dorsal/arxiv
View SchemaEntropy, time irreversibility and Schroedinger equation in a primarily discrete space-time
| Authors | J. P. Badiali |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0409138 |
| URL | https://arxiv.org/abs/quant-ph/0409138 |
| DOI | 10.1088/0305-4470/38/13/002 |
| Journal | J.Phys.A38:2835-2847,2005 |
Abstract
In this paper we show that the existence of a primarily discrete space-time may be a fruitful assumption from which we may develop a new approach of statistical thermodynamics in pre-relativistic conditions. The discreetness of space-time structure is determined by a condition that mimics the Heisenberg uncertainty relations and the motion in this space-time model is chosen as simple as possible. From these two assumptions we define a path-entropy that measures the number of closed paths associated with a given energy of the system preparation. This entropy has a dynamical character and depends on the time interval on which we count the paths. We show that it exists an like-equilibrium condition for which the path-entropy corresponds exactly to the usual thermodynamic entropy and, more generally, the usual statistical thermodynamics is reobtained. This result derived without using the Gibbs ensemble method shows that the standard thermodynamics is consistent with a motion that is time-irreversible at a microscopic level. From this change of paradigm it becomes easy to derive a $H-theorem$. A comparison with the traditional Boltzmann approach is presented. We also show how our approach can be implemented in order to describe reversible processes. By considering a process defined simultaneously by initial and final conditions a well defined stochastic process is introduced and we are able to derive a Schroedinger equation, an example of time reversible equation.
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"abstract": "In this paper we show that the existence of a primarily discrete space-time\nmay be a fruitful assumption from which we may develop a new approach of\nstatistical thermodynamics in pre-relativistic conditions. The discreetness of\nspace-time structure is determined by a condition that mimics the Heisenberg\nuncertainty relations and the motion in this space-time model is chosen as\nsimple as possible. From these two assumptions we define a path-entropy that\nmeasures the number of closed paths associated with a given energy of the\nsystem preparation. This entropy has a dynamical character and depends on the\ntime interval on which we count the paths. We show that it exists an\nlike-equilibrium condition for which the path-entropy corresponds exactly to\nthe usual thermodynamic entropy and, more generally, the usual statistical\nthermodynamics is reobtained. This result derived without using the Gibbs\nensemble method shows that the standard thermodynamics is consistent with a\nmotion that is time-irreversible at a microscopic level. From this change of\nparadigm it becomes easy to derive a $H-theorem$. A comparison with the\ntraditional Boltzmann approach is presented. We also show how our approach can\nbe implemented in order to describe reversible processes. By considering a\nprocess defined simultaneously by initial and final conditions a well defined\nstochastic process is introduced and we are able to derive a Schroedinger\nequation, an example of time reversible equation.",
"arxiv_id": "quant-ph/0409138",
"authors": [
"J. P. Badiali"
],
"categories": [
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"doi": "10.1088/0305-4470/38/13/002",
"journal_ref": "J.Phys.A38:2835-2847,2005",
"title": "Entropy, time irreversibility and Schroedinger equation in a primarily discrete space-time",
"url": "https://arxiv.org/abs/quant-ph/0409138"
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