Pub Date : 2024-05-16DOI: 10.1007/s10955-024-03275-y
Emanuele Caglioti, Francesca Pieroni
We solve the Random Euclidean Matching problem with exponent 2 for the Gaussian distribution defined on the plane. Previous works by Ledoux and Talagrand determined the leading behavior of the average cost up to a multiplicative constant. We explicitly determine the constant, showing that the average cost is proportional to ((log , N)^2,) where N is the number of points. Our approach relies on a geometric decomposition allowing an explicit computation of the constant. Our results illustrate the potential for exact solutions of random matching problems for many distributions defined on unbounded domains on the plane.
我们解决了在平面上定义的高斯分布的指数为 2 的随机欧氏匹配问题。勒杜(Ledoux)和塔拉格朗(Talagrand)之前的研究确定了平均成本的领先行为,直到一个乘法常数。我们明确地确定了这个常数,表明平均成本与 ((log , N)^2,) 成正比,其中 N 是点的数量。我们的方法依赖于几何分解,允许明确计算常数。我们的结果表明,对于许多定义在平面无界域上的分布,随机匹配问题有可能得到精确的解决。
{"title":"Random Matching in 2D with Exponent 2 for Gaussian Densities","authors":"Emanuele Caglioti, Francesca Pieroni","doi":"10.1007/s10955-024-03275-y","DOIUrl":"https://doi.org/10.1007/s10955-024-03275-y","url":null,"abstract":"<p>We solve the Random Euclidean Matching problem with exponent 2 for the Gaussian distribution defined on the plane. Previous works by Ledoux and Talagrand determined the leading behavior of the average cost up to a multiplicative constant. We explicitly determine the constant, showing that the average cost is proportional to <span>((log , N)^2,)</span> where <i>N</i> is the number of points. Our approach relies on a geometric decomposition allowing an explicit computation of the constant. Our results illustrate the potential for exact solutions of random matching problems for many distributions defined on unbounded domains on the plane.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141062583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-15DOI: 10.1007/s10955-024-03277-w
Michele Coti Zelati, Theodore D. Drivas, Rishabh S. Gvalani
{"title":"Mixing by Statistically Self-similar Gaussian Random Fields","authors":"Michele Coti Zelati, Theodore D. Drivas, Rishabh S. Gvalani","doi":"10.1007/s10955-024-03277-w","DOIUrl":"https://doi.org/10.1007/s10955-024-03277-w","url":null,"abstract":"","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140978100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-07DOI: 10.1007/s10955-024-03272-1
Michael Wilkinson, Boris Veytsman
We consider a random field (phi ({textbf{r}})) in d dimensions which is largely concentrated around small ‘hotspots’, with ‘weights’, (w_i). These weights may have a very broad distribution, such that their mean does not exist, or is dominated by unusually large values, thus not being a useful estimate. In such cases, the median ({overline{W}}) of the total weight W in a region of size R is an informative characterisation of the weights. We define the function F by (ln {overline{W}}=F(ln R)). If (F'(x)>d), the distribution of hotspots is dominated by the largest weights. In the case where (F'(x)-d) approaches a constant positive value when (Rrightarrow infty ), the hotspots distribution has a type of scale-invariance which is different from that of fractal sets, and which we term ultradimensional. The form of the function F(x) is determined for a model of diffusion in a random potential.
我们考虑一个 d 维的随机场 (phi ({textbf{r}})),它主要集中在小的 "热点 "周围,具有 "权重",(w_i)。这些权重可能具有非常广泛的分布,以至于它们的平均值不存在,或者被异常大的值所支配,因此不是一个有用的估计值。在这种情况下,大小为 R 的区域中总权重 W 的中值({overline{W}}/)是权重的一个信息特征。我们用 (ln {overline{W}}=F(ln R)) 来定义函数 F。如果 (F'(x)>d),热点的分布就会被最大的权重所支配。当(F'(x)-d)接近一个恒定的正值时,热点分布具有一种不同于分形集的标度不变量,我们称之为超维度。函数 F(x) 的形式是针对随机势中的扩散模型确定的。
{"title":"Scale Dependence of Distributions of Hotspots","authors":"Michael Wilkinson, Boris Veytsman","doi":"10.1007/s10955-024-03272-1","DOIUrl":"https://doi.org/10.1007/s10955-024-03272-1","url":null,"abstract":"<p>We consider a random field <span>(phi ({textbf{r}}))</span> in <i>d</i> dimensions which is largely concentrated around small ‘hotspots’, with ‘weights’, <span>(w_i)</span>. These weights may have a very broad distribution, such that their mean does not exist, or is dominated by unusually large values, thus not being a useful estimate. In such cases, the median <span>({overline{W}})</span> of the total weight <i>W</i> in a region of size <i>R</i> is an informative characterisation of the weights. We define the function <i>F</i> by <span>(ln {overline{W}}=F(ln R))</span>. If <span>(F'(x)>d)</span>, the distribution of hotspots is dominated by the largest weights. In the case where <span>(F'(x)-d)</span> approaches a constant positive value when <span>(Rrightarrow infty )</span>, the hotspots distribution has a type of scale-invariance which is different from that of fractal sets, and which we term <i>ultradimensional</i>. The form of the function <i>F</i>(<i>x</i>) is determined for a model of diffusion in a random potential.\u0000</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-07DOI: 10.1007/s10955-024-03271-2
Byung-Hoon Hwang, Myeong-Su Lee, Seok-Bae Yun
Unlike the case for classical particles, the literature on BGK type models for relativistic gas mixture is extremely limited. There are a few results in which such relativistic BGK models for gas mixture are employed to compute transport coefficients. However, to the best knowledge of authors, relativistic BGK models for gas mixtures with complete presentation of the relaxation operators are missing in the literature. In this paper, we fill this gap by suggesting a BGK model for relativistic gas mixtures for which the existence of each equilibrium coefficients in the relaxation operator is rigorously guaranteed in a way that all the essential physical properties are satisfied such as the conservation laws, the H-theorem, the capturing of the correct equilibrium state, the indifferentiability principle, and the recovery of the classical BGK model in the Newtonian limit.
{"title":"Relativistic BGK Model for Gas Mixtures","authors":"Byung-Hoon Hwang, Myeong-Su Lee, Seok-Bae Yun","doi":"10.1007/s10955-024-03271-2","DOIUrl":"https://doi.org/10.1007/s10955-024-03271-2","url":null,"abstract":"<p>Unlike the case for classical particles, the literature on BGK type models for relativistic gas mixture is extremely limited. There are a few results in which such relativistic BGK models for gas mixture are employed to compute transport coefficients. However, to the best knowledge of authors, relativistic BGK models for gas mixtures with complete presentation of the relaxation operators are missing in the literature. In this paper, we fill this gap by suggesting a BGK model for relativistic gas mixtures for which the existence of each equilibrium coefficients in the relaxation operator is rigorously guaranteed in a way that all the essential physical properties are satisfied such as the conservation laws, the H-theorem, the capturing of the correct equilibrium state, the indifferentiability principle, and the recovery of the classical BGK model in the Newtonian limit.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-07DOI: 10.1007/s10955-024-03264-1
Yuki Sato, Kiyoshi Kanazawa
The Lillo–Mike–Farmer (LMF) model is an established econophysics model describing the order-splitting behaviour of institutional investors in financial markets. In the original article (Lillo et al. in Phys Rev E 71:066122, 2005), LMF assumed the homogeneity of the traders’ order-splitting strategy and derived a power-law asymptotic solution to the order-sign autocorrelation function (ACF) based on several heuristic reasonings. This report proposes a generalised LMF model by incorporating the heterogeneity of traders’ order-splitting behaviour that is exactly solved without heuristics. We find that the power-law exponent in the order-sign ACF is robust for arbitrary heterogeneous order-submission probability distributions. On the other hand, the prefactor in the ACF is very sensitive to heterogeneity in trading strategies and is shown to be systematically underestimated in the original homogeneous LMF model. Our work highlights that predicting the ACF prefactor is more challenging than the ACF exponent because many microscopic details (complex ingredients in actual data analyses) start to matter.
{"title":"Exact Solution to a Generalised Lillo–Mike–Farmer Model with Heterogeneous Order-Splitting Strategies","authors":"Yuki Sato, Kiyoshi Kanazawa","doi":"10.1007/s10955-024-03264-1","DOIUrl":"https://doi.org/10.1007/s10955-024-03264-1","url":null,"abstract":"<p>The Lillo–Mike–Farmer (LMF) model is an established econophysics model describing the order-splitting behaviour of institutional investors in financial markets. In the original article (Lillo et al. in Phys Rev E 71:066122, 2005), LMF assumed the homogeneity of the traders’ order-splitting strategy and derived a power-law asymptotic solution to the order-sign autocorrelation function (ACF) based on several heuristic reasonings. This report proposes a generalised LMF model by incorporating the heterogeneity of traders’ order-splitting behaviour that is exactly solved without heuristics. We find that the power-law exponent in the order-sign ACF is robust for arbitrary heterogeneous order-submission probability distributions. On the other hand, the prefactor in the ACF is very sensitive to heterogeneity in trading strategies and is shown to be systematically underestimated in the original homogeneous LMF model. Our work highlights that predicting the ACF prefactor is more challenging than the ACF exponent because many microscopic details (complex ingredients in actual data analyses) start to matter.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-04DOI: 10.1007/s10955-024-03268-x
Aaron Beyen, Christian Maes, Irene Maes
Adding activity or driving to a thermal system may modify its phase diagram and response functions. We study that effect for a Curie–Weiss model where the thermal bath switches rapidly between two temperatures. The critical temperature moves with the nonequilibrium driving, opening up a new region of stability for the paramagnetic phase (zero magnetization) at low temperatures. Furthermore, phase coexistence between the paramagnetic and ferromagnetic phases becomes possible at low temperatures. Following the excess heat formalism, we calculate the nonequilibrium thermal response and study its behaviour near phase transitions. Where the specific heat at the critical point makes a finite jump in equilibrium (discontinuity), it diverges once we add the second thermal bath. Finally, (also) the nonequilibrium specific heat goes to zero exponentially fast with vanishing temperature, realizing an extended Third Law.
{"title":"Phase Diagram and Specific Heat of a Nonequilibrium Curie–Weiss Model","authors":"Aaron Beyen, Christian Maes, Irene Maes","doi":"10.1007/s10955-024-03268-x","DOIUrl":"https://doi.org/10.1007/s10955-024-03268-x","url":null,"abstract":"<p>Adding activity or driving to a thermal system may modify its phase diagram and response functions. We study that effect for a Curie–Weiss model where the thermal bath switches rapidly between two temperatures. The critical temperature moves with the nonequilibrium driving, opening up a new region of stability for the paramagnetic phase (zero magnetization) at low temperatures. Furthermore, phase coexistence between the paramagnetic and ferromagnetic phases becomes possible at low temperatures. Following the excess heat formalism, we calculate the nonequilibrium thermal response and study its behaviour near phase transitions. Where the specific heat at the critical point makes a finite jump in equilibrium (discontinuity), it diverges once we add the second thermal bath. Finally, (also) the nonequilibrium specific heat goes to zero exponentially fast with vanishing temperature, realizing an extended Third Law.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-04DOI: 10.1007/s10955-024-03274-z
Fabian Koch, Suvendu Mandal, Tanja Schilling
We analyse the motion of one particle in a polymer chain. For this purpose, we use the framework of the exact (non-stationary) generalized Langevin equation that can be derived from first principles via the projection-operator method. Our focus lies on determining memory kernels from either exact expressions for autocorrelation functions or from simulation data. We increase the complexity of the underlying system starting out from one-dimensional harmonic chains and ending with a polymer driven through a polymer melt. Here, the displacement or the velocity of an individual particle in the chain serves as the observable. The central result is that the time-window in which the memory kernels show structure before they rapidly decay decreases with increasing complexity of the system.
{"title":"Analysis of the Dynamics in Linear Chain Models by means of Generalized Langevin Equations","authors":"Fabian Koch, Suvendu Mandal, Tanja Schilling","doi":"10.1007/s10955-024-03274-z","DOIUrl":"https://doi.org/10.1007/s10955-024-03274-z","url":null,"abstract":"<p>We analyse the motion of one particle in a polymer chain. For this purpose, we use the framework of the exact (non-stationary) generalized Langevin equation that can be derived from first principles via the projection-operator method. Our focus lies on determining memory kernels from either exact expressions for autocorrelation functions or from simulation data. We increase the complexity of the underlying system starting out from one-dimensional harmonic chains and ending with a polymer driven through a polymer melt. Here, the displacement or the velocity of an individual particle in the chain serves as the observable. The central result is that the time-window in which the memory kernels show structure before they rapidly decay decreases with increasing complexity of the system.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-03DOI: 10.1007/s10955-024-03273-0
Vir B. Bulchandani, S. L. Sondhi, J. T. Chalker
We study the competition between Haar-random unitary dynamics and measurements for unstructured systems of qubits. For projective measurements, we derive various properties of the statistical ensemble of Kraus operators analytically, including the purification time and the distribution of Born probabilities. The latter generalizes the Porter–Thomas distribution for random unitary circuits to the monitored setting and is log-normal at long times. We also consider weak measurements that interpolate between identity quantum channels and projective measurements. In this setting, we derive an exactly solvable Fokker–Planck equation for the joint distribution of singular values of Kraus operators, analogous to the Dorokhov–Mello–Pereyra–Kumar (DMPK) equation modelling disordered quantum wires. We expect that the statistical properties of Kraus operators we have established for these simple systems will serve as a model for the entangling phase of monitored quantum systems more generally.
{"title":"Random-Matrix Models of Monitored Quantum Circuits","authors":"Vir B. Bulchandani, S. L. Sondhi, J. T. Chalker","doi":"10.1007/s10955-024-03273-0","DOIUrl":"https://doi.org/10.1007/s10955-024-03273-0","url":null,"abstract":"<p>We study the competition between Haar-random unitary dynamics and measurements for unstructured systems of qubits. For projective measurements, we derive various properties of the statistical ensemble of Kraus operators analytically, including the purification time and the distribution of Born probabilities. The latter generalizes the Porter–Thomas distribution for random unitary circuits to the monitored setting and is log-normal at long times. We also consider weak measurements that interpolate between identity quantum channels and projective measurements. In this setting, we derive an exactly solvable Fokker–Planck equation for the joint distribution of singular values of Kraus operators, analogous to the Dorokhov–Mello–Pereyra–Kumar (DMPK) equation modelling disordered quantum wires. We expect that the statistical properties of Kraus operators we have established for these simple systems will serve as a model for the entangling phase of monitored quantum systems more generally.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-27DOI: 10.1007/s10955-024-03263-2
Anton Arnold, Gayrat Toshpulatov
This paper is concerned with a modified entropy method to establish the large-time convergence towards the (unique) steady state, for kinetic Fokker–Planck equations with non-quadratic confinement potentials in whole space. We extend previous approaches by analyzing Lyapunov functionals with non-constant weight matrices in the dissipation functional (a generalized Fisher information). We establish exponential convergence in a weighted (H^1)-norm with rates that become sharp in the case of quadratic potentials. In the defective case for quadratic potentials, i.e. when the drift matrix has non-trivial Jordan blocks, the weighted (L^2)-distance between a Fokker–Planck-solution and the steady state has always a sharp decay estimate of the order (mathcal Obig ( (1+t)e^{-tnu /2}big )), with (nu ) the friction parameter. The presented method also gives new hypoelliptic regularization results for kinetic Fokker–Planck equations (from a weighted (L^2)-space to a weighted (H^1)-space).
{"title":"Exponential Stability and Hypoelliptic Regularization for the Kinetic Fokker–Planck Equation with Confining Potential","authors":"Anton Arnold, Gayrat Toshpulatov","doi":"10.1007/s10955-024-03263-2","DOIUrl":"https://doi.org/10.1007/s10955-024-03263-2","url":null,"abstract":"<p>This paper is concerned with a modified entropy method to establish the large-time convergence towards the (unique) steady state, for kinetic Fokker–Planck equations with non-quadratic confinement potentials in whole space. We extend previous approaches by analyzing Lyapunov functionals with non-constant weight matrices in the dissipation functional (a generalized Fisher information). We establish exponential convergence in a weighted <span>(H^1)</span>-norm with rates that become sharp in the case of quadratic potentials. In the defective case for quadratic potentials, i.e. when the drift matrix has non-trivial Jordan blocks, the weighted <span>(L^2)</span>-distance between a Fokker–Planck-solution and the steady state has always a sharp decay estimate of the order <span>(mathcal Obig ( (1+t)e^{-tnu /2}big ))</span>, with <span>(nu )</span> the friction parameter. The presented method also gives new hypoelliptic regularization results for kinetic Fokker–Planck equations (from a weighted <span>(L^2)</span>-space to a weighted <span>(H^1)</span>-space).</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-27DOI: 10.1007/s10955-024-03262-3
Thomas Borsoni
We establish a connection between the relative Classical entropy and the relative Fermi–Dirac entropy, allowing to transpose, in the context of the Boltzmann or Landau equation, any entropy–entropy production inequality from one case to the other; therefore providing entropy–entropy production inequalities for the Boltzmann–Fermi–Dirac operator, similar to the ones of the Classical Boltzmann operator. We also provide a generalized version of the Csiszár–Kullback–Pinsker inequality to weighted (L^p) norms, (1 le p le 2) and a wide class of entropies.
我们在相对经典熵和相对费米-狄拉克熵之间建立了联系,从而可以在玻尔兹曼方程或朗道方程的背景下,将任何熵-熵生成不等式从一种情况转置到另一种情况;因此为玻尔兹曼-费米-狄拉克算子提供了熵-熵生成不等式,类似于经典玻尔兹曼算子的熵-熵生成不等式。我们还提供了Csiszár-Kullback-Pinsker不等式的广义版本,它适用于加权(L^p)规范、(1 le p le 2) 和一大类熵。
{"title":"Extending Cercignani’s Conjecture Results from Boltzmann to Boltzmann–Fermi–Dirac Equation","authors":"Thomas Borsoni","doi":"10.1007/s10955-024-03262-3","DOIUrl":"https://doi.org/10.1007/s10955-024-03262-3","url":null,"abstract":"<p>We establish a connection between the relative Classical entropy and the relative Fermi–Dirac entropy, allowing to transpose, in the context of the Boltzmann or Landau equation, any entropy–entropy production inequality from one case to the other; therefore providing entropy–entropy production inequalities for the Boltzmann–Fermi–Dirac operator, similar to the ones of the Classical Boltzmann operator. We also provide a generalized version of the Csiszár–Kullback–Pinsker inequality to weighted <span>(L^p)</span> norms, <span>(1 le p le 2)</span> and a wide class of entropies.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}