A Note on the Principle of Detailed Balancing

Fowler, Richard H.; Milne, E. A.

doi:10.1073/pnas.11.7.400

Cited by 32 publications

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“…In the early decades of the 20 th century, it became apparent, from considerations of chemical kinetics and quantum mechanics, that a type of dynamic, stochastic reversibility must hold on the microscopic level [6][7][8][9][10][11]. For instance, in 1924 G. N.…”

Section: Microscopic Reversibilitymentioning

confidence: 99%

On thermodynamic and microscopic reversibility

Crooks

2011

J. Stat. Mech.

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Abstract. The word "reversible" has two (apparently) distinct applications in statistical thermodynamics. A thermodynamically reversible process indicates an experimental protocol for which the entropy change is zero, whereas the principle of microscopic reversibility asserts that the probability of any trajectory of a system through phase space equals that of the time reversed trajectory. However, these two terms are actually synonymous: a thermodynamically reversible process is microscopically reversible, and vice versa. ‡

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Section: Microscopic Reversibilitymentioning

confidence: 99%

On thermodynamic and microscopic reversibility

Crooks

2011

J. Stat. Mech.

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“…A quarter of a century after Wegscheider the authors Fowler and Milne [10] formulated in a very vague form a general principle called the principle of detailed balance stating that in real thermodynamic equilibrium all the subprocesses (whatever they mean) should be in dynamic equilibrium separately in such a way that they do not stop but they proceed with the same velocity in both directions. Obviously, this also means that time is reversible at equilibrium, that is why this property may also be called microscopic reversibility.…”

Section: 4mentioning

confidence: 99%

Microscopic reversibility or detailed balance in ion channel models

Nagy

Tóth

2012

J Math Chem

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Mass action type deterministic kinetic models of ion channels are usually constructed in such a way as to obey the principle of detailed balance (or, microscopic reversibility) for two reasons: first, the authors aspire to have models harmonizing with thermodynamics, second, the conditions to ensure detailed balance reduce the number of reaction rate coefficients to be measured. We investigate a series of ion channel models which are asserted to obey detailed balance, however, these models violate mass conservation and in their case only the necessary conditions (the so-called circuit conditions) are taken into account. We show that ion channel models have a very specific structure which makes the consequences true in spite of the imprecise arguments. First, we transform the models into mass conserving ones, second, we show that the full set of conditions ensuring detailed balance (formulated by Feinberg) leads to the same relations for the reaction rate constants in these special cases, both for the original models and the transformed ones.

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“…Why do detailed balance and ergodicity guarantee the correct distribution of C pkq as k Ñ 8? Detailed balance or local balance was formulated as a concept important to equilibrium physics studies in the early twentieth century [28]. It is a key component in Metropolis QMC algorithms [58] and is the statement that Ω pC 1 q P C 1 ÑC 2 " Ω pC 2 q P C 2 ÑC 1 , (1.5)…”

Section: Quantum Monte Carlomentioning

confidence: 99%

Fermion Bag Approach to Lattice Hamiltonian Field Theories

Huffman

2018

EPJ Web Conf.

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Fermion Bag Approach for Hamiltonian Lattice Field TheoriesAbstract Understanding the critical behavior near quantum critical points for strongly correlated quantum many-body systems remains intractable for the vast majority of scenarios. Challenges involve determining if a quantum phase transition is first-or second-order, and finding the critical exponents for second-order phase transitions.Learning about where second-order phase transitions occur and determining their critical exponents is particularly interesting, because each new second-order phase transition defines a new quantum field theory.Quantum Monte Carlo (QMC) methods are one class of techniques that, when applicable, offer reliable ways to extract the nonperturbative physics near strongly coupled quantum critical points. However, there are two formidable bottlenecks to the applicability of QMC: (1) the sign problem and (2) algorithmic update inefficiencies. In this thesis, I overcome both these difficulties for a class of problems by extending the fermion bag approach recently developed by Shailesh Chandrasekharan to the Hamiltonian formalism and by demonstrating progress using the example of a specific quantum system known as the t-V model, which exhibits a transition from a semimetal to an insulator phase for a single flavor of four-component Dirac fermions.I adapt the fermion bag approach, which was originally developed in the context of Lagrangian lattice field theories, to be applicable within the Hamiltonian formalism, and demonstrate its success in two ways: first, through solutions to new sign iv problems, and second, through the development of new efficient QMC algorithms. In addressing the first point, I present a solution to the sign problem for the t-V model.While the t-V model is the simplest Gross-Neveu model of the chiral Ising universality class, the specter of the sign problem previously prevented its simulation with QMC for 30 years, and my solution initiated the first QMC studies for this model.The solution is then extended to many other Hamiltonian models within a class that involves fermions interacting with quantum spins. Some of these models contain an interesting quantum phase transition between a massless/semimetal phase to a massive/insulator phase in the so called Gross-Neveu universality class. Thus, the new solutions to the sign problem allow for the use of the QMC method to study these universality classes.The second point is addressed through the construction of a Hamiltonian fermion bag algorithm. The algorithm is then used to compute the critical exponents for the second-order phase transition in the t-V model. By pushing the calculations to significantly larger lattice sizes than previous recent computations (64 2 sites versus 24 2 sites), I am able to compute the critical exponents more reliably here compared to earlier work. I show that the inclusion of these larger lattices causes a significant shift in the values of the critical exponents that was not evident for the smaller lattices. This shift puts the critic...

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A Note on the Principle of Detailed Balancing

Abstract: Investigations are also being carried out upon potassium and rubidium, in order to test out the conjecture, that the weak radioactivity of these elements is due to the presence of minute traces of the unknown alkali element with atomic number 87.

Cited by 32 publications

References 0 publications

On thermodynamic and microscopic reversibility

On thermodynamic and microscopic reversibility

Microscopic reversibility or detailed balance in ion channel models

Fermion Bag Approach to Lattice Hamiltonian Field Theories

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