canonical ensemble
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2022 ◽  
Author(s):  
Satish Ramakrishna

Abstract The Cohen-Kaplan-Nelson bound is imposed on the grounds of logical consistency (with classical General Relativity) upon local quantum field theories. This paper puts the bound into the context of a thermodynamic principle applicable to a field with a particular equation of state in an expanding universe. This is achieved without overtly appealing to either a decreasing density of states or a minimum coupling requirement, though they might still be consistent with the results described. We do so by defining an appropriate Helmholtz free energy which when extremized relative to a key parameter (the Hubble radius L) provides a scaling formula for the entropy with the Hubble radius (an exponent r used in the text). We deduce that the CKN bound is one possible solution to this extremization problem (with r = 3/2 ), but there are others consistent with r = 2. The paper establishes that the holographic principle applied to cosmology is consistent with minimizing the free energy of the universe in the canonical ensemble, upon the assumption that the ultraviolet cutoff is a function of the causal horizon scale.


Author(s):  
Satish Ramakrishna

Abstract The Cohen-Kaplan-Nelson bound is imposed on the grounds of logical consistency (with classical General Relativity) upon local quantum field theories. This paper puts the bound into the context of a thermodynamic principle applicable to a field with a particular equation of state in an expanding universe. This is achieved without overtly appealing to either a decreasing density of states or a minimum coupling requirement, though they might still be consistent with the results described. We do so by defining an appropriate Helmholtz free energy which when extremized relative to a key parameter (the Hubble radius L) provides a scaling formula for the entropy with the Hubble radius (an exponent r used in the text). We deduce that the CKN bound is one possible solution to this extremization problem (with r=3/2), but there are others consistent with r=2. The paper establishes that the holographic principle applied to cosmology is consistent with minimizing the free energy of the universe in the canonical ensemble, upon the assumption that the ultraviolet cutoff is a function of the causal horizon scale.


2022 ◽  
pp. 39-91
Author(s):  
R.K. Pathria ◽  
Paul D. Beale
Keyword(s):  

2021 ◽  
Author(s):  
Satish Ramakrishna

Abstract The Cohen-Kaplan-Nelson bound is imposed on the grounds of logical consistency (with classical General Relativity) upon local quantum field theories. This paper puts the bound into the context of a thermodynamic principle applicable to a field with a particular equation of state in an expanding universe. This is achieved without overtly appealing to either a decreasing density of states or a minimum coupling requirement, though they might still be consistent with the results described. The paper establishes that the holographic principle applied to cosmology is consistent with minimizing the free energy of the universe in the canonical ensemble, upon the assumption that the ultraviolet cutoff is a function of the causal horizon scale.


Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Chenxi Zhou ◽  
Bin Yang ◽  
Wenliang Fan ◽  
Wei Li

Objective. System modeling is an important method to study the working mechanisms of the brain. This study attempted to build a model of the brain from the perspective of thermodynamics at the system level, which brought a new perspective to brain modeling. Approach. Regarding brain regions as systems, voxels as particles, and intensity of signals as energy of particles, the thermodynamic model of the brain was built based on the canonical ensemble theory. Two pairs of activated regions and two pairs of inactivated brain regions were selected for comparison in this study, and the thermodynamic properties based on the proposed model were analyzed. In addition, the thermodynamic properties were extracted as input features for the detection of Alzheimer’s disease. Main Results. The experimental results verified the assumption that the brain follows thermodynamic laws. This demonstrated the feasibility and rationality of the proposed brain thermodynamic modeling method, indicating that thermodynamic parameters drawn from our model can be applied to describe the state of the neural system. Meanwhile, the brain thermodynamic model achieved good accuracy in the detection of Alzheimer’s disease, suggesting the potential application of thermodynamic models in auxiliary diagnosis. Significance. (1) In the previous studies, only some thermodynamic parameters in physics were analogized and applied to brain image analysis, while, in this study, a complete system model of the brain was proposed through the principles of thermodynamics. And, based on the neural system models proposed, thermodynamic parameters were obtained to describe the observation and evolution of the neural system. (2) Based on the proposed thermodynamic models, we found and confirmed that the neural system also follows the laws of thermodynamics: the activation of system always leads to increased internal energy, increased free energy, and decreased entropy as what is discovered in many other systems besides classic thermodynamic system. (3) The detection of neural disease was demonstrated to benefit from the thermodynamic model, which confirmed that the thermodynamic model proposed can indeed describe the evolution of the neural system diseases. And it further implied the immense potential of thermodynamics in auxiliary diagnosis.


2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Seyed Hossein Hendi ◽  
Somayeh Hajkhalili ◽  
Mubasher Jamil ◽  
Mehrab Momennia

AbstractIn this paper, we investigate the thermodynamics and phase transitions of a four-dimensional rotating Kaluza–Klein black hole solution in the presence of Maxwell electrodynamics. Calculating the conserved and thermodynamic quantities shows that the first law of thermodynamics is satisfied. To find the stable black hole’s criteria, we check the stability in the canonical ensemble by analyzing the behavior of the heat capacity. We also consider a massive scalar perturbation minimally coupled to the background geometry of the four-dimensional static Kaluza–Klein black hole and investigate the quasinormal modes by employing the Wentzel–Kramers–Brillouin (WKB) approximation. The anomalous decay rate of the quasinormal modes spectrum is investigated by using the sixth-order WKB formula and quasi-resonance modes of the black hole are studied with averaging of Padé approximations as well.


2021 ◽  
Author(s):  
Satish Ramakrishna

Abstract The Cohen-Kaplan-Nelson bound is imposed on the grounds of logical consistency (with classical General Relativity) upon local quantum field theories. This paper puts the bound into the context of a thermodynamic principle applicable to a field with a particular equation of state in an expanding universe. This is achieved without overtly appealing to either a decreasing density of states or a minimum coupling requirement, though they might still be consistent with the results described. The paper establishes that the holographic principle applied to cosmology is consistent with minimizing the free energy of the universe in the canonical ensemble, upon the assumption that the ultraviolet cutoff is a function of the causal horizon scale.


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