{"title":"Frontmatter","authors":"","doi":"10.1515/jnet-2023-frontmatter3","DOIUrl":"https://doi.org/10.1515/jnet-2023-frontmatter3","url":null,"abstract":"","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136222215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Any real physical process that produces entropy, dissipates energy as heat, or generates mechanical work must do so on a finite timescale. Recently derived thermodynamic speed limits place bounds on these observables using intrinsic timescales of the process. Here, we derive relationships for the thermodynamic speeds for any composite stochastic observable in terms of the timescales of its individual components. From these speed limits, we find bounds on thermal efficiency of stochastic processes exchanging energy as heat and work and bound the rate of entropy change in a system with entropy production and flow. Using the time set by an external clock, we find bounds on the first time to reach any value for the entropy production. As an illustration, we compute these bounds for Brownian particles diffusing in space subject to a constant-temperature heat bath and a time-dependent external force.
{"title":"Relations between timescales of stochastic thermodynamic observables","authors":"Erez Aghion, Jason R. Green","doi":"10.1515/jnet-2022-0104","DOIUrl":"https://doi.org/10.1515/jnet-2022-0104","url":null,"abstract":"Abstract Any real physical process that produces entropy, dissipates energy as heat, or generates mechanical work must do so on a finite timescale. Recently derived thermodynamic speed limits place bounds on these observables using intrinsic timescales of the process. Here, we derive relationships for the thermodynamic speeds for any composite stochastic observable in terms of the timescales of its individual components. From these speed limits, we find bounds on thermal efficiency of stochastic processes exchanging energy as heat and work and bound the rate of entropy change in a system with entropy production and flow. Using the time set by an external clock, we find bounds on the first time to reach any value for the entropy production. As an illustration, we compute these bounds for Brownian particles diffusing in space subject to a constant-temperature heat bath and a time-dependent external force.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":6.6,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49521938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The wide-spread opinion is that original quantum mechanics is a reversible theory, but this statement is only true for undecomposed systems that are those systems for which sub-systems are out of consideration. Taking sub-systems into account, as it is by definition necessary for decomposed systems, the interaction Hamiltonians –which are absent in undecomposed systems– can be a source of irreversibility in decomposed systems. Thus, the following two-stage task arises: How to modify von Neumann’s equation of undecomposed systems so that irreversibility appears, and how this modification affects decomposed systems? The first step was already done in Muschik (“Concepts of phenomenological irreversible quantum thermodynamics: closed undecomposed Schottky systems in semi-classical description,” J. Non-Equilibrium Thermodyn., vol. 44, pp. 1–13, 2019) and is repeated below, whereas the second step to formulate a quantum thermodynamics of decomposed systems is performed here by modifying the von Neumann equations of the sub-systems by a procedure wich is similar to that of Lindblad’s equation (G. Lindblad, “On the generators of quantum dynamical semigroups,” Commun. Math. Phys., vol. 48, p. 119130, 1976), but different because the sub-systems interact with one another through partitions.
{"title":"Concepts of phenomenological irreversible quantum thermodynamics II: time dependent statistical ensembles of bipartite systems","authors":"W. Muschik","doi":"10.1515/jnet-2023-0023","DOIUrl":"https://doi.org/10.1515/jnet-2023-0023","url":null,"abstract":"Abstract The wide-spread opinion is that original quantum mechanics is a reversible theory, but this statement is only true for undecomposed systems that are those systems for which sub-systems are out of consideration. Taking sub-systems into account, as it is by definition necessary for decomposed systems, the interaction Hamiltonians –which are absent in undecomposed systems– can be a source of irreversibility in decomposed systems. Thus, the following two-stage task arises: How to modify von Neumann’s equation of undecomposed systems so that irreversibility appears, and how this modification affects decomposed systems? The first step was already done in Muschik (“Concepts of phenomenological irreversible quantum thermodynamics: closed undecomposed Schottky systems in semi-classical description,” J. Non-Equilibrium Thermodyn., vol. 44, pp. 1–13, 2019) and is repeated below, whereas the second step to formulate a quantum thermodynamics of decomposed systems is performed here by modifying the von Neumann equations of the sub-systems by a procedure wich is similar to that of Lindblad’s equation (G. Lindblad, “On the generators of quantum dynamical semigroups,” Commun. Math. Phys., vol. 48, p. 119130, 1976), but different because the sub-systems interact with one another through partitions.","PeriodicalId":16428,"journal":{"name":"Journal of Non-Equilibrium Thermodynamics","volume":null,"pages":null},"PeriodicalIF":6.6,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42969255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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