Pub Date : 2020-09-23DOI: 10.1103/physrevb.102.224302
G. Di Meglio, D. Rossini, E. Vicari
We investigate the effects of dissipation on the quantum dynamics of many-body systems at quantum transitions, especially considering those of the first order. This issue is studied within the paradigmatic one-dimensional quantum Ising model. We analyze the out-of-equilibrium dynamics arising from quenches of the Hamiltonian parameters and dissipative mechanisms modeled by a Lindblad master equation, with either local or global spin operators acting as dissipative operators. Analogously to what happens at continuous quantum transitions, we observe a regime where the system develops a nontrivial dynamic scaling behavior, which is realized when the dissipation parameter $u$ (globally controlling the decay rate of the dissipation within the Lindblad framework) scales as the energy difference $Delta$ of the lowest levels of the Hamiltonian, i.e., $usim Delta$. However, unlike continuous quantum transitions where $Delta$ is power-law suppressed, at first-order quantum transitions $Delta$ is exponentially suppressed with increasing the system size (provided the boundary conditions do not favor any particular phase).
{"title":"Dissipative dynamics at first-order quantum transitions","authors":"G. Di Meglio, D. Rossini, E. Vicari","doi":"10.1103/physrevb.102.224302","DOIUrl":"https://doi.org/10.1103/physrevb.102.224302","url":null,"abstract":"We investigate the effects of dissipation on the quantum dynamics of many-body systems at quantum transitions, especially considering those of the first order. This issue is studied within the paradigmatic one-dimensional quantum Ising model. We analyze the out-of-equilibrium dynamics arising from quenches of the Hamiltonian parameters and dissipative mechanisms modeled by a Lindblad master equation, with either local or global spin operators acting as dissipative operators. Analogously to what happens at continuous quantum transitions, we observe a regime where the system develops a nontrivial dynamic scaling behavior, which is realized when the dissipation parameter $u$ (globally controlling the decay rate of the dissipation within the Lindblad framework) scales as the energy difference $Delta$ of the lowest levels of the Hamiltonian, i.e., $usim Delta$. However, unlike continuous quantum transitions where $Delta$ is power-law suppressed, at first-order quantum transitions $Delta$ is exponentially suppressed with increasing the system size (provided the boundary conditions do not favor any particular phase).","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80654112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-23DOI: 10.1103/PRXQUANTUM.2.010352
A. Nahum, S. Roy, B. Skinner, J. Ruhman
Quantum many-body systems subjected to local measurements at a nonzero rate can be in distinct dynamical phases, with differing entanglement properties. We introduce theoretical approaches to measurement-induced phase transitions (MPT) and also to entanglement transitions in random tensor networks. Many of our results are for "all-to-all" quantum circuits with unitaries and measurements, in which any qubit can couple to any other, and related settings where some of the complications of low-dimensional models are reduced. We also propose field theory descriptions for spatially local systems of finite dimensionality. To build intuition, we first solve the simplest "minimal cut" toy model for entanglement dynamics in all-to-all circuits, finding scaling forms and exponents within this approximation. We then show that certain all-to-all measurement circuits allow exact results by exploiting the circuit's local tree-like structure. For this reason, we make a detour to give universal results for entanglement phase transitions in a class of random tree tensor networks, making a connection with the classical theory of directed polymers on a tree. We then compare these results with numerics in all-to-all circuits, both for the MPT and for the simpler "Forced Measurement Phase Transition" (FMPT). We characterize the two different phases in all-to-all circuits using observables that are sensitive to the amount of information propagated between the initial and final time. We demonstrate signatures of the two phases that can be understood from simple models. Finally we propose Landau-Ginsburg-Wilson-like field theories for the MPT, the FMPT, and for entanglement transitions in tensor networks. This analysis shows a surprising difference between the MPT and the other cases. We discuss variants of the measurement problem with additional structure, and questions for the future.
{"title":"Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory","authors":"A. Nahum, S. Roy, B. Skinner, J. Ruhman","doi":"10.1103/PRXQUANTUM.2.010352","DOIUrl":"https://doi.org/10.1103/PRXQUANTUM.2.010352","url":null,"abstract":"Quantum many-body systems subjected to local measurements at a nonzero rate can be in distinct dynamical phases, with differing entanglement properties. We introduce theoretical approaches to measurement-induced phase transitions (MPT) and also to entanglement transitions in random tensor networks. Many of our results are for \"all-to-all\" quantum circuits with unitaries and measurements, in which any qubit can couple to any other, and related settings where some of the complications of low-dimensional models are reduced. We also propose field theory descriptions for spatially local systems of finite dimensionality. To build intuition, we first solve the simplest \"minimal cut\" toy model for entanglement dynamics in all-to-all circuits, finding scaling forms and exponents within this approximation. We then show that certain all-to-all measurement circuits allow exact results by exploiting the circuit's local tree-like structure. For this reason, we make a detour to give universal results for entanglement phase transitions in a class of random tree tensor networks, making a connection with the classical theory of directed polymers on a tree. We then compare these results with numerics in all-to-all circuits, both for the MPT and for the simpler \"Forced Measurement Phase Transition\" (FMPT). We characterize the two different phases in all-to-all circuits using observables that are sensitive to the amount of information propagated between the initial and final time. We demonstrate signatures of the two phases that can be understood from simple models. Finally we propose Landau-Ginsburg-Wilson-like field theories for the MPT, the FMPT, and for entanglement transitions in tensor networks. This analysis shows a surprising difference between the MPT and the other cases. We discuss variants of the measurement problem with additional structure, and questions for the future.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85816905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-22DOI: 10.21468/SCIPOSTPHYSCORE.4.2.016
Maciej Lebek, P. Jakubczyk
We analyze the thermodynamic Casimir effect in strongly anizotropic systems from the vectorial $Ntoinfty$ class in a slab geometry. Employing the imperfect (mean-field) Bose gas as a representative example, we demonstrate the key role of spatial dimensionality $d$ in determining the character of the effective fluctuation-mediated interaction between the confining walls. For a particular, physically conceivable choice of anisotropic dispersion and periodic boundary conditions, we show that the Casimir force at criticality as well as within the low-temperature phase is repulsive for dimensionality $din (frac{5}{2},4)cup (6,8)cup (10,12)cupdots$ and attractive for $din (4,6)cup (8,10)cup dots$. We argue, that for $din{4,6,8dots}$ the Casimir interaction entirely vanishes in the scaling limit. We discuss implications of our results for systems characterized by $1/N>0$ and possible realizations in the context of quantum phase transitions.
{"title":"Thermodynamic Casimir forces in strongly anisotropic systems within the $Nto infty$ class","authors":"Maciej Lebek, P. Jakubczyk","doi":"10.21468/SCIPOSTPHYSCORE.4.2.016","DOIUrl":"https://doi.org/10.21468/SCIPOSTPHYSCORE.4.2.016","url":null,"abstract":"We analyze the thermodynamic Casimir effect in strongly anizotropic systems from the vectorial $Ntoinfty$ class in a slab geometry. Employing the imperfect (mean-field) Bose gas as a representative example, we demonstrate the key role of spatial dimensionality $d$ in determining the character of the effective fluctuation-mediated interaction between the confining walls. For a particular, physically conceivable choice of anisotropic dispersion and periodic boundary conditions, we show that the Casimir force at criticality as well as within the low-temperature phase is repulsive for dimensionality $din (frac{5}{2},4)cup (6,8)cup (10,12)cupdots$ and attractive for $din (4,6)cup (8,10)cup dots$. We argue, that for $din{4,6,8dots}$ the Casimir interaction entirely vanishes in the scaling limit. We discuss implications of our results for systems characterized by $1/N>0$ and possible realizations in the context of quantum phase transitions.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"821 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84976255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-10DOI: 10.21468/SCIPOSTPHYSCORE.4.2.010
Lenart Zadnik, M. Fagotti
We study an effective Hamiltonian generating time evolution of states on intermediate time scales in the strong-coupling limit of the spin-1/2 XXZ model. To leading order, it describes an integrable model with local interactions. We solve it completely by means of a coordinate Bethe Ansatz that manifestly breaks the translational symmetry. We demonstrate the existence of exponentially many jammed states and estimate their stability under the leading correction to the effective Hamiltonian. Some ground state properties of the model are discussed.
{"title":"The Folded Spin-1/2 XXZ Model: I. Diagonalisation, Jamming, and Ground State Properties","authors":"Lenart Zadnik, M. Fagotti","doi":"10.21468/SCIPOSTPHYSCORE.4.2.010","DOIUrl":"https://doi.org/10.21468/SCIPOSTPHYSCORE.4.2.010","url":null,"abstract":"We study an effective Hamiltonian generating time evolution of states on intermediate time scales in the strong-coupling limit of the spin-1/2 XXZ model. To leading order, it describes an integrable model with local interactions. We solve it completely by means of a coordinate Bethe Ansatz that manifestly breaks the translational symmetry. We demonstrate the existence of exponentially many jammed states and estimate their stability under the leading correction to the effective Hamiltonian. Some ground state properties of the model are discussed.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85183854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-02DOI: 10.1103/PHYSREVRESEARCH.3.013232
Roi Holtzman, Geva Arwas, O. Raz
Computations implemented on a physical system are fundamentally limited by the laws of physics. A prominent example for a physical law that bounds computations is the Landauer principle. According to this principle, erasing a bit of information requires a concentration of probability in phase space, which by Liouville's theorem is impossible in pure Hamiltonian dynamics. It therefore requires dissipative dynamics with heat dissipation of at least $k_BTlog 2$ per erasure of one bit. Using a concrete example, we show that when the dynamic is confined to a single energy shell it is possible to concentrate the probability on this shell using Hamiltonian dynamic, and therefore to implement an erasable bit with no thermodynamic cost.
{"title":"Hamiltonian memory: An erasable classical bit","authors":"Roi Holtzman, Geva Arwas, O. Raz","doi":"10.1103/PHYSREVRESEARCH.3.013232","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.3.013232","url":null,"abstract":"Computations implemented on a physical system are fundamentally limited by the laws of physics. A prominent example for a physical law that bounds computations is the Landauer principle. According to this principle, erasing a bit of information requires a concentration of probability in phase space, which by Liouville's theorem is impossible in pure Hamiltonian dynamics. It therefore requires dissipative dynamics with heat dissipation of at least $k_BTlog 2$ per erasure of one bit. Using a concrete example, we show that when the dynamic is confined to a single energy shell it is possible to concentrate the probability on this shell using Hamiltonian dynamic, and therefore to implement an erasable bit with no thermodynamic cost.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83875666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Z. Amimer, S. Bekhechi, B. N. Brahmi, R. Boudefla, H. Ez‐zahraouy, A. Rachadi
Using the Monte-Carlo method, we study the magnetic properties of the Ashkin-Teller model (ATM) under the effect of the crystal field with spins $S = 1$ and $sigma = 3/2$. First, we determine the most stable phases in the phase diagrams at temperature $T = 0$ using exact calculations. For higher temperatures, we use the Monte-Carlo simulation. We have found rich phase diagrams with the ordered phases: a Baxter $3/2$ and a Baxter $1/2$ phases in addition to a $leftlangle sigma Srightrangle$ phase that does not show up either in ATM spin 1 or in ATM spin $3/2$ and, lastly, a $leftlangle sigmarightrangle = 1/2$ phase with first and second order transitions.
{"title":"Study of the Ashkin Teller model with spins S = 1 and σ = 3/2 subjected to different crystal fields using the Monte-Carlo method","authors":"Z. Amimer, S. Bekhechi, B. N. Brahmi, R. Boudefla, H. Ez‐zahraouy, A. Rachadi","doi":"10.5488/CMP.23.33707","DOIUrl":"https://doi.org/10.5488/CMP.23.33707","url":null,"abstract":"Using the Monte-Carlo method, we study the magnetic properties of the Ashkin-Teller model (ATM) under the effect of the crystal field with spins $S = 1$ and $sigma = 3/2$. First, we determine the most stable phases in the phase diagrams at temperature $T = 0$ using exact calculations. For higher temperatures, we use the Monte-Carlo simulation. We have found rich phase diagrams with the ordered phases: a Baxter $3/2$ and a Baxter $1/2$ phases in addition to a $leftlangle sigma Srightrangle$ phase that does not show up either in ATM spin 1 or in ATM spin $3/2$ and, lastly, a $leftlangle sigmarightrangle = 1/2$ phase with first and second order transitions.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"134 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80679557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-08-24DOI: 10.1103/PHYSREVB.103.014305
M. Natsheh, A. Gambassi, A. Mitra
The periodically driven O(N) model is studied near the critical line separating a disordered paramagnetic phase from a period doubled phase, the latter being an example of a Floquet time crystal. The time evolution of one-point and two-point correlation functions are obtained within the Gaussian approximation and perturbatively in the drive amplitude. The correlations are found to show not only period doubling, but also power-law decays at large spatial distances. These features are compared with the undriven O(N) model in the vicinity of the paramagnetic-ferromagnetic critical point. The algebraic decays in space are found to be qualitatively different in the driven and the undriven cases. In particular, the spatio-temporal order of the Floquet time crystal leads to position-momentum and momentum-momentum correlation functions which are more long-ranged in the driven than in the undriven model. The light-cone dynamics associated with the correlation functions is also qualitatively different as the critical line of the Floquet time crystal shows a light-cone with two distinct velocities, with the ratio of the two velocities scaling as the square-root of the dimensionless drive amplitude. The Floquet unitary, which describes the time evolution due to a complete cycle of the drive, is constructed for modes with small momenta compared to the drive frequency, but having a generic relationship with the square-root of the drive amplitude. At intermediate momenta, which are large compared to the square-root of the drive amplitude, the Floquet unitary is found to simply rotate the modes. On the other hand, at momenta which are small compared to the square-root of the drive amplitude, the Floquet unitary is found to primarily squeeze the modes, to an extent which increases upon increasing the wavelength of the modes, with a power-law dependence on it.
{"title":"Critical properties of the Floquet time crystal within the Gaussian approximation","authors":"M. Natsheh, A. Gambassi, A. Mitra","doi":"10.1103/PHYSREVB.103.014305","DOIUrl":"https://doi.org/10.1103/PHYSREVB.103.014305","url":null,"abstract":"The periodically driven O(N) model is studied near the critical line separating a disordered paramagnetic phase from a period doubled phase, the latter being an example of a Floquet time crystal. The time evolution of one-point and two-point correlation functions are obtained within the Gaussian approximation and perturbatively in the drive amplitude. The correlations are found to show not only period doubling, but also power-law decays at large spatial distances. These features are compared with the undriven O(N) model in the vicinity of the paramagnetic-ferromagnetic critical point. The algebraic decays in space are found to be qualitatively different in the driven and the undriven cases. In particular, the spatio-temporal order of the Floquet time crystal leads to position-momentum and momentum-momentum correlation functions which are more long-ranged in the driven than in the undriven model. The light-cone dynamics associated with the correlation functions is also qualitatively different as the critical line of the Floquet time crystal shows a light-cone with two distinct velocities, with the ratio of the two velocities scaling as the square-root of the dimensionless drive amplitude. The Floquet unitary, which describes the time evolution due to a complete cycle of the drive, is constructed for modes with small momenta compared to the drive frequency, but having a generic relationship with the square-root of the drive amplitude. At intermediate momenta, which are large compared to the square-root of the drive amplitude, the Floquet unitary is found to simply rotate the modes. On the other hand, at momenta which are small compared to the square-root of the drive amplitude, the Floquet unitary is found to primarily squeeze the modes, to an extent which increases upon increasing the wavelength of the modes, with a power-law dependence on it.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"149 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91519295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-08-18DOI: 10.1142/s0217979220502811
I. Rond'on, O. Sotolongo-Costa, J. Gonz'alez
A general growth model based on non-extensive statistical physics is presented. The obtained equation is expressed in terms of nonadditive $q$ entropy. We show that the most common unidimensional growth laws such as power law, exponential, logistic, Richards, Von Bertalanffy, Gompertz can be obtained. This model belongs as a particular case reported in (Physica A 369, 645 (2006)). The new evolution equation resembles the textquotedblleft universality textquotedblright revealed by West for ontogenetic growth (Nature 413, 628 (2001)).We show that for early times the model follows a power law growth as $ N(t) approx t ^ D $, where the exponent $D equiv frac{1}{1-q}$ classify different growth. Several examples are presented and discussed.
提出了一种基于非泛化统计物理的一般增长模型。所得方程以不可加性$q$熵的形式表示。我们证明了最常见的一维增长律如幂律、指数律、logistic律、Richards律、Von Bertalanffy律、Gompertz律等都可以得到。这个模型属于(Physica a 369,645(2006))报道的一个特殊案例。新的进化方程类似于韦斯特揭示的个体发育的textquotedblleft普遍性textquotedblright (Nature 413, 628(2001))。我们表明，在早期，模型遵循幂律增长$ N(t) approx t ^ D $，其中指数$D equiv frac{1}{1-q}$分类不同的增长。提出并讨论了几个例子。
{"title":"A generalized q growth model based on nonadditive entropy","authors":"I. Rond'on, O. Sotolongo-Costa, J. Gonz'alez","doi":"10.1142/s0217979220502811","DOIUrl":"https://doi.org/10.1142/s0217979220502811","url":null,"abstract":"A general growth model based on non-extensive statistical physics is presented. The obtained equation is expressed in terms of nonadditive $q$ entropy. We show that the most common unidimensional growth laws such as power law, exponential, logistic, Richards, Von Bertalanffy, Gompertz can be obtained. This model belongs as a particular case reported in (Physica A 369, 645 (2006)). The new evolution equation resembles the textquotedblleft universality textquotedblright revealed by West for ontogenetic growth (Nature 413, 628 (2001)).We show that for early times the model follows a power law growth as $ N(t) approx t ^ D $, where the exponent $D equiv frac{1}{1-q}$ classify different growth. Several examples are presented and discussed.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"102 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80624386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-08-16DOI: 10.1103/PHYSREVRESEARCH.3.013273
Arnab K. Pal, S. Reuveni, Saar Rahav
We derive a thermodynamic uncertainty relation (TUR) for systems with unidirectional transitions. The uncertainty relation involves a mixture of thermodynamic and dynamic terms. Namely, the entropy production from bidirectional transitions, and the net flux of unidirectional transitions. The derivation does not assume a steady-state, and the results apply equally well to transient processes with arbitrary initial conditions. As every bidirectional transition can also be seen as a pair of separate unidirectional ones, our approach is equipped with an inherent degree of freedom. Thus, for any given system, an ensemble of valid TURs can be derived. However, we find that choosing a representation that best matches the systems dynamics over the observation time will yield a TUR with a tighter bound on fluctuations. More precisely, we show a bidirectional representation should be replaced by a unidirectional one when the entropy production associated with the transitions between two states is larger than the sum of the net fluxes between them. Thus, in addition to offering TURs for systems where such relations were previously unavailable, the results presented herein also provide a systematic method to improve TUR bounds via physically motivated replacement of bidirectional transitions with pairs of unidirectional transitions. The power of our approach and its implementation are demonstrated on a model for random walk with stochastic resetting and on the Michaelis-Menten model of enzymatic catalysis.
{"title":"Thermodynamic uncertainty relation for systems with unidirectional transitions","authors":"Arnab K. Pal, S. Reuveni, Saar Rahav","doi":"10.1103/PHYSREVRESEARCH.3.013273","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.3.013273","url":null,"abstract":"We derive a thermodynamic uncertainty relation (TUR) for systems with unidirectional transitions. The uncertainty relation involves a mixture of thermodynamic and dynamic terms. Namely, the entropy production from bidirectional transitions, and the net flux of unidirectional transitions. The derivation does not assume a steady-state, and the results apply equally well to transient processes with arbitrary initial conditions. As every bidirectional transition can also be seen as a pair of separate unidirectional ones, our approach is equipped with an inherent degree of freedom. Thus, for any given system, an ensemble of valid TURs can be derived. However, we find that choosing a representation that best matches the systems dynamics over the observation time will yield a TUR with a tighter bound on fluctuations. More precisely, we show a bidirectional representation should be replaced by a unidirectional one when the entropy production associated with the transitions between two states is larger than the sum of the net fluxes between them. Thus, in addition to offering TURs for systems where such relations were previously unavailable, the results presented herein also provide a systematic method to improve TUR bounds via physically motivated replacement of bidirectional transitions with pairs of unidirectional transitions. The power of our approach and its implementation are demonstrated on a model for random walk with stochastic resetting and on the Michaelis-Menten model of enzymatic catalysis.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"77 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87161440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-08-12DOI: 10.1103/physrevb.102.195148
Daniel Alcalde Puente, I. Eremin
Machine learning is becoming widely used in analyzing the thermodynamics of many-body condensed matter systems. Restricted Boltzmann Machine (RBM) aided Monte Carlo simulations have sparked interest recently, as they manage to speed up classical Monte Carlo simulations. Here we employ the Convolutional Restricted Boltzmann Machine (CRBM) method and show that its use helps to reduce the number of parameters to be learned drastically by taking advantage of translation invariance. Furthermore, we show that it is possible to train the CRBM at smaller lattice sizes, and apply it to larger lattice sizes. To demonstrate the efficiency of CRBM we apply it to the paradigmatic Ising and Kitaev models in two-dimensions.
{"title":"Convolutional restricted Boltzmann machine aided Monte Carlo: An application to Ising and Kitaev models","authors":"Daniel Alcalde Puente, I. Eremin","doi":"10.1103/physrevb.102.195148","DOIUrl":"https://doi.org/10.1103/physrevb.102.195148","url":null,"abstract":"Machine learning is becoming widely used in analyzing the thermodynamics of many-body condensed matter systems. Restricted Boltzmann Machine (RBM) aided Monte Carlo simulations have sparked interest recently, as they manage to speed up classical Monte Carlo simulations. Here we employ the Convolutional Restricted Boltzmann Machine (CRBM) method and show that its use helps to reduce the number of parameters to be learned drastically by taking advantage of translation invariance. Furthermore, we show that it is possible to train the CRBM at smaller lattice sizes, and apply it to larger lattice sizes. To demonstrate the efficiency of CRBM we apply it to the paradigmatic Ising and Kitaev models in two-dimensions.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85111296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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